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P.V. Nickles (Eds.)

K.A. Janulewicz

X-Ray Lasers 2006 Proceedings of the 10th International Conference, August 20–25 , 2006, B erlin , 2006, Germany

With 41 5 Figures

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Dr. P.V. Nickles Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy Max Bornstrasse 2A D-12489 Berlin Germany Dr. K.A. Janulewicz Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy Max Bornstrasse 2A D-12489 Berlin Germany

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Overview of Tabletop X-Ray Laser Development at the Lawrence Livermore National Laboratory J. Dunn1, V. N. Shlyaptsev2, J. Nilsen1, R. F. Smith1, R. Keenan1, S. J. Moon1, J. Filevich3, J. Rocca3, A. J. Nelson1, J. R. Hunter1, M. C. Marconi3, Y. L. Li1*, A. L. Osterheld1, R. Shepherd1, H. Fiedorowicz4, A. Bartnik4, A. Ya. Faenov5, T.A. Pikuz5, P. Zeitoun6, S. Hubert7, S. Jacquemot7 and M. Fajardo8 1

Lawrence Livermore National Laboratory, Livermore, CA 94551, USA. University of California Davis-Livermore, Livermore, CA 94551, USA. 3 NSF ERC for Extreme Ultraviolet Science and Technology and Dept. of Elect. and Comp. Engineering, Colorado State Univ., Fort Collins, USA. 4 Inst. of Optoelectronics, Military Univ. of Technology, Warsaw, Poland. 5 Multicharged Ions Spectra Data Center of VNIIFTRI, Moscow, Russia. 6 Laboratoire d’Optique Appliquée, ENSTA, 91761 Palaiseau, France 7 Commissariat á l’Énergie Atomique, 91680 Bruyères-le-Chatel, France. 8 Centro de Fisica dos Plasmas, Inst. Superior Técnico, Lisbon, Portugal *Present address: Argonne National Laboratory, Argonne, IL 60439 USA 2

Summary. It is almost a decade since the first tabletop x-ray laser experiments were implemented at the Lawrence Livermore National Laboratory (LLNL). The decision to pursue the picosecond-driven schemes at LLNL was largely based around the early demonstration of the tabletop Ne-like Ti x-ray laser at the Max Born Institute (MBI) as well as the established robustness of collisional excitation schemes. These picosecond x-ray lasers have been a strong growth area for x-ray laser research. Rapid progress in source development and characterization has achieved ultrahigh peak brightness rivaling the previous activities on the larger facilities. Various picosecond soft-x-ray based applications have benefited from the increased repetition rates. We will describe the activities at LLNL in this area.

1 Introduction By the mid-1990s there were a number of remarkable advances in soft xray laser experimental and theoretical research that established the viability of tabletop pumped devices. The first demonstration of a tabletop x-ray laser was reported in 1994 using the collisional excitation scheme on a fast capillary discharge apparatus [1]. The Ne-like Ar 3p – 3s J = 0 – 1 line at

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46.9 nm was shown to lase and within two years was operating in saturation [2]. On the laser-driven schemes, there were a variety of approaches described. A 10 Hz Pd-like Xe ion x-ray laser scheme with gL ~ 11 at 41.8 nm for 40 fs irradiation of a Xe gas cell using field-induced tunneling ionization followed by collisional excitation [3]. Observation of a Ne-like titanium 3p - 3s J = 0 - 1 transition at 32.6 nm transient collisional excitation scheme produced high gain g = 19 cm-1 and a gainlength product of 9.5 [4]. A laser-driven recombination scheme based on the H-like Li n = 2 – 1 transition was also demonstrated at 13.5 nm [5]. The rapid technology advances of compact, high peak power, short pulse lasers accelerated this work and subsequent laser-pumped soft x-ray amplifiers. This was the landscape of the tabletop x-ray lasers during 1996 when the decision at LLNL was made to start a small-scale experimental x-ray laser effort. This new approach for generating x-ray lasers with a higher repetition rate and smaller drive energy was a different direction compared to the renowned large-scale experiments using the two-beam Novette/Nova-based x-ray laser. The latter had been active for more than a decade but were now winding down as the plans for the National Ignition Facility were implemented. In this paper, we describe some of the main achievements in the tabletop x-ray laser research at LLNL over the last 10 years, as summarized in Fig. 1.

2 First Experimental Steps The transient collisional excitation scheme, as reported earlier by Shlyaptsev [6] and demonstrated by the MBI group [4], was the most appealing candidate for implementing at LLNL. It was first and foremost a collisional excitation scheme that had been well-studied by many laboratories in the Ne-like and Ni-like closed shell ion configuration. The use of the long nanosecond pulse to generate the initial plasma column and establish the ionization conditions had the advantages of creating the x-ray amplifier pre-conditions using a small amount of laser energy. After a given delay, when the plasma density profile expands and relaxes to aid the propagation of the x-ray laser and secondly the absorption of the picosecond laser pulse, the main short pulse was fired. The short pulse rapidly heated the plasma raising the electron temperature and strongly pumping the upper level of the inversion by monopole electron excitation. The use of the two separate laser pulses to optimize the conditions for the x-ray laser was the main reason that the drive energy could be reduced.

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These were similar advantages to the pre-pulse technique that had been reported previously by Nilsen and colleagues [7].

Fig. 1. Time-line showing major activities and achievements on the tabletop x-ray laser work at LLNL in the years 1997 through 2006.

The tabletop experimental activities first started at LLNL in January 1997 when the short pulse, tabletop Janus Picosecond Laser was available. There were several stages involved before the x-ray laser experiments could begin. The laser at the time was a single high power short pulse beam producing ~3 J at 1054 nm wavelength in a 500 fs pulse with a repetition rate of 1 shot/4 minutes. The beam diameter, along with the optimization of other parameters, was increased to improve the available compressed energy to 7.5 J giving the laser a 15 TW peak power specification. Initial experiments were conducted with a ~1.5 ps short pulse. The long pulse came from the Janus laser: Rod shots of 5 J energy at

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1064 nm in a 800 ps (FWHM) pulse could be fired at 1 shot/3 minutes. The two lasers were synchronized to within 80 ps rms jitter relative timing. The beams had orthogonal polarization and were combined into one beam path with a polarizer, the long pulse in transmission and the short pulse in reflection [8, 9]. The single beam line to the target chamber was focused with a 4-m focal length plano-concave cylindrical lens and a 0.61-m focal length on-axis parabola. The laser line focus was 1.2 cm × 80 µm (L × W) and the two laser beams were imaged and carefully overlapped at the target plane.

Fig. 2. First Ne-like ion x-ray laser spectrum observed for a 6 mm Ti target on 3 June 1997 using the Janus and Janus-ps lasers at LLNL [9].

The main diagnostic for the x-ray laser lines looking on-axis was a 1200 line mm-1 flat-field grating spectrometer with a back-thinned 1024 × 1024 charge-coupled device (CCD) detector to cover 13 - 35 nm. A gold-coated mirror collection optic imaged the plasma gain region with 1:1 magnification onto a 100 µm wide entrance slit. The instrument spatially resolved the position of the gain region. Additional instruments included a CCD x-ray slit camera with 25 µm spatial resolution for line focus uniformity and a CCD flat crystal KAP (001), 2d = 26.58 Å, spectrometer. All x-ray instruments used CCD detector systems that were LLNL designed, fabricated and optically calibrated. The first targets used to study the Ne-like ion scheme were polished low- to mid-Z metals including Ti, Fe, and Ge. There was additional theoretical support for lasing on Ti under a range of different picosecond pulse durations [10]. The Ge target did not demonstrate lasing with the laser energies available. Initially Ti did not lase when the two laser pulses

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were separated by a delay of 800 ps peak-to-peak. Unexpectedly, some jitter in the laser synchronization delayed the short pulse to 1 ns which was sufficient to generate better plasma conditions for lasing [9]. Those first results are shown in Fig. 2 and further optimization of the x-ray signal was achieved with delays of 1.6 ns. The strongest lasing was on the 3p – 3s line at 32.6 nm with the 3d – 3p line also visible at ~5% intensity. Small signal gains of 24 cm-1 and gain length gL products approaching 15 for 1 cm targets were achieved [8]. Strong lasing was also observed on the Ne-like Fe 3p – 3s line at 25.5 nm. The main leap forward though was the demonstration of shorter wavelength lasing utilizing the Ni-like ion 4d – 4p scheme, specifically for Pd at 14.7 nm. The Ni-like schemes, with atomic number in the mid-forties, had not lased well under various pulse configurations on the larger lasers. There was a good match with the pslaser pumping conditions here and gains of 35 cm-1 and gL products of 12.5 were reported [11]. One major difference between the Ne-like and Nilike lasing was the lower output on the Ni-like schemes. This would be attributed to the shorter gain lifetime conditions for the Ni-like ion and would be improved by using traveling wave excitation.

3 Compact Multipulse Terawatt Laser Early in 1998, the tabletop laser was redesigned to accommodate an additional 50 mm rod amplifier to generate a long stretched pulse beam with 600 ps (FWHM) at the full aperture of 8.4 cm diameter. This allowed the tabletop laser to generate two full energy ~7 J beams for the x-ray laser on two standard laser tables. The laser was renamed the Compact Multipulse Terawatt (COMET) laser and was a stand-alone facility optimized for x-ray laser studies [12]. The vacuum compressor was upgraded with new 13” diameter, 1700 line mm-1, gold-coated gratings. A series of experiments were conducted over the next few years to both characterize and improve the x-ray laser parameters required for applications. The careful measurement of various Ni-like 4d – 4p transition wavelengths was carried out in lasing plasmas and compared with optimized level multiconfiguration Dirac-Fock code as well as high resolution spectra from non-lasing vacuum spark or laser-produced plasmas [13]. This was largely to gain better understanding of the Ni-like ion energy level structure (that is complex) as well as the precise transition wavelength knowledge required to develop and optimize the reflectivity of x-ray optics. The Ni-like x-ray lasers also seemed to be a good match with

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the small ps-lasers and lower Z materials were observed to lase for the first time [14]. The next step was improving the output of a number of the Ne-like and Ni-like x-ray lasers. The Ne-like ion x-ray lasers studied to date were very close to saturation. A traveling wave excitation scheme was implemented before the final focusing optics utilizing a segmented reflection echelon that split the beam into delayed vertical slices [15]. This produced a segmented but contiguous line focus for both beams, initially with 5 steps then increased to 7 when the focus was lengthened to 1.6 cm. The traveling wave focus consisted of 0.22 cm long steps delayed by 7.7 ps relative to its neighbor. In addition the long pulse was defocused to 150 µm (FWHM) while retaining an 80 µm (FWHM) short pulse. This improved the x-ray laser propagation by reducing the negative effect of lateral density gradients. The combination of these two methods was very effective and increased the Pd x-ray laser output up to 100 times and into saturation for targets approaching 1 cm in length. Estimated output energy was now above 10 µJ and in saturation. Further optimization of the laser energy parameters and relative pulse delay gave narrow beam divergence ~2.5 mrad (FWHM) and improved x-ray brightness for the 14.7 nm laser. Nilike Mo laser at 18.9 nm was driven into saturation [15] and multilayercoated imaging optics allowed direct measurements of the near-field and far-field patterns of both the Mo and Pd lasers [16, 17]. The speckle pattern and various structures observed in the far-field x-ray beam were recently attributed to a combination of low spatial coherence, high longitudinal coherence and short pulse duration of these transient x-ray sources [18]. One of the projects in 2001 was to study gas puff targets heated by transient pumping. The argon laser successfully lased on both 3p – 3s and 3d – 3p lines at 46.9 nm and 45.1 nm, respectively [19]. However, further work in studying the ionization and absorption conditions during both laser pulses would be useful to optimize the amplification process.

4 Applications, New source Development and Characterization The Pd laser and the experimental setup described above became the workhorse for many of the studies up until the grazing incidence pumping (GRIP) method was adopted for the high repetition rate x-ray source development. In many cases the source characterization was in parallel with the application development. The plan for developing the x-ray laser interferometry of laser-produced plasmas based on the LLNL ps duration

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14.7 nm line was discussed with Jorge Rocca’s group at Colorado State University and a second French team led by Philippe Zeitoun in 1999. In the former case, a skewed Mach-Zehnder interferometer using diffraction grating optics as beam splitters was developed from the design used at 46.9 nm [20]. The instrument was robust, had a high signal throughput and achieved uniform fringes with high visibility. This Diffraction Grating Interferometer (DGI) was an excellent match for the tabletop transient xray lasers and led to new picosecond resolution and micron spatial resolution data from laser-produced plasma phenomena [21 – 23]. The use of the interferometry on Pd plasmas when combined with the near-field imaging technique of the gain region yielded quantitative measurements of the density profile of the x-ray laser amplifier medium [24]. Fig. 3(a) and (b) show the effect of different short pulse durations on x-ray amplification for the same pre-pulse conditions used to generate the 14.7 nm Pd laser [15]. This study showed the beneficial effect on the x-ray laser output of using longer 6 – 13 ps short pulse drives together with optimized laser parameters [24]. The experiment used various, sophisticated x-ray laser diagnostics to understand and achieve better amplification conditions.

Fig. 3. The nearfield image of the Pd 14.7 nm x-ray laser, with both laser pulses fired, overlaid on a 2-D density map measured by 14.7 nm interferometry of the 600 ps heated Pd plasma at Δt = 700 ps. The short pulse would fire at this time. (a) Conditions for a 0.5 ps short pulse. (b) For a 13.4 ps short pulse where the x-ray laser output is substantially higher, more compact and less affected by refraction.

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The second interferometry effort was based on a Michelson design using thin foil multilayer beamsplitters: A measurement of the longitudinal coherence of the Pd line operating in saturation was made for two different short pulse durations of ~6 ps, shown in Fig. 4(a), and ~13 ps [25]. This indicated that the Pd line was spectrally narrow approaching λ/Δλ of 5 × 104. This observation is consistent with the high gain determined from various transient pumping experiments over the last decade. Another experiment was performed to measure the x-ray laser pulse duration of the Pd line under various laser parameters [26]. Figure 4 (b) shows the duration of the 14.7 nm under similar pumping conditions of Fig. 4(a). The measured duration is typically 4 – 5 ps when heated by a 6 ps pulse. Shorter pulse durations are achieved below 3 ps when the optical laser pulse duration is reduced or the x-ray laser is operated out of saturation. This is in close agreement with results reported for the Ag x-ray laser [27]. The spectral and temporal measurements allow us to note that the psdriven Pd laser is operating in the few times transform-limited regime [28] in agreement with similar work as reported by other groups [29 – 31].

Fig. 4. (a) Fringe visibility of saturated Pd x-ray laser line heated by a 6 ps short pulse measured as a function of the differential arm separation of the Michelson interferometer. (b) Pulse duration of Pd 14.7 nm laser line measured with a fast 500 fs x-ray streak camera under similar heating and saturated output conditions.

We mention some recent activities. The Pd laser was shown to be a novel materials surface probe where the x-ray laser, incident on the surface, can photo-ionize the electrons in low energy valence and shallow core levels. The resultant kinetic energy of the ejected electrons is measured using time-of-flight spectroscopy to retrieve the original electron energy level structure [32]. This allows a ps snapshot of the electronic structure of the material while undergoing rapid changes [32]. A stable and high repetition soft x-ray laser source would have advantages for this type

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of work since large photon numbers in single bursts are not necessary. High repetition rate ~10 Hz lasing has been demonstrated in our laboratory using the grazing incidence pumping geometry where the required laser pump energy can be reduced to the range of 150 mJ to ~1 J [33]. This scheme has been quickly adopted in numerous laboratories and is presented in various papers in this journal. A photoelectron microscopy tool based on high repetition, fs-heated vacuum ultraviolet radiation has been utilized for detailed surface chemistry studies [34]. This is one area where the higher photon energy and more monochromatic energy of the xray laser would make a strong application.

5 Conclusions We have given a brief overview of the last 10 years of research in tabletop x-ray lasers at LLNL. With the development of the Compact Multipulse Terawatt (COMET) laser as a dedicated x-ray laser facility a number of advances were made in the source development, including optimization of the output, optimization of key parameters and establishment of several applications. In this time several studies were conducted that broke new ground for ps-driven x-ray lasers: The gas puff x-ray laser at 46.9 nm illustrated the potential for a debris-less gain medium. The Grazing Incidence Pumping (GRIP) was shown to operate with laser energy as low as 150 mJ and is the route forward for the development of a high average power, high repetition rate 10 – 30 nm source. The collisional excitation scheme has been the continuous link through this research and will likely continue to in the near future.

Acknowledgments Work performed under the auspices of the US Department of Energy by the University of California Lawrence Livermore National Laboratory under Contract No. W-7405-Eng-48 and in part by US Department of Energy grant No. #DE-FG52-06NA26152, and in part, by the Ministry of Science and High Education of Poland under grant No 3 T11B 031 26 and by the NATO Collaborative Grant PST.CLG.979339.

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References 1. 2. 3. 4. 5. 6. 7. 8. 9.

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13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.

J. J. Rocca et al., Phys. Rev. Lett. 73(16), 2192 - 2195 (1994). J. J. Rocca et al., Phys. Rev. Lett. 77(8), 1476 - 1479 (1996). B. E. Lemoff et al., Phys. Rev. Lett. 74(9), 1574 - 1577 (1995). P. V. Nickles et al., SPIE Proceedings 2520, 373 - 378 (1995); P. V. Nickles et al., Phys. Rev. Lett. 78(14), 2748 - 2751 (1997). D. V. Korobkin et al., Phys. Rev. Lett. 77(26), 5206 - 5209 (1996). V. N. Shlyaptsev et al., SPIE Proceedings 2012, 111 - 118 (1993). J. Nilsen, B. J. MacGowan, L. B. Da Silva, and J. C. Moreno, Phys. Rev. A 48(6), 4682 - 4685 (1993). J. Dunn, A. L. Osterheld, R. Shepherd, W. E. White, V. N. Shlyaptsev, A. B. Bullock, and R. E. Stewart, SPIE Proceedings 3156, 114 - 121 (1997). J. Dunn, A. L. Osterheld, R. Shepherd, W. E. White, V. N. Shlyaptsev, and R. E. Stewart, "Table-Top Transient Collisional Excitation X-ray Laser Research at LLNL: Status June 1997", Lawrence Livermore National Laboratory, Livermore, CA UCRL-ID-127872 (1997). J. Nilsen, Phys. Rev. A 55(4), 3271 - 3274 (1997). J. Dunn, A. L. Osterheld, R. Shepherd, W. E. White, V. N. Shlyaptsev, and R.E. Stewart, Phys. Rev. Lett. 80, 2825 - 2828 (1998). COMET has 4 independent, synchronized beams: The two main beams, a third ~20 mJ (1ω or 2ω) short pulse probe beam and a fourth beam that uses energy from the long pulse arm for either 3 J in 600 ps or ~2 J compressed. Y. Li, J. Nilsen, J. Dunn, A. L. Osterheld, A. Ryabtsev, and S. Churilov, Phys. Rev. A 58, R2668 - 2671 (1998). J. Dunn et al., Opt. Lett. 24, 101 – 3 (1999). J. Dunn, Y. Li, A. L. Osterheld, J. Nilsen, J. R. Hunter, V. N. Shlyaptsev, Phys. Rev. Lett. 84, 4834 - 7 (2000). Y. L. Li, J. Dunn, J. Nilsen, T. W. Barbee, Jr., A. L. Osterheld, and V. N. Shlyaptsev, J. Opt. Soc. Am. B 17, 1098 - 1101 (2000). J. Nilsen et al., J. Opt. Soc. Am. B 20, 191 - 194 (2003). O. Guilbaud, A. Klisnick, K. Cassou, S. Kazamias, D. Ros, G. Jamelot, D. Joyeux, and D. Phalippou, Europhys. Lett. 74, 823 – 829 (2006). H. Fiedorowicz, A. Bartnick, J. Dunn, R. F. Smith, J. R. Hunter, J. Nilsen, A. L. Osterheld, and V. N. Shlyaptsev, Opt. Lett. 26, 1403 - 1405 (2001). J. Filevich, K. Kanizay, M. C. Marconi, J. L. A. Chilla, and J. J. Rocca, Opt. Lett. 25, 356 - 358 (2000). R. F. Smith et al., Phys. Rev. Lett. 89(6), 065004-1 (2002). J. Filevich et al., Appl. Opt. 43(19), 3938 - 46 (2004). J. Filevich et al., Phys. Rev. Lett. 94, 035005 (2005). R. F. Smith et al., Phys. Rev. E 72, 036404 (2005). R. F. Smith et al., Opt. Lett. 28, 2261 - 3 (2003). J. Dunn et al., SPIE Proceedings 5197, 51 - 59 (2003). A. Klisnick et al., Phys. Rev. A. 65, 033810 (2002). J. Dunn et al., SPIE Proceedings 5197, 43 - 50 (2003).

Overview of Tabletop X-Ray Laser Development 29. 30. 31. 32. 33. 34.

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Y. Abou-Ali et al., Opt. Comm. 215, 397 - (2003). A. Klisnick et al., J. Quant. Spectrosc. Radiat. Transf. 99, 370 – 380 (2006). D. Benredjem et al., Phys. Rev. A 73, 063820 (2006). A. J. Nelson et al., Appl. Phys. Lett. 87, 154102 (2005). R. Keenan et al., Phys. Rev. Lett. 94, 103901 (2005). T. Munakata et al., Surf. Sci, 532, 1140 – 144 (2003).

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Recent Progress in X-Ray Laser Development and Applications at LIXAM A. Klisnick1, D. Ros1, G. Jamelot1, S. Kazamias1, M. Pitmann1, K. Cassou1, F. Plé1, O. Guilbaud1, I. R. Al’Miev1, C. Möller1, D. Benredjem1, J. Dubau1, D. Joyeux2, C.-G. Wahlström3, T. Kühl4, B. Rus5, H. Bercegol6, O. Larroche7, J.-P. Chambaret8, Ph. Zeitoun8 and P. Velarde9 1

LIXAM, CNRS, Univ Paris-Sud, UMR n° 8624, Orsay, F-91405 LCFIO, CNRS, Univ Paris-Sud, UMR n° 8501, Orsay, F-91405 3 Department of Physics, Lund University, Lund, S-22100 Lund 4 Gesellschaft fur Schwerionenforschung (GSI), Darmstadt, D-64291 5 Department of X-ray Lasers, Institute of Physics /PALS Centre, 18221 Prague 8, Czech Republic 6 CEA-CESTA/ DLP, BP 2, Le Barp, F-33114 7 CEA-DIF, BP 12, Bruyères-le-Chatel, F-91680 8 LOA, ENSTA, CNRS, Ecole Polytechnique, UMR n° 7639, Palaiseau, F-91761 9 Institute of Nuclear Fusion (DENIM) - Universidad Politécnica de Madrid, Spain 2

Summary. We present an overview of the recent progress achieved in the development of X-ray lasers and demonstration of applications by the LIXAM team, in collaboration with other groups. Lasing at 10 Hz was demonstrated at 18.9 nm in Ni-like Mo with a 30 µW average power, using transient pumping in the grazing incidence geometry. New numerical simulations have been developed to study spatial and temporal features of current and future X-ray lasers. The technique of interference microscopy with an X-ray laser beam was applied to the investigation of laser-induced damages in optical materials exposed to sub-ns laser pulses. Finally the construction of a 0.5 PW, 0.1 Hz Ti-Sa laser, the driver of the LASERIX facility, was successfully completed.

1 Introduction Since the last X-ray laser conference in Beijing, the research activity of the X-ray laser team at LIXAM has covered three different aspects of the development of X-ray lasers, namely fundamental studies, both experimental and theoretical; demonstration of applications; and the construction of an advanced laser driver for our future LASERIX facility.

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We have now started to explore the new potential opened by highenergy Ti:Sa lasers as a pump for transient X-ray lasers. This step is of particular importance for our future activity since the driver of LASERIX was chosen to be based of the Ti:Sa technology. We have carried out an extensive optimization and detailed characterization of the Grazing Incidence Pumping (GRIP) in a Ni-like Mo plasma, using the multiterawatt, 10 Hz facility at the Lund Laser Center, Sweden. The main results will be outlined in section 2. In section 3 we describe the development of new numerical simulations aimed at understanding and improving the spatial and temporal features of transient X-ray lasers. Section 4 deals with the development of a new application based on the technique of interference microscopy and applied to the investigation of laser-induced damages to optical surfaces. In section 5, we show that the construction of the Ti:Sa laser chain, the driver of LASERIX, has been completed and the expected performances have been successfully demonstrated. We outline the main directions for future work with this new laser.

2 Demonstration of a 10 Hz, 3µJ GRIP transient X-ray laser We have recently carried out an experimental campaign, involving collaboration with GSI and Lund University, at the Lund Laser Center (Sweden) using the multiterawatt laser facility. The general aim of this experiment was to demonstrate transient pumping at 10 Hz with a Ti:Sa driver. This is an important step towards the operation of our future LASERIX facility. Thanks to the 10 Hz repetition rate of the Lund laser system we were able to perform an extensive multiparameter scan for the optimization of a Ni-like Mo X-ray laser, in the Grazing Incidence Pumping (GRIP) geometry. This optimization work led to a substantial improvement of the output beam characteristics, in particular the average power that reached up to 30µW, and to an improved efficiency [1]. The main results of this optimization are presented in a companion paper [2]. Here we discuss a more specific goal of this experiment which was to get a detailed insight into the spatial behaviour of the X-ray laser pumped in the GRIP geometry, by implementing appropriate imaging diagnostics. The GRIP concept was initially proposed by Shlyaptsev [3] and first demonstrated by Keenan [4]. The main idea is to reduce the density at which the short pulse energy is absorbed into the preformed plasma by adjusting the grazing incidence angle φ, of the short pulse beam irradiating the preformed plasma. This allows to possibly match the position of the

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plasma heated zone with the zone of maximum gain. As a result we expect that varying the angle φ will not only influence the X-ray laser beam output but also the spatial features of the source, like its size and position. As will be discussed in section 3, the knowledge of these features is essential because they largely influence the spatial profile of the beam. In order to investigate the influence of varying the GRIP angle on the spatial behaviour of the X-ray laser plasma we implemented two diagnostics, as shown in Fig . 1. The first diagnostic is a near-field imaging device giving the position and size of the XRL source at the plasma exit plane. The second diagnostic is a pinhole camera viewing the keV plasma emission from above, yielding the position and size of the zone heated by the short pulse. Both diagnostics were used together while varying the GRIP angle.

Fig. 1. Geometry of the experiment, showing the two main diagnostics used. Typical images obtained for the XRL source (left) and keV plasma emission (right) are also shown.

The results obtained are summarized in Fig. 2. Fig. 2a shows the estimated mean fluence of the XRL as a function of the GRIP angle. Each data point is averaged over ~10 shots. One can see that the data exhibits a clear optimum for a GRIP angle of 19°. The corresponding mean fluence is 0.33 J/cm2, while the integrated energy is 3µJ. Figure 2b shows the distance relative to the target surface of the XRL source, as a function of the GRIP angle. It can be seen that this distance gets smaller when the GRIP angle is increased, i.e. the XRL source is shifted towards higher densities, as expected from the theory. The data obtained from the keV

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pinhole camera also confirm this trend for the plasma heated zone, as discussed in [5]. The distance of the XRL source is minimum at the optimal angle of 19°. For larger angles the XRL is shifted to larger distances and this could be a result of increased refraction.

Fig. 2. Influence of varying the GRIP angle. (a) mean fluence of the XRL output at the exit plane; (b) distance of the XRL source from the target surface.

3 Numerical simulations of current and future X-ray lasers Three different works dealing with different aspects of the simulation of transient XRLs were performed recently. The first work arose from the observation of contrasted small-scale structures in the beam profile of TCE XRLs, routinely observed in our experiments [6] and also reported by other groups [7]. We also observed that the typical size and shape of those structures vary from shot to shot. In order to understand the origin of these structures and of their fluctuating shape, we developed a model described elsewhere [8, 9]. Figure 3 shows the beam profiles calculated by this model for three different sizes of the XRL source aperture, as shown in the inserts. These results account very well for the experimental observations. Further our model brings out a simple relationship between the angular size of the structures and the size of the XRL source: the angular size β is inversely proportional to the size of the source a. This result hence suggests that the shot-to-shot variation of the microstructures in the beam profile is due to shot-to-shot variation of the source size. Our model also predicts that the visibility of the microstructures decreases as the square root of the ratio between the duration and the coherence time of the XRL pulse [9]. The second simulation work, discussed in more detail in [10], was carried out in collaboration with LOA (France) and DENIM (Spain). A 2D-eulerian hydrocode ARWEN, developed by the Spanish group, was used to investigate the possibility of spatially shaping the preformed

Recent Progress in X-Ray Laser Development and Applications

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Fig. 3. Beam profiles calculated from the model described in [9], using XRL source (shown in the insert of each image) with different horizontal width: (a) 10µm; (b) 20 µm; (c) 40 µm.

Fig. 4. 2D- electron density profiles calculated from the hydrocode ARWEN [11] at two successive stages of expansion, for two different transverse profiles of the pump laser beam: (left) Gaussian; (right) super-Gaussian.

plasma of transient X-ray lasers, by properly shaping the transverse profile of the pump laser beam. Figure 4 illustrates the possibility of substantially reducing the vertical refraction of the XRL beam and enlarging the vertical width of the gain zone, by using a super-Gaussian pump beam profile, instead of a Gaussian one. In the super-Gaussian case, the density profile is flatter at the two times of plasma expansion shown in Fig. 4. Such a profile will improve the conditions of propagation of the XRL beam along the amplifying plasma [11].

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Finally the third simulation work deals with the seeding of a transient Xray laser plasma with high-order harmonic radiation. This topic has recently received an increased interest, following recent successful experimental demonstrations [12, 13] and due to the potential major impact of this technique. To account for the complex problem of amplification of a broadband, femtosecond source into a narrow-band, picosecond amplifier, we have recently upgraded the numerical code COLAX. This code, initially described in [14], uses a Maxwell-Bloch formalism to calculate the temporal and spatial evolution of the electric field associated with the amplified radiation. In particular the Maxwell equation is coupled to the equation describing the time-dependency of the atom dipole polarisation density. Until now the code was used in the adiabatic approximation, where the polarisation is assumed proportional to the electric field at each time. We find that the adiabatic approximation, which is widely used, is not valid in our case, as illustrated in Fig. 5.

Fig. 5. Distribution of field intensity in the amplifying plasma, at a given time during the propagation of an harmonic pulse (narrow elongated feature in each image), which is incident from the left. Left image: time-dependent treatment of the polarization density. Right image: adiabatic approximation.

The left image of Fig. 5 shows the spatial distribution of amplified intensity at some time during the propagation of the harmonic pulse, calculated with a time-dependent treatment. One can see that amplification does not occur within the short harmonic pulse but later, in a wake induced by this pulse. This wake is totally absent in the adiabatic case shown in the right image of Fig. 5. Here amplification of harmonic radiation takes place within the harmonic pulse and ASE is the dominant feature at the forefront of the amplified radiation pulse. This result, discussed in more detail in

Recent Progress in X-Ray Laser Development and Applications

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[15], is a first step towards more quantitative simulations that can be compared with experimental results. However it constitutes an important validation of the approach used in COLAX.

4 Interference microscopy for laser-induced damage studies We have carried out a new XRL interferometry experiment, using the PALS facility in Prague, in collaboration with IOP and CEA-CESTA. The main aim of this experiment was to apply the technique of interference microscopy to the investigation of laser-induced damages to optical surfaces exposed to 3ω laser pulses. The application part of the experimental set-up is shown in Fig. 6, while the X-ray laser beam is generated in another target chamber, not represented.

Fig. 6. Experimental set-up showing the XRL beam path to the sample and the interferometer. The damaging 3w beam is incident from the top on the front surface of the sample, while the XRL beam samples the rear surface.

The surface sampled by the XRL beam is the rear surface of a 10 mm thick beam-splitter, irradiated on the front face by a 3ω laser pulse. Several optical in-situ and post-shot inspection diagnostics were implemented but the main diagnostic was a microscope interferometer designed to map the target surface with a high spatial resolution [16]. The effect of the 3ω irradiation on the rear surface was studied by taking a sequence of three interferograms: (i) before irradiation as a reference, (ii) during or soon after the 3ω pulse, and (iii) 20 min later to detect any permanent damage. The results obtained, presented in more detail in [17], are summarized in

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Fig. 7, where lineouts along each of the three interferograms are shown. The main feature is apparent in the interferograms taken 5 ns after the 3ω irradiation. One can see that in the zone exposed to the 3ω laser beam, the interference fringes disappear, while they are totally recovered in the interferograms taken 20 minutes later. This transient loss of reflectivity of the sampled surface was rather unexpected and its interpretation is not fully understood yet. One possibility involves heating of the surface over a thin layer, leading to an increase of the surface roughness and hence to the observed loss of reflectivity.

Fig. 7. Lineouts across three interferograms taken successively, on the same sampled surface, at three stages of 3ω irradiation: before, during (t=5 ns) and after irradiation by the 3ω laser pulse. In the area exposed to the 3ω irradiation fringes are observed to disappear, while they are fully recovered in the post-mortem shot.

5 Conclusion and prospects In conclusion we have demonstrated a 3µJ XRL operating at 10 Hz, yielding a high average power of 30µW. Detailed information about the spatial behaviour of the source with respect to the GRIP angle were obtained, using spatially resolved X-ray diagnostics. New developments in the numerical simulations of transient X-ray lasers were carried out. The results obtained will be very important to guide future experimental works aimed at improving the quality of the XRL beam. The technique of interference microscopy was applied to the investigation of laser-induced damages in optical components. The results obtained show that the surface sampled by the XRL beam is subject to

Recent Progress in X-Ray Laser Development and Applications

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transient alteration induced by the 3ω damaging laser beam, although the exact nature of the processes involved is not fully understood yet. All these works open promising prospects for the research program that will be carried out at the LASERIX facility. The current status and high potential of this facility is described in a companion paper [18]. The construction of the LASERIX laser driver was recently completed and the expected performances were demonstrated, namely an energy (before compression) of up 30 J at a record repetition rate of 0.1 Hz [19]. This performance was obtained because two major limiting factors were successfully overcome: (i) homogenization of the 2ω laser beams which are used to pump the final amplifier and (ii) parasitic lasing which can take place in the transverse direction of the large aperture TiSa crystal amplifier. Future work with the LASERIX laser includes the implementation of the GRIP pumping using the front-end at 2 J, 10 Hz. Our goal is then to investigate seeding with high-order harmonic radiation. The use of the full energy of LASERIX will be possible in mid-2007. This will then allow to extend pumping towards shorter wavelengths, possibly significantly below 10 nm, at a substantially improved repetition rate of 0.1 Hz.

Acknowledgments Financial support by the Access to Research Infrastructures activity in the 6th Framework Programme of the EU, Contract RII3-CT-2003-506350, LASERLAB Europe is gratefully acknowledged.

References 1. Cassou, K et al, 'Optimization towards ', accepted in Opt. Lett, 2006 2. Kazamias S. et al., ' A 10 Hz, 3 µJ transient X-ray laser pumped in grazing incidence geometry ', These Proceedings, 2006. 3. Shlyaptsev V. et al., in ′Soft x-ray laser and application V′, SPIE Proc. 5197, 221, 2003. 4. Keenan, R., 'High-Repetition-Rate Grazing-Incidence Pumped X-Ray Laser Operating at 18.9 nm', Phys. Rev Lett 94, 103901, 2005. 5. Zielbauer, B. et al., 'X-ray imaging of the heating zone of non-normal incidence pumped XRL plasma', These Proceedings, 2006.

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6. Klisnick, A. et al., in soft x-ray laser and application IV, Proc. SPIE Vol 4505, 75, 2001. 7. Dunn, J. et al., in soft x-ray laser and application IV, Proc. SPIE Vol 4505, 62, 2001. 8. Guilbaud, O. et al., ‘Origin of microstructures in picosecond X-ray laser beams’, These Proceedings, 2006. 9. Guilbaud, O. et al., ‘Origin of microstructures in picosecond X-ray laser beams’, Euro. Phys. Lett. 74, 823, 2006. 10. Cassou, K. et al., ‘2-D Hydrodynamic simulation of laser plasma generation for transiently pumped soft x-ray amplifier’, These Proceedings, 2006. 11. Cassou, K. et al., ‘Transverse spatial improvement of a transiently pumped soft X-ray amplifier’, to appear in Phys. Rev A, 2006. 12. Zeitoun, P. et al., ‘xxx’, Nature 431, 426, 2004. 13. Rocca, J. et al., ‘Advances in high repetition rate soft X-ray lasers’, These Proceedings, 2006. 14. Larroche, O. et al., Phys. Rev. A 62, 043815 2000. 15. Al Miev, I. et al., ‘Seeding high–order harmonic in a transient X-ray laser amplifier’, These Proceedings, 2006. 16. Rus, B. et al., ‘Advanced optical damage studies using X-ray laser interferometric microscopy’, in soft x-ray laser and application IV, Proc. SPIE Vol 4505, 75, 2005. 17. Jamelot, G. et al., ‘X-ray laser interferometric microscopy for advanced optical damage studies’, These Proceedings, 2006. 18. Ros, D. et al., ‘LASERIX : a multi X-Ray/XUV beamline high repetition-rate facility’, These Proceedings, 2006. 19. Plé, F. et al., ‘A high repetition-rate, petawatt class Ti:Sapphire laser dedicated to coherent X-UV generation at LASERIX’, These Proceedings, 2006.

A High Repetition-Rate, Petawatt Class Ti:Sapphire Laser Dedicated to Coherent X-UV Generation at LASERIX. F. Plé (1,2), M. Pittman (1), J-P. Chambaret (3) and G. Jamelot (1) 1

LIXAM, UMR n° 8624, Université Paris-Sud 11 / CNRS, Bâtiment 350, 91405 Orsay cedex, France 2 AMPLITUDE Technologies. CE2926. 91029 Evry cedex. France 3 LOA, UMR n°7639, ENSTA / CNRS / Ecole Polytechnique,Chemin de la Hunière. 91761 Palaiseau cedex. France

Summary. We have recently demonstrated amplification in a Ti:Sapphire laser system up to 30 Joules before compression at the record repetition rate of 0.1 Hz. This CPA Ti: Sapphire laser system is the first femtosecond petawatt class laser system running at a high repetition rate of 0.1Hz. Such performances have been obtained thanks to the particular design of the last booster amplifier. In this paper, we will present the last results obtained on this system and the different strategies we have carried out for counteracting the two most limiting factors for high energy amplification that are the parasitic lasing in the large aperture Ti: Sapphire crystal and the spatial homogenisation of the pump laser beams. This laser will be used as a driver of the LASERIX facility.

1 Introduction As high power amplification in CPA1 Ti:Sa laser system has continually evolved towards higher and higher energy levels, new technological issues have appeared. Two most limiting factors have arisen for very high energy amplification in Ti:Sa laser crystals: the pump laser beam homogenization and parasitic self-lasing2. Pump lasers profiles dedicated to such energy amplification are hard to be controlled. As the pump diameter increases, spatial effects in rods amplification induce large non-uniformities in the laser-beam intensity profile and present a big issue for crystal safety and amplification efficiency. An other issue is self parasitic lasing in high dimension Ti:Sa crystals. This parasitic effect is due to the formation of a transverse laser cavity in which the crystal faces act as mirrors1. Because of the geometrical characteristics of new large-aperture Ti:Sa amplifiers, the

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transverse gain could be very high and generate huge parasitic effects. These two points was the object of particular developments

2 The LASERIX driver The laser developed by the LIXAM as a driver for LASERIX3 is a classical CPA Ti:Sa laser system. It is based on a Femtolaser oscillator, a 1 KHz regenerative amplifier and 4 multipass amplifiers. The first three elements were provided by Thales Lasers and deliver a chirp pulse of 500 ps / 25 mJ with a spectral bandwidth of 25 nm FWHM. This part is seeded in two cryogenically booster amplifiers developed by Amplitude Technologies which provide a laser pulse of 2 joules to be injected in the last booster amplifier This last amplifier takes shape around one large aperture Ti:Sa crystal. It is 1.95 cm long (αl=3.5) and its diameter is 10 cm. This crystal is pumped by 8 Nd:YAG homogenised laser beams of 12.5 joules of energy and 30ns FWHM long delivered by Quantel. We are expecting 40 joules at the end of this last amplifier THALES LASER Öffner Stretcher

1kHz Regenerative Amplifier

AMPLITUDE TECHNOLOGIES 10 Hz - 4 Pass Preamplifier S

10Hz - 4 Pass Cryogenic Power Amplifier

10Hz - 4 Pass Cryogenic Power Amplifier P

P

P

P

P

P

P

P

J

Oscillator V

F emtolaser

azzler

D

Fig. 1. Front end of the CPA laser system of the LASERIX facility.

3 Experimental results Pumping laser beam shaping was performed by using a homogenizing system based on Micro-Lenses Array4 (MLA). Thanks to this method, we have succeeded at the same time to shape each elementary beam into homogenise super-Gaussian intensity profile and to up collimate the pumping laser beams from 2 cm to 6cm without using any afocal system. This particular method, dedicated to low coherent laser system, allows pumping the crystal with fluency greater than 2 J / cm² with superGaussian intensity profiles.

A High Repetition-Rate, Petawatt Class Ti:Sapphire Laser

25

Fig. 2. Image of the 60 mm diameter intensity pump profile measured on the crystal.

To limit parasitic self lasing effects, we have chosen to perform index matching with a high index of refraction liquid. In fact, the crystal we are using in the last stage of amplification is two highly doped in Ti3+ to use solid state index matching method. We had to match as better as possible the index of refraction of the Ti:Sa crystal to limit Fresnel refraction on the edge of the crystal5. Reflections on the two faces are settled by the AR coating.

Fig. 3. Image of the gain medium inside the Ti:Sa crystal. We observe a strong depletion of the gain owing to parasitic self lasing.

Finally, we flow the crystal with a derivative of diiodomethane (CH2I2) doped with an absorber for 800 nm radiation. Thank to this method and by seeding the IR pulse before the end of the pumping6, we succeeded in amplifying up to 30 joules with a transverse gain higher than 2000 and

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75 joules of pumping energy instead of the 100 joules theoretically available. Shot to shot energy at 0.1 Hz 35

Energy (Joules)

30 25 20 15 10 5 0 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Fig. 4. Shot to shot energy at the end of the last booster amplifier.

Preliminary pulse compression has been made for demonstration with a two gratings compressor by sampling some part of this energy. SPIDER measurements of the pulse duration give results in the range of 40 fs. Two big vacuum compressors are currently under development for high-energy compression

4 Conclusion We have developed a femtosecond Petawatt class laser system running at 0.1 Hz as a laser driver of the future LASERIX X-ray laser facility. We plan now to amplify with all the pumping energy to achieve the energy level require for the project and to compress half of this energy as soon as the laser should be installed in its dedicated building.

Acknowledgments This work was supported by the Conseil Général de l’Essonne and the Ministère de l'Education Nationale within the framework of the CPER 2000-2006. LASERIX is a X-ray laser facility of the University Paris-Sud 11 that will be installed in a new building of the LOA at the Ecole Nationale Supérieure des Techniques Avancées (ENSTA) in Palaiseau.

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The contribution of the LIXAM, and particularly of Annie Klisnick and David Ros to the choice of titanium:sapphire technology for the LASERIX driver was highly appreciated. We warmly thank researchers and engineers from LOA for their fruitful collaboration.

References 1. D. Strickland and G. Mourou, : Compression of Amplified Chirped Optical Pulses, Opt. Comm. 56, 219, 1985. 2. F. G. Patterson, J. Bonlie, D. Price, and B. White : Suppression of parasitic lasing in large-aperture Ti:Sapphire laser amplifiers, Opt. Lett. 24, 14, 1999. 3. D. Ros, G. Jamelot, M. Pittman, F. Plé, S. Kazamias, A. Klisnick, J-C. Lagron, K. Cassou, O. Guilbaud, J-P. Chambaret, S. Sebban, P. Zeitoun : LASERIX : a multi X-Ray/XUV beamline high repetition-rate facility, in these Proceedings 4. A. DiChiara, E.A. Chowdhury, G. Ongadi, and B.C. Walker : TEM00 terawatt amplification by use of micro-optic spatial mode conversion, Opt. Letters, 28, 21, 2003. 5. M. P. Kalashnikov, V. Karpov, H. Schnönnagel, and W. Sandner : 100-terawatt titanium-sapphire laser system, Laser physics 12, Nr.2, 2002. 6. V. Chvykov, V. Yanovsky, S. W. Bahk, G. Kalintchenko, and G. Mourou : Suppression of parasitic lasing in multi-pass Ti:Sapphire amplifiers, CLEO conference, Baltimore (2003).

Recent Advances of the X-Ray Laser Research at APRC K. Nagashima, M. Kishimoto, T. Kawachi, N. Hasegawa, M. Tanaka, Y. Ochi, M. Nishikino, K. Sukegawa, H. Yamatani, Y. Kunieda and Y. Kato X-Ray Laser Group, Advanced Photon Research Center, Quantum Beam Science Directorate, Japan Atomic Energy Agency

Summary. We are developing plasma x-ray lasers pumped by ultra-short pulse lasers and have concentrated our efforts on developing a silver x-ray laser (13.9 nm) with spatially full coherence by means of a double target method. Recently, we have succeeded in developing a unique new pumping laser system, which is a CPA laser consisting of OPCPA and zigzag-slab type glass amplifiers. The OPCPA was adopted for improving the controllability of pumping pulses instead of a regenerative amplifier and the zigzag-slab amplifiers were adopted for increasing the repetition rate.

1 Introduction Collisional excitation scheme is the main current in plasma x-ray laser (XRL) research. This scheme succeeded in lasing in 1984 for the first time by using a huge-scale laser facility [1]. Then, many efforts have been made in order to reduce the pumping energy [2, 3]. Two advanced schemes were demonstrated by using CPA ultra-short pulse lasers. They were transient collisional excitation (TCE) scheme [4] and optical field ionization (OFI) scheme [5]. The TCE scheme was a method similar to the previous collisional excitation using a pre-pulse technique [2] and succeeded in reducing the pumping energy less than 10 J [4, 6]. Recently, a further advanced scheme, which is called grazing incidence pumping (GRIP), succeeded in reducing the pumping energy less than 1 J [7]. It means that we can now get XRL light by using commercial-based Ti:sapphire CPA lasers. So, it can be said that the trend of reducing the pumping energy has reached a satisfactory level. However, the beam quality of XRL stays at a poor level. An essential cause for the poor beam quality is that the XRL is light by amplified spontaneous emission (ASE) and the spatial mode is not

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selected in almost cases. Some groups tried to improve the beam quality by means of double pass amplification [8], double target configuration [9] and waveguide with a curved target [10]. An XRL beam with spatially full coherence beam was generated by the double target configuration [11], where an XRL seeder from the first target was amplified in an XRL amplifier on the second target. Recently, a higher harmonic seed was amplified in an XRL medium (the medium was generated by the OFI scheme) and a temporally full coherent beam was generated [12]. We think that this new trend of improving beam quality is essential in XRL research from now on.

2 Concept of MOPA The key concept for improving the beam quality is MOPA (masteroscillator/power-amplifier), which means amplification of seeding light. The seeding light is expected to be spatially and temporally full coherent, if it is possible. The several configurations of MOPA are considered as shown in Fig. 1. Seeder

Amplifier

(a)

Amplifier

Seeder

(b) Seeder

Mirror Amplifier

(c)

Mirror Spatial filter Amplifier

Coherent seeder

(d)

Fig. 1. Configurations of MOPA

Figure 1 (a) is a case where the sizes of the media are equal between the seeder and the amplifier. In this case (the seeding light has some divergence), the amplifier works as a spatial filter and spatially full coherence is realized by adjusting the distance between the seeder and the

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amplifier [11]. Figure 1 (b) is a case where the size of the amplifier is larger than that of the seeder. If the seeder is coherent, it is the simplest configuration of MOPA. In this case, the most important problem is how to make a large-scale amplifier. Figure 1 (c) is a case where the seeder is not coherent satisfactorily and the spatial mode is selected by a spatial filter. Figure 1 (d) is a case of optics-free, which is equivalent to (c). A candidate of the seeder is higher harmonic light (HHL) or XRL itself. The HHL has higher spatial and temporal coherences compared with those of XRL. In general, the spectral width of HHL is considerably broad compared with that of XRL. So, when the HHL seed is amplified in the XRL amplifier, the spectral range is limited by the bandwidth of the XRL. The amplifier works as a spectral filter and the pulse length of the amplified beam is determined by Fourier transform limit. In this sense, it seems that a combination of the HHL seeder and the XRL amplifier is the most suitable for improving temporal coherence. It is thought that the XRL seeder is better for improving only the spatial coherence.

3 Progress of Our Research We have developed TCE-XRLs using a high power CPA laser (Ti:sapphire front-end and rod-type Nd:glass power amplifier) [13]. An original point of our experimental device is an use of coaxial pulses (pre-pulse and main pulse). The two successive pulses are focused with a line shape by the same focusing optics. So, we have no additional optics for the pre-pulse. XRL seeder

Seeding beam XRL amplifier

Main pulse

Amplified beam

Pre-pulse

Traveling wave pumping

Fig. 2. Configuration of double target method

The saturated amplification was achieved by travelling wave pumping using a 6-step mirror [14]. Our original approach for improving the beam quality is double target method, where an XRL seeder and an XRL amplifier are generated on the two targets (see Fig. 2) and the XRL amplifier works as a spatial filter. The diffraction-limited beam was generated by this method, and it was found that the beam was spatially full

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coherent from Young’s double slit experiments (the spatial coherent length was longer than the beam diameter) [15]. For the present pumping laser system, the pumping conditions are equal between the two targets. The optimum condition for the amplifier was obtained when the gain was not maximal. It means that the optimum condition for the amplifier is different from that for the seeder. Therefore the pumping condition should be controlled individually between the seeder and the amplifier.

HHL seeder XRL beam

Gas jet

Ti:sapphire laser

XRL amplifier

Amplified HHL

Main pulse

Pre-pulse

Traveling wave pumping

Fig. 3. Configuration of amplification of higher harmonic light

We have tried amplification of HHL seeder [16]. The experimental configuration is shown in Fig. 3. In the experiment, the 29th HHL of Ti:sapphire laser (the wavelength 780 nm, the pulse length 80 fs) was generated in argon gas and the HHL was amplified in an XRL medium of neon-like manganese (the wavelength λ = 26.9 nm). The spectral width (FWHM) of the HHL was measured to be 0.12 nm and the pulse length was less than 80 fs. On the other hand, the spectral width of the XRL was estimated to be Δλ/λ ~ 10-4 (where λ is the wavelength). Therefore, it is thought the pulse length of the amplified HHL was determined by Fouriertransform limit and was about λ 2/2cΔλ ~ 0.5 ps (where c is light speed). In this case, the XRL amplifier works as a spectral filter and the amplified HHL has fully temporal coherence.

4 New Pumping Laser System The present pumping laser system consists of a Ti:sapphire oscillator, a pulse stretcher, a Ti:sapphire regenerative amplifier, a pulse controller, Nd:glass rod-type amplifiers and two pulse compressors [13]. The pulse controller makes a pre-pulse and a main pulse coaxially. This pumping beam is divided into two beams before the final rod amplifiers. The two beams irradiate two targets, which makes the XRL seeder and the XRL

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amplifier. There are some problems in the present pumping system. Firstly, an unexpected pre-pulse is generated in the regenerative amplifier. It makes the pulse controllability low. Secondly, the two beams have an identical pumping condition in spite that the different pulse conditions are expected between the seeder and the amplifier. Thirdly, the repetition rate of the system is very low. It is limited to 0.001 Hz by the cooling time of the glass rod. OPCPA amp. 10 Hz, 3 mJ

Pulse stretcher

Ti:sap oscillator 80 MHz, 3 nJ

Pulse controller.1

Zigzag slab amp.1 0.1 Hz, 10 J

Pulse compressor.1

Pulse controller.2

Zigzag slab amp.2 0.1 Hz, 10 J

Pulse compressor.2

Fig. 4. Block diagram of new pumping laser system

Now we are installing a new pumping laser system, which is able to solve the above-mentioned problems. The main advances are a change of the front-end amplifier from the regenerative amplifier to an OPCPA amplifier and a change of the main amplifier from the Nd:glass rod-type amplifiers to Nd:glass zigzag-slab-type amplifiers. The components of the new laser system are shown in Fig. 4. The OPCPA amplifier generates no unexpected pre-pulse and no ASE. So, the pulse controllability is improved considerably. The zigzag-slab-type amplifier can make the repetition rate up to 0.1 Hz, because the thermal effects are compensated in the zigzag-slab geometry. Furthermore, the pulse controller is improved and it can make two pre-pulses and one main pulse. The pumping beam is divided into two beams before the pulse controllers and the two pulse controllers can make individual pumping conditions for the two beams. So, we can optimize the pumping pulses for the XRL seeder and the XRL amplifier individually. We have confirmed the stable operation of the zigzag-slab-type amplifier at 0.1 Hz with the output energy of about 10 J.

5 Preliminary experiments using the new laser system A spatial pattern of the pumping beam from the zigzag-slab-type amplifier is square and has fairly good uniformity. So, it is supposed that the pattern

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after focusing to a line shape is improved compared with that from the rodtype amplifier. We carried out an experiment for lasing at 13.9 nm by temporarily replacing the rod-type amplifier to the zigzag-slab-type amplifier. The result is plotted in Fig. 5 (single target experiment). The small signal gain coefficient is 41.9 and the output energy is saturated at a gain-length product of 16.3, which is an appropriate value. The spatial divergence of the XRL beam was about 3 mrad. It is about a half of the previous value. The reason of this low divergence may be due to the improved focusing.

XRL Output Energy (mJ)

10 1 10-1 10-2

g ~ 41.9 gL ~ 16.3

10-3

0

0.2 0.4 0.6 0.8 Target Length (cm)

1.0

Fig. 5. XRL lasing at 13.9 nm using the zigzag-slab-type amplifiers

As above-mentioned, the pulse controllability is improved by replacing the regenerative amplifier to the OPCPA amplifier, because there are no prepulse and no ASE. We examined a pre-pulse effect using the OPCPA amplifier and the new pulse controller. The experiment was carried out for lasing at 13.9 nm. The pumping pulses consisted of a pre-pulse with 200 ps pulse length and a main pulse with 5 ps pulse length. The interval between the two pulses was 2.75 ns and the total pumping energy was about 10 J. From the experiments, it was found that the XRL beam direction and the output energy were strongly dependent on the pre-pulse. The results are plotted in Fig. 6. The horizontal beam direction was plotted in Fig. 6a as a function of energy ratio of the pre-pulse over the main pulse. The plotted values are relative angles from the direction at Pre/Main = 4.3 %. Increasing the pre-pulse energy ratio, an expansion speed of the preplasma increases and the scale length of the plasma density becomes longer. So, the refraction of the XRL beam due to the density gradient decreases with increasing the pre-pulse energy ratio. It is thought that the

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8 7 6 5 4 3 2 1 0

700 XRL beam horizontal direction (a)

0

0.01 0.02 0.03 0.04 0.05 Energy ratio of Pre / Main

XRL output energy [ nJ]

Relative angle [ mrad]

expansion speed is equal to the sound velocity and is proportional to the square root of the pre-pulse energy. It is consistent with the plotted values. Since the effective gain area increases with increasing the density scale length, it is reasonable that the XRL output energy increases with the prepulse energy ratio as shown in Fig. 6b.

600

(b)

500 400 300 200 100 0

0

0.01 0.02 0.03 0.04 0.05 Energy ratio of Pre / Main

Fig. 6. Effects of pre-pulse on the XRL beam direction and the output energy

6 Conclusions We have succeeded in lasing at 13.9 nm with spatially full coherence by means of the double target method, which is a MOPA concept using the XRL seeder and the XRL amplifier. Now, the trend of XRL research is toward improvement of the beam quality. We expect to make advances in this trend by developing the new pumping laser system, which consists of the OPCPA amplifier and the zigzag-slab-type glass amplifiers. It was proved that the OPCPA has a capability for improving the pulse controllability and the zigzag-slab amplifier has a capability for stable operation with the output energy of 10 J and the repetition rate of 0.1 Hz.

References 1. 2. 3. 4. 5. 6. 7.

D. L. Matthews et al., Phys. Rev. Lett. 54, 110 (1985) J. Nilsen et al., Phys. Rev. A 48, 4682 (1993) S. Basu et al., Appl. Rev. B 57, 303 (1993) P. V. Nickles et al., Phys. Rev. Lett. 78, 2748 (1997) B. E. Lemoff et al., Phys. Rev. Lett. 74, 1574 (1995) J. Dunn et al., Phys. Rev. Lett. 80, 2825 (1998) R. Keenan et al., Phys. Rev. Lett. 94, 103901 (2005)

36 8. 9. 10. 11. 12. 13. 14. 15. 16.

K. Nagashima et al. A. Carillon et al., Phys. Rev. Lett. 68, 2917 (1992) C. L. S. Lewis et al., Opt. Commun. 91, 71 (1992) R. Kodama et al., Phys. Rev. Lett. 73, 3215 (1994) M. Tanaka et al., Opt. Lett. 28, 1680 (2003) Ph. Zeitoun et al., Nature 431, 426 (2004) T. Kawachi et al., Appl. Opt. 42, 2198 (2003) T. Kawachi et al., Phys. Rev. A 66, 033815 (2002) M. Nishikino et al., Phys. Rev. A 68, 061802 (2003) N. Hasegawa et al., Inst. Phys. Conf. Ser. 186, 273 (2004)

X-Ray Lasing Using the GRIP Scheme J.E. Balmer, M. Grünig, C. Imesch and F. Staub Institute of Applied Physics, University of Bern

Summary. We report on x-ray laser experiments using the grazing-incidence pumping (GRIP) scheme with 8-ps duration, 1054-nm pump pulses and energies up to 3 J. Intense x-ray lasing from targets of Mo, Pd, Ag, and Sn has been obtained by optimizing the prepulse configurations (long pulse – short pulse – grazing incidence).

1 Introduction Important progress towards higher efficiency, reduced size, and higher repetition rate of soft-x-ray lasers has been achieved in recent years by adopting the transient-collisional-excitation (TCE) scheme as proposed by Afanasiev and Shlyaptsev [1]. In this scheme, a first nanosecond-duration laser pulse at 1011-1012 W/cm2 generates the plasma and the required closed-shell (Ne-like or Ni-like) ionization conditions. A second, much shorter (picosecond) laser pulse at 1014-1015 W/cm2 then rapidly heats the preformed plasma and generates a transient population inversion. If the fast temperature rise is of the order of the time scale of the collisional redistribution of the excited levels, it allows efficient pumping without perturbing the ionization. Very high x-ray laser gain coefficients (>100 cm−1) have been predicted with the possibility of saturated gain for target lengths of less than 1 cm. Experimentally, saturated operation of TCE x-ray lasers with gain coefficients as high as 62 cm−1 has been demonstrated by several groups [2]. The advantage of this scheme is that less than 10 J of laser energy from a chirped-pulse amplification (CPA) laser are sufficient to drive the inversion. Very recently, a novel irradiation geometry, the grazing-incidence pumping (GRIP) technique has been introduced [3], which has resulted in a further reduction of the pump pulse energy to ~1 J for saturated lasing at wavelengths down to 13.2 nm [4]. In the GRIP scheme, a preformed plasma is generated, much as in the TCE scheme, by irradiating the target with a long (~200 ps) laser pulse at normal incidence. The plasma is allowed to expand for a given time to

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J. Balmer et al.

allow the electron density gradients to relax. The short (~ps) pump pulse then irradiates the expanding plasma plume at a grazing angle. The angle of incidence θ is chosen in such a way that the turning point density of the 2 pump radiation, ne - given by refraction as ne = necθ , where nec is the critical density for the pump laser wavelength - coincides with the density for which maximum gain is obtained for a given x-ray laser wavelength. Absorption of the pump energy thus occurs directly and very efficiently into the gain region. In this paper we report on the first phase of implementation of the GRIP scheme into the Nd:glass laser system used for x-ray laser experiments at our laboratory. The laser has recently been upgraded into a CPA (chirpedpulse amplification) system and currently produces a maximum of 6 J on target in a compressed pulse of 8 ps duration. One or several prepulse(s) can be introduced either along a separate beam line or, optionally, along the GRIP beam line. At the available shot rates of 5/hour for the 3 J experiments and 2/hour for the 6 J experiments, the optimization of the various prepulse configurations becomes a rather formidable task. Nonetheless, intense x-ray lasing was observed from Ni-like plasmas of Mo, Pd, Ag, and Sn at 18.9, 14.7, 13.9, and 11.9 nm, respectively, using a single prepulse irradiating the target along the GRIP beam line.

2 Experimental setup The experiments were conducted using the CPA upgrade to the existing Nd:glass laser system operated at our laboratory for a number of years. At the front end, the upgrade includes a commercial 100 mW, 200 fs Nd:glass oscillator followed by a double-pass, single-grating pulse stretcher and a diode-pumped Nd:glass regenerative amplifier producing a pulse energy of ~1 mJ. Due to gain narrowing during the amplification process, the bandwidth and the duration of the pulses are reduced to ~2 nm and 550 ps, respectively, at this point. The pulses are further amplified in the 5-stage main amplifier chain consisting of flashlamp-pumped Nd:glass rods having diameters of 10, 16, 25, 45, and 90 mm. The maximum energy output of the system is limited by the damage threshold of the 1740 line/mm compressor gratings, given by the manufacturer as 250 mJ/cm2. With the laser operated at the current beam diameter of 80 mm and for an angle of incidence of 61° on the gratings, this translates into a maximum energy of ~25 J incident on the first grating. Taking into account the 4-pass geometry of the compressor, the diffraction efficiency of the gratings of ~90 %, and the 2:1 peak-to-average ratio of

X-Ray Lasing Using the GRIP Scheme

39

the beam fluence distribution, a maximum of ~8 J was available for x-ray laser experiments in this phase. The experimental setup used for the x-ray laser experiments is shown schematically in Fig. 1. The main pulse beam was focused at a grazing angle of 22.5° using a multilayer-coated f = 91.4 cm parabolic mirror. This angle has been imposed, as shown in the figure, by the availability of an entrance port on the existing target chamber. The line focus was measured at low power to be 30 μm in width and 7.5 mm (FWHM) in length. The experience from previous experiments with our system implies that the line focus width will be approximately doubled at high power. A longduration (500 ps) prepulse was introduced along a separate beam line and focused by a single plan-convex lens tilted at the appropriate angle to produce a line focus of similar dimensions. An additional prepulse could be propagated along the main pulse beam line, thus producing a compressed 8-ps prepulse as an option. The main diagnostics of the plasma emission was an on-axis, time-integrating spectrometer that consists of a 1200 lines/mm, aberration-corrected, concave Hitachi grating (radius of curvature: 5649 mm), working at a grazing-incidence angle of 3 ° . The grating disperses the incident radiation on a 40 mm diameter P20 phosphor screen, which was imaged to a cooled CCD camera with a pixel size of 23 μm square. The wavelength coverage of the spectrometer was ~12 nm with a spectral resolution of ~0.2 nm.

3 J/8 ps + pp

On-axis parabola f = 91cm

< 4 J/500 ps

22.5° XRL

Spectrometer/ CCD

Fig. 1. Experimental setup for x-ray laser experiments at a fixed angle of incidence of 22.5°.

40

J. Balmer et al.

3 Soft-x-ray laser results In a first phase of GRIP experiments, a number of prepulse configurations were investigated in order to find the optimum prepulse conditions. The targets used were 25 mm wide slabs of Mo and Pd, having a diamondmachined surface finish. The targets were positioned in such a way that the line focus hit the surface close to the edge on the spectrometer side. Overfilling of the target on this side to avoid cold, absorbing plasma did not seem to be of major importance. A list of prepulse configurations for which x-ray lasing was observed is given in Table1. We note that in all the cases investigated, the existence of a short (compressed) prepulse was found to be beneficial to x-ray lasing; in fact it turned out that best results were obtained with a single prepulse incident along the GRIP path. This configuration was thus used for further optimization with respect to the prepulse-to-main pulse time interval. Figure 2 shows a set of on-axis spectra from targets of Mo, Pd, Ag, and Sn, irradiated with a 120 mJ prepulse preceding the 3 J main pulse by 13 2 2.4 ns. This translates into irradiances of ~8×10 W/cm for the main 12 2 pulse and ~4×10 W/cm for the prepulse. Lasing in Sn at 11.9 nm was found to be very weak under these irradiation conditions; most likely due to the fact that the 22.5° angle of incidence is too far from optimum for this element (see discussion below). In order to find the optimum delay conditions between prepulse and main pulse, a systematic study was conducted to investigate the x-ray laser output intensity as a function of the prepulse-to-main pulse time interval for a range of prepulse amplitudes, as shown in Figure 3 for the case of a Pd target. As can be seen, lasing on the 14.7-nm line is observed for prepulse amplitudes of 0.5-16 % and main pulse delays of up to 11 ns. Table 1 Prepulse configurations with x-ray lasing observed

prepulse(s)

main pulse

delay

Target

0.8 J/15 ps, along prepulse path (w/o pulse compression) 4 J/500 ps, along prepulse path + 0.15 J/8 ps along GRIP path 0.15 J/8 ps, along GRIP path + 0.5 J/8 ps along GRIP path 0.5 J/8 ps, along GRIP path

2 J/15 ps

300-700 ps 300 ps 5 ns 5 ns 800 ps 800 ps

Mo

3 J/8 ps 3 J/8 ps 3 J/8 ps

Pd Pd Pd

X-Ray Lasing Using the GRIP Scheme

41

λ

2nd order

Mo

Pd

Ag

Sn

Mo Pd Ag Sn (x50)

Intensity (counts)

8000 6000 4000 2000 0 5

10

15

20

25

30

Wavelength (nm)

Fig. 2. On-axis spectra from targets of Mo, Pd, Ag, and Sn irradiated at a fixed angle of incidence of 22.5°.

7000

2.8% 4.5% 8% 16% 0.5%

Intensity (counts)

6000 5000 4000 3000 2000 1000 0 0

2

4

6

8

10

12

Main pulse delay (ns)

Fig. 3. 14.7 nm laser intensity from a Pd target vs. main pulse delay, for a range of prepulse amplitudes.

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J. Balmer et al.

This is in distinct difference to the results of Refs. 3 and 4, where substantially narrower temporal windows of ~50 ps and ~800 ps have been reported for lasing in Mo and Ag, respectively. Of course, those experiments were driven either just above the threshold for lasing (Mo) or just above saturation (Ag), with main pulse energies of ~100 mJ and ~1 J, respectively. With a main pulse energy of 3 J as in our case, lasing should be expected to be well into the saturation regime and thus less critical with respect to the conditions of the preformed plasma. This has not been confirmed yet by measurement, but a comparison with previous data [5] suggests that a maximum value of the x-ray pulse energy of ~3 μJ has been attained in our current experiments, a factor of 4-5 higher than the values quoted in Ref. 4 at saturation, for a comparable pump pulse duration.

4 Discussion As shown above, lasing in Sn at 11.9 nm was found to be very weak under the current irradiation conditions or, more specifically, at the fixed 22.5° angle of incidence. (In the meantime, intense lasing has been obtained also from Sn targets, however, at increased main pulse energy of 6 J). The optimum angle of incidence for Sn has been reported to be 23° for a Ti:sapphire pump laser wavelength of 800 nm. Since the optimum angle scales with wavelength as θNd = θTi λNd /λTi ≈ 1.32θTi, this translates into an optimum angle of 30° for the 1054 nm Nd laser wavelength used in our case. Experiments at this angle will be conducted upon installation of a new target chamber in the very near future. An interesting point in the results shown in Fig.3 is the fact that, with the exception of the lowest energy prepulse (0.5 %), all the curves exhibit a double-humped dependence of the x-ray laser intensity on the time interval between prepulse and main pulse. This behaviour is not understood yet and will require more work in the future. A possible explanation could be that two temporal regimes exist for lasing, one during the ionizing phase of the plasma and the other during the recombining phase of the interaction. Between these two regimes, the plasma is overionized and gain is reduced. However, this is rather speculative and will require simulations to be performed, which is outside the scope of this work. Also, the irradiation history has been checked for spurious prepulses -5 and it was found that the pulse contrast ratio is better than ~10 for times down to the 1-ns response time of the photodiode used.

X-Ray Lasing Using the GRIP Scheme

43

4 Summary In summary, we have demonstrated intense x-ray lasing from nickel-like plasmas of Mo, Pd, Ag, and Sn by utilizing a short (8 ps) prepulse irradiating the target at a grazing angle of incidence of 22.5°, i.e., collinear with the 3 J, 8 ps main pulse. Saturated lasing has not been proved yet, but comparison with signal levels achieved in previous work suggests that saturation has well been reached in these experiments. This is supported by the fact that a large range of prepulse energies and time intervals gives rise to intense x-ray lasing, as has been demonstrated in the case of Pd.

References 1.

2.

3.

4.

5.

Yu.V. Afanas'ev and V.N. Shlyaptsev: 'Formation of a population inversion of transitions in Ne-like ions in steady-state and transient plasmas', Sov. J. Quant. Electron. 19, 1606, 1989. M.P. Kalashnikov et al.: 'Saturated operation of a transient collisional x-ray laser', Phys. Rev. A 57, 4778, 1998; J. Dunn et al.: 'Gain saturation regime for laser-driven tabletop, transient Ni-like ion X-ray lasers', Phys. Rev. Lett. 84, 4834, 2000. V.N. Shlyaptsev et al.: “Numerical study of transient and capillary x-ray lasers and their applications”, Proc. SPIE, Vol. 5197, 221-228, 2003; R. Keenan et al., “Efficient pumping scheme for high-average brightness collisonal x-ray lasers”, ibid., 213-220. Y. Wang et al.: “Demonstration of high-repetition-rate tabletop soft-x-ray lasers with saturated output at wavelengths down to 13.9 nm and gain down to 10.9 nm”, Phys. Rev. A 72, 053807-1-7, 2005; J.J. Rocca et al.: “Saturated 13.2 nm high-repetition-rate laser in nickel-like cadmium”, Opt. Lett. 30, 2581-2583, 2005. J.E. Balmer et al.: “Towards full characterization of nickel-like soft-x-ray lasers”, Proc. SPIE, Vol. 4505, 93-99, 2001.

Development of 0.1-Hz Repetition Driver Laser for the TCE X-Ray Lasers Y. Ochi, N. Hasegawa, T. Kawachi, K. Nagashima, M. Kishimoto, M. Tanaka, M. Nishikino, K. Sukegawa, H. Yamatani and Y. Kunieda Kansai Photon Science Institute, Japan Atomic Energy Agency

Summary. We developed new power amplifier using a zigzag slab Nd:glass to generate the TCE x-ray lasers more frequently. The chirped laser light at the wavelength of 1053 nm was amplified to > 10 J and then compressed to be ~1.6 ps at repetition rate of 0.1 Hz. By using the amplified laser light, gain saturated x-ray laser with the Ni-like silver at wavelength of 13.9 nm was obtained.

1 Introduction Developments of the chirped pulse amplification (CPA) [1] laser and the transient collisional excitation scheme [2] enabled us to generate the soft x-ray lasers with laboratory-scale laser system. There have been much progresses on x-lay lasing with a several materials using the CPA laser amplified by Nd:glass power amplifiers [3-6]. In particular for the Ni-like silver laser at the wavelength of 13.9 nm, saturated amplification with energy out put of 25 μJ due to the traveling pumping was achieved [6]. Furthermore, spatially full-coherent beam with diffraction limited beam divergence of 0.2 mrad was demonstrated by means of the oscillatoramplifier scheme using double targets [7]. Now our interest is moving to application studies using the highly coherent soft x-ray beam. However, the present repetition of soft x-ray laser generation is limited to be 1 shot/20 minutes by cooling time of glass rods used for the typical power amplifier. This repetition is not sufficient for making practical application study. Herein we report the development of new power amplifier for the CPA laser using zig-zag slab Nd:glass which provides > 10 J energy light at 0.1 Hz repetition. The zigzag slab is suitable for high repetition operation because the thermal distortion effects in the glass are principally canceled by propagating the zigzag pass. Specification of the power amplifier system is presented in the next

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Y. Ochi et al.

section. The result of x-ray lasing experiment with the Ni-like silver is discussed in section 3.

2 Development of power amplifier using zigzag slab Nd:glass Figure 1 shows a schematic design of the power amplifier system. First, the p-polarized laser light from a pre-amplifier is shaped to be 10 mm square by a serrated aperture (SA). Then the laser light propagates through a thin plate polarizer (PL-1) and the polarization is changed to be "s" by passing through combination of a Faraday rotator (FR) and a half wave plate (H-WP). The image at the SA is transferred onto a mirror-2 (M-2) by means of a spherical lens pair (SLP-1). A vacuum tube ended by optical windows is placed between the lens pair in order to avoid the air breaking down around the focus point. Without a high-voltage supply to a pockels cell (PC), the polarization rotates 90 degrees (sÆp) by making a round trip of combination of a quarter wave plate (Q-WP) and PC. Then the image on the M-2 is relayed onto a mirror-3 (M-3) by means of a SLP-2. During high-voltage is supplied to the PC, the p-polarization is kept and then the image relay between the M-2 and the M-3 is repeated. The first zigzag slab amplifier (ZSA-1) is placed between the M-2 and the M-3, therefore 10x10 mm2 seed light is amplified whenever it passes the ZSA-1. The ZSA-1 consists of a silca-phosphate laser glass doped with 1.0 wt% Nd and 8 flash lamps. The dimension of the laser glass is 15 mm in width, 17 in height, and 99 mm in length. Preliminary result of the amplification test shows that the stored energy density of 0.3 J/cm3 is available. Here the laser light is amplified up to ~1 J which is determined by the typical damage threshold of the optical coating, i.e. 2 J/cm2. Then the amplified light is extracted by switching the PC voltage off. The original image of the SA is transferred to nearby a mirror-4 (M-4) by means of the SLP-1. Then the image is vertically extended to be 10x90 mm2 and transferred to the second zigzag slab amplifier (ZSA-2) by means of cylindrical lens pairs (CLP-1, 2). The ZSA-2 consists of the silca-phosphate laser glass doped with 1.0 wt% Nd and 24 flash lamps. The dimension of the laser glass is 15 mm in width, 110 in height, and 205 mm in length. The ZSA-2 provides >10 J by a double-pass amplification. After the ZSA-2, the amplified light is horizontally extended to be 90x90 mm2 and the image is transferred to the compressor by means of another cylindrical lens pair.

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Development of the 0.1-Hz Repetition Driver Laser for the TCE X-Ray

CLP-1

47

to compressor

CLP-2

s

M-4 p

FR

p

H-WP s

SA PL-1

ZSA-2 M-1

s s

pre-amp.

s

SLP-1

s

Q-WP M-2 PC

multi-pass amplification M-3

p

PL-2

SLP-2

ZSA-1

Fig. 1. Schematic design of the power amplifier. SA, PL, FR, H- or Q- WP, SLP, M, PC, CLP, and ZSA represent a soft aperture, a polarizer, a Faraday rotator, a half or quarter wave plate, a spherical lens pair, a flat mirror, a pockels cell, a cylindrical lens pair, and a zigzag slab amplifier, respectively. The italic signs mean polarization directions of the laser light.

3 X-ray lasing experiment

Intensity (arb. unit)

By using the laser pulse amplified by the zigzag slab amplifiers, we made x-ray lasing experiment with Ni-like silver. It is noted that the shot repetition was not 0.1 Hz in this experiment. The shot interval was about 1 minute owing to the target alignment and data acquirement. The laser pulse consisted a main pulse of 1.6 ps duration and 1/8 intensity pre-pulse at 1.1 ns before the main pulse. The laser pulse focused on the silver target in the line shape of 20 μm width and 0.8 cm length. The total irradiation energy was 7.3±1.3 J, corresponding to the intensity of 2.5x1015 W/cm2 for the main pulse and 3.2x1014 W/cm2 for the pre-pulse. 400

Ni-like silver

300 200 100 7

13.9 Wavelength (nm)

Fig. 2. Typical spectrum of the Ni-like silver laser.

23

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Y. Ochi et al.

Typical spectrum obtained by a flat field spectrometer with a backilluminated CCD camera is shown in Fig.2. It can be seen that the Ni-like silver laser line is dominantly strong. In this case, the output energy of the Ni-like silver is about 1 μJ and the beam divergence in the direction perpendicular to the target was ~3 mrad. Intensity (arb. unit)

104 103 102

10 1

0

0.2

0.4

0.6

0.8

1.0

Target length (cm)

Fig. 3. Gain property of the Ni-like silver laser.

Figure 3 shows the gain property of the Ni-like silver for the target length from 0.25 cm to 0.78 cm. The output energy exponentially increases until the target length of 0.4 cm and linearly in following region. The small signal gain and the gain-length product is 41.9 and 16.3, respectively. Consequently, the gain saturated amplification of the Ni-like silver is demonstrated by the laser light amplified by the zigzag slab Nd:glass amplifiers.

4 Summary We have developed new power amplifier of the XRL driver laser by using the zigzag slab Nd:glass. With this power amplifier, the laser light was amplified up to >10 J at repetition rate of 0.1 Hz and compressed to be ~1.6 ps. The gain saturated Ni-like silver laser was demonstrated by using this laser system. We will construct one more laser line for applying the oscillator-amplifier scheme. Then we will provide the fully coherent XRL beam for application researches at 0.1-Hz repetition.

Development of the 0.1-Hz Repetition Driver Laser for the TCE X-Ray

49

References 1. Strickland, D. and Mourou, G. Opt. Commun., 56, 219, 1985. 2. Afanasiev, Y. A. and Shlyaptsev, V.N., Sov. J. Quantum Electron, 19, 1606, 1989. 3. Nickles, P.V., N. Shlyaptsev, V., Kalachnikov, M., Schnürer, M., Will, I., Sandner, W., Phys. Rev. Lett., 78, 2748, 1997. 4. Dunn, J., Osterheld, A.L., Shepherd, R., White, W.E., Shlyaptsev, V.N., and Stewart, R.E., Phys. Rev. Lett., 80, 2825, 1998. 5. Klisnick, A., Zeitou, Ph., Ros, D., Carillon, A., Fourcade, P., Hubert, S., Jamelot, G., Lewis, C.L.S., MacPhee, A., O’Rourcke, R., Keenan, R., Nickles, P.V., Janulewicz, K., Kalachinikov, M., Warwick, J., Chanteloup, J.C., Migus, A., Salmon, E., Saurtret, C., and Zou, J.P., Opt. Soc. Am. B, 17, 1093. 2000. 6. Kawachi, T., Kado, M., Tanaka, M., Sasaki, A., Hasegawa, N., Kilpio, A. V., Namba, S., Nagashima, K., Lu, P., Takahashi, K., Tang, H., Tai, R., Kishimoto, M., Koike, M., Daido, H. and Kato, Y., Phys. Rev. A, 66, 033815, 2002. 7. Nishikino, M., Tanaka, M., Nagashima, K., Kishimoto, M., Kado, M., Kawachi, T., Sukegawa, K., Ochi, Y., Hasegawa, N. and Kato, Y., Phys. Rev. A, 68, 061802(R), 2003.

Modulation of Plasma Density to Achieve Highly Efficient X-Ray Lasers With Good Beam Quality J. Zhao, Q. L. Dong and J. Zhang* Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100080, China

Summary. A plasma with a modulated density profile at the required electron density for high gain operation could be obtained using a normally incident 300 ps laser pulse followed by a grazing incident 300 ps laser pulse. Sudden heating of the modulated plasma region by another grazing incident 300 fs laser pulse would then yield a highly efficient x-ray laser beam with a defecting angle of 2 mrad and a divergence angle of 3 mrad. Saturation operation of the x-ray laser beam at 32.6 nm could be achieved with a total pump energy of less than 100 mJ.

1 Pump scheme to modulate the plasma density Since the first demonstration of x-ray lasing in Ne-like Se ions [1,2], the pumping process for soft x-ray lasers has gradually been transfered into two steps. The first is to generate a plasma with an abundant population of Ne-like or Ni-like ions. After a certain delay time, a main pulse then irradiates the plasma to generate soft x-ray lasers. To improve the pump efficiency, much effort has been made on both of these two aspects. To solve the problem of refraction due to the steep electron density gradient in the plasma, the pre-pulse (or multi-pulse) technique was introduced with a long delay time [3-5]. The driver energy has also been reduced dramatically to a few joules by short-pulse CPA pumping [6,7]. The pumping efficiency has been further improved by the grazing-incidence pumping (GRIP) scheme, which allows the main pulse to dump more energy in the gain region of the plasma [8-13]. Plasma with a shallowgradient electron density profile and long spatial gain region is crucial to increase the absorption and pumping efficiency of the main pulse. There are several techniques to optimize the plasma to more efficiently generate x-ray lasers. The exploding foil technique was firstly used to produce a flat electron density profile with a scale length of more than 100 µm [1-3]. Refraction was minimized using this technique. However, only

52

J. Zhao, Q. L. Dong and J. Zhang

very high energy pump lasers can burn through the thin foil and a large fraction of the laser energy is lost through radiation and conduction, so that it is practical only on large ICF laser systems with kJ energy output. The multi-pulse technique can generate a large, uniform plasma with a flat stage in the electron profile using three normal incidence pulses [4]. The flat stage has the advantage of little refraction and therefore the generated x-ray laser beam can be more efficiently amplified. However, the electron density in the flat stage (about 7×1020 cm−3 in [4]) is much higher than that required for a specific x-ray lasing (say 2×1020cm−3 for Ne-like Ti ions). Furthermore, the three-pulse configuration is also rather complicated for practical applications.

30 0p s

Delay T ime 5ns

300ps

30 0f s

Gain Region X-ray laser output Target

Fig. 1. The pulse configuration for modulating the plasma density to generate a plasma with a shallow gradient of electron density at the gain region, suitable for pumping Ne-like x-ray lasers.

We propose a new technique to modulate the plasma density to form a flat, uniform electron density distribution at a required electron density (gain region) for a specific x-ray laser, schematically as shown in Fig. 1. The modulation is accomplished by a grazing-incidence 300 ps laser pulse, irradiating an initial plasma (with no Ne-like ions) generated by a normal incidence 300 ps weak laser pulse. Because of a longer path length, the energy of the grazing incidence 300 ps pulse is more efficiently used to ionize the plasma to the ground state of Ne-like (or Ni-like) ions. Each time partition of the 300 ps pulse is refracted and dumps its energy at a predetermined electron density [11]. As the heated electrons expand forward, a flat stage with a shallow gradient electron density is generated. By changing the incidence angle of the second 300 ps pulse and the delay time between the two 300 ps pulses, the electron density at the flat stage can be optimized as the gain region for the desired soft x-ray laser, the uniformity and width of the gain region can be modulated, respectively.

Modulation of Plasma Density to Achieve Highly Efficient X-Ray Lasers

53

The modulated plasma pumped by a grazing incidence main pulse with a 300 fs duration can then generate highly efficient x-ray lasers with a good beam quality. To test the method for realizing the modulation of the plasma density, we consider, as an example, a Ne-like Ti x-ray laser at 32.6 nm. A modified 1D Lagrangian hydrodynamic code MED103 coupled with an atomic physics data package is used to obtain the time evolution of the laser-plasma interaction and the gain coefficients. In addition to the 2D ray-tracing code, which calculates the variation of the output intensity versus the plasma length, a 3D ray-tracing code is developed to calculate the near-field and far-field distributions of the output intensity of the x-ray laser beam.

2 Density modulation for the Ne-like Ti x-ray laser The wavelength of the pump laser is 800 nm. The pump geometry is the standard line focus on a 100 µm thick slab target. The pump laser pulses have a Gaussian profile. The purpose to modulate the plasma density before the main pump laser pulse is to generate a wide uniform flat electron density distribution at 2.0×1020 cm−3, which is the gain region for the Ne-like Ti x-ray laser. The duration of the two long pump pulses are fixed to 300 ps.

(a)

(b)

Fig. 2. The electron density profiles at the peak abundance time of Ne-like ions under (a) different incident angles from the surface of the target when the delay time is 5 ns (b) different intervals when the incident angle is 20◦.

54

J. Zhao, Q. L. Dong and J. Zhang

A 300 ps weak pulse of 1×1011W/cm2 is normally focused on the slab target to generate an initial plasma (with no Ne-like ions). By changing the grazing incidence angle of the second 300 ps pulse and the interval between the two pulses, the profile of plasma density can modulated. The peak intensity of the second pulse is simultaneously optimized, to ionize the plasma to the Ne-like state without over-ionization. Fig. 2 gives the electron density profiles at the peak abundance time of Ne-like ions under (a) different incident angles to the surface of the target when the delay time is 5 ns (b) different intervals when the incident angle is 20◦. The smaller incidence angle of the second pulse is used, the more uniform electron density in the plasma is generated. The second pulse with an incidence angle of 20◦ has the turning point at about 2.0×1020 cm−3, which is the required electron density for the Ne-like Ti x-ray laser, gives the widest gain region about 70 µm. The longer time the plasma expands before the second pulse, the wider the flat stage of electron density distribution is, as shown in Fig. 2 (b). But if the interval is too long, for example 7 ns, the electron density at the flat stage will be further reduced.

Moving

1

9 4

4

9

1

4 1

9

Fig. 3. The time evolution of electron density profiles during the second pulse from 5200 ps to 5550 ps. The peak time is 5360 ps. The distribution of the ground state Ne-like Ti ions at the end time of the second pulse is also plotted.

Modulation of Plasma Density to Achieve Highly Efficient X-Ray Lasers

55

In our simulation, the optimum plasma density profile is produced by the second pulse, which arrives 5 ns later with a peak intensity of 2.8×1011 W/cm2 and a grazing incidence angle of 20◦. To understand the mechanism of the modulation of the electron density profile by the grazing incidence 300 ps pulse, the time evolution of the electron density profile is given in Fig. 3. The surface of the target is located at 100 µm. The second pulse is divided into many time partitions. Each partition of the second pulse is reflected and dumps most of its energy at the turning point of ne=nc×sin2(θ), where nc=1.1×1021/λ2 (cm−3) is the critical density for the wavelength of the pump laser [11]. The electron density of 2.0×1020cm−3 corresponds to an incidence angle of 20◦. Heated by the earlier partitions of the second pulse, electrons move away from the target surface. Thus, at the intensity ascending side of the 300 ps pulse, the turning point of the laser beams moves fast forward along with the electrons, a deep valley of electron density is generated. At the descending side, another shallow valley ∼20 µm (which is important for generating good beam quality of xray laser) is produced.

Fig. 4. The time evolution of electron temperature in the plasma. Till the end of the second pulse the maximum temperature is reached, which represents the highest fraction of Ne-like ions.

Fig. 4 shows the time evolution of the electron temperature, which indicates the absorption of the second pulse in the plasma. The peak temperature also moves forward along the axial distance. At the end of the second pulse, the maximum temperature is reached corresponding to the highest fraction of Ne-like Ti ions in Fig. 3. Because of the increased path

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J. Zhao, Q. L. Dong and J. Zhang

5900

5900

5800

5800

5700

0.7

5600 5500 0.5

5400 5300 180

Time ( ps )

Time ( ps )

length and energy absorption of the grazing incidence 300 ps pulse, a plasma with a high fraction of Ne-like Ti ions is efficiently produced.

230

280

Distance ( μm )

5700

0.7

5600 5500 0.5

5400 5300 160 180 200 220 240 260

330 0.3

(a)

Distance ( μm )

0.3

(b)

Fig. 5. The spatiotemporal distribution of the ground state Ne-like ions fraction, generated by (a) the optimized grazing incident 300 ps pulse with an incident angle of 20◦ and (b) the normal incident 300 ps pulse. The fraction in the plot is from 70 % (black) to 30 % (white) by steps of 20 %.

We also investigate the distribution of the ground state Ne-like ions generated by the optimized 300 ps pulse with a peak intensity of 2.8×1011 W/cm2 and a grazing incidence angle of 20◦ in Fig. 5 (a), compared to the case where the second 300 ps pulse irradiates into the initial plasma at a normal incidence angle, shown in Fig. 5 (b). For the normal incident 300 ps pulse, most energy is dumped at the critical surface of the plasma, a peak intensity of 5.0×1011 cm−3 is required to get the same population of Ne-like ions as the grazing incident 300 ps pulse. The grazing incident case has shown a wider distribution of Ne-like ions with a less pump energy.

3 The main 300 fs pump laser pulse As the consequence of the modulation, a plasma with a fairly uniform, long-extent (∼80 µm) gain region at the electron density of 1.0×1020 cm−3 ∼ 2.0×1020 cm−3 is generated, with the same local position as the high fraction of Ne-like Ti ions. It is one of the advantages for the grazing incidence main pump pulse to dump its energy at the gain region and reach a high population inversion, simultaneously. This plasma with a shallow electron density gradient has advantages not only for the propagation and amplification of the x-ray beam, but also for the propagation and absorption of the main pump pulse. An efficient x-ray laser beam with a

Modulation of Plasma Density to Achieve Highly Efficient X-Ray Lasers

1

57

2

Fig. 6. The electron density and gain profiles at 1 ps after the onset of the main pulse. The first deep valley of electron density is generated by the ascending side of the second pulse, while the second shallow valley by the descending side.

good beam quality can be expected. As the last step of the pumping of the Ne-like Ti x-ray laser, the plasma is suddenly heated up by the following main CPA laser pulse with a 300 fs duration, shown in Fig. 1. The main pulse irradiates the plasma at the same incidence angle (turning point) as the 300 ps pulse. This configuration ensures that most energy is absorbed in the region with a high fraction of Ne-like ions. The peak intensity of the main pump pulse is optimized to be 3.0×1014 W/cm2. The optimized delay time between the main pulse and the second pulse is 240 ps. The spatial distribution of the gain coefficient is shown in Fig. 6. Maximum gain coefficient happens at the turning point of the main pulse, which is in the second shallow valley of electron density distribution, generated by the descending side of the second pulse. This valley of ∼20 µm can be used as a channel for the propagation of the main pump pulse (high pump efficiency) and x-ray laser beams (high amplification efficiency and good beam quality) with no refraction.

4 Characteristics of the output of the x-ray laser beam Using 2D and 3D ray-tracing codes developed by ourselves, the characteristics of the output profile of the Ne-like Ti x-ray laser beam can be investigated in detail. In the 3D ray-tracing code, the variation of the plasma density, gain coefficient in the pump laser (radial) direction is given by MED103, whereas a Gaussian profile is assumed for the transverse direction. The time dependence of gain coefficients is not taken into account, because of the inherent travelling wave pump of the grazing incidence pumping scheme. The refraction and saturation effects in both

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J. Zhao, Q. L. Dong and J. Zhang

8

1.6x10

4

1.4x10

0

1.2x10

-4

1.0x10

-8

8.0x10

205

210

215

220

Radial ( μm)

(a)

225

6.0x10 4.0x10

11 11 11 11 10 10

6

Vertical ( mrad )

Transverse ( μm)

Fig. 7. Ray-tracing results of the output of x-ray laser intensity versus the plasma length at incident angles of 18◦, 20◦ and 22◦.

4 2 0 -2 -4 -6 -6 -4 -2 0

10

2

4

6

Horizontal ( mrad )

11 1.6x10 11 1.4x10 11 1.2x10 11 1.0x10 10 8.0x10 10 6.0x10 10 4.0x10

(b)

Fig. 8. The patterns of (a) near field and (b) far field distributions of the output intensity of the Ne-like Ti soft x-ray laser beam at 32.6 nm, generated by a 0.15 cm long target. The intensity is depicted by a grey scale with an arbitrary unit.

radial and transverse directions are considered. About 1×107 rays are traced to calculate the output profiles of the x-ray laser beam. Figure 7 gives the 2D ray-tracing results of the output intensity of the x-ray laser beam versus the plasma length at incidence angles of 18◦, 20◦ and 22◦. Optimized output of the intensity is obtained with an incidence angle of 20◦. Saturation is achieved at a plasma length of 0.15 cm. The focal width is assumed to be 30 µm. The near and far field distributions of the output intensity at 32.6 nm, generated by a 0.15 cm long target, are calculated by the 3D ray-tracing code, as shown in Fig. 8. The target surface is located at 100 µm. The active region is ∼20 µm wide at the radial direction. Good

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59

output beam quality of the x-ray laser beam is shown with a deflecting angle of 2 mrad. Horizontal divergence (FWHM) is ∼3 mrad, vertical divergence (FWHM) is about 10 mrad. The pump energy of the three pump laser pulses are 13.5, 37.8 and 40.5 mJ, respectively. The total energy to pump the Ne-like Ti x-ray laser beam is only about 92 mJ, which is less than half of the pump energy with an optimized double pulse pump scheme used in Ref. [14].

5 Conclusion By modulating the plasma density with a 300 ps normal incidence pulse followed by a 300 ps grazing incidence second pulse, an optimized plasma with a large, uniform gain region for x-ray lasers, is generated. Suddenly heated by a 300 fs grazing incidence main pulse, an efficient x-ray laser with a good beam quality can be reached, because little refraction occurs during the propagation of the main pump pulse and x-ray beams. The 3D ray-tracing calculation shows a horizontal divergence (FWHM) of 4mrad and a deflecting angle of 2 mrad. For the Ne-like Ti x-ray laser at 32.6 nm, saturation is achieved with a total pump energy only about 92 mJ.

Acknowledgements This work is jointly supported by the National Natural Science Foundation of China (under Grant Nos. 10474137, 10574161, 10510490) and the National Hi-tech ICF Program.

References 1

2 3

4 5

D. L. Matthews, P. L. Hagelstein, M. D. Rosen, M. J. Eckart, N. M. Ceglio, A. U. Hazi, H. Medecki, B. J. MacGowan, J. E. Trebes, B. L. Whitten, et al., Phys. Rev. Lett 54, 110 (1985). M. D. Rosen, Phys. Rev. Lett 54, 106 (1985). L. B. Da Silva, B. J. MacGowan, D. L. Matthews, M. D. Rosen, H. A. Baldis, G. D. Enright, B. LaFontaine, and D. M. Villeneuve, Proceedings of the SPIE The International Society for Optical Engineering 1229, 128 (1990). J. Nilsen and J. C. Moreno, Phys. Rev. Lett 75, 2453 (1995). J. Zhang, A. G. MacPhee, J. Lin, E. Wolfrum, R. Smith, C. Danson, M. H. Key, C. L. S. Lewis, D. Neely, J. Nilsen, et al., Science 276, 1097 (1997).

60 6

7

8 9

10 11 12 13 14

J. Zhao, Q. L. Dong and J. Zhang P. J. Warwick, C. L. S. Lewis, M. P. Kalachnikov, P. V. Nickles, M. Schnurer, A. Behjat, A. Demir, G. J. Tallents, D. Neely, and E. Wolfrum, J. Opt. Soc. Am. B 15, 1808 (1998). M. P. Kalachnikov, P. V. Nickles, M. Schnurer, W. Sandner, V. N. Shlyaptsev, C. Danson, D. Neely, E. Wolfrum, J. Zhang, A. Behjat, et al., Phys. Rev. A 57, 4778 (1998). D. Alessi, B. M. Luther, Y. Wang, M. A. Larotonda, M. Berrill, and J. J. Rocca, Opt. Express 13, 2093 (2005). J. J. Rocca, Y. Wang, M. A. Larotonda, B. M. Luther, D. Alessi, M. Berrill, A. Weith, M. C. Marconi, C. S. Menoni, and V. N. Shlyaptsev, Soft X-Ray Lasers and Applications VI 5919, 591901 (pages 12) (2005). J. Dunn, R. Keenan, and V. N. Shlyaptsev, Soft X-Ray Lasers and Applications VI 5919, 591905 (pages 8) (2005). R. Keenan, J. Dunn, P. K. Patel, D. F. Price, R. F. Smith, and V. N. Shlyaptsev, Phys. Rev. Lett 94, 103901 (2005). J. Tummler, K. A. Janulewicz, G. Priebe, and P. V. Nickles, Phys. Rev. E 72, 037401 (2005). B. M. Luther, Y. Wang, M. A. Larotonda, D. Alessi, M. Berrill, M. C. Marconi, J. J. Rocca, and V. N. Shlyaptsev, Opt. Lett 30, 165 (2005). J. Zhao, Q. L. Dong, F. Yan, and J. Zhang, Phys. Rev. A 73, 033816 (2006).

Origin of Microstructures in Picosecond X-Ray Laser Beams O. Guilbaud1, A. Klisnick1, K. Cassou1, S. Kazamias1, D. Ros1, G. Jamelot1, D. Joyeux2 and D. Phalippou2 1

LIXAM, Laboratoire d'Interaction du rayonnement X Avec la Matière, Univ Paris-Sud, CNRS, UMR n° 8624, Orsay, F-91405, France. 2

LCFIO, Laboratoire Charles Fabry de l'Institut d'Optique, CNRS, UMR n° 8501, Orsay, F-91403 France.

Summary. Beam sections of transient collisional excitation (TCE) and optical field ionization (OFI) soft X-ray lasers exhibit highly contrasted intensity modulations forming complex patterns. We present model calculations that reproduce these experimental observations both qualitatively and quantitatively. The low spatial coherence, high longitudinal coherence and short pulse duration of the source are shown to control the visibility of the beam structures. Besides, simple relationships relating the spatial and temporal characteristics of the emitting source to the main features of the beam small-scale structures can be derived.

1 Introduction Important progress has been achieved in reducing the pumping energy of plasma based soft x-ray lasers (SXRL). Optical Field Ionization (OFI) [0] and Transient Collisional Excitation (TCE)[0] x-ray lasers are efficient enough to be pumped by a 1J Ti:Sapphire laser facility at 10 Hz. Compact devices that can be operated at high repetition rates are know available for a wide range of applications. Both schemes, OFI and TCE (including recent upgrades as Grazing Incidence Pumping methods [0]), have several common properties. In both cases, very high gain values (10 – 100 cm-1) are obtained during 10 ps to 30 ps after the pumping laser pulse intensity peak, leading to the emission of a short (a few ps) and intense soft x-ray pulse in the range of 40 nm to 6 nm. Because they are based on a single path amplification of spontaneous emission, their spatial coherence is low. On the other hand, because of the moderate ion temperature reached

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during the peak gain, the Doppler broadening is small leading to high values of the temporal coherence. Many works have indeed pointed out the proximity between the coherence time and the pulse duration values of these SXRL, and despite their ASE nature, the emitted XUV pulses are close to the Fourier transform limit [0][0].

Fig. 1 Experimental far field images of Ni-like Silver TCE soft x-ray laser. (a) and (b) were obtained in the experiment described in reference [0]. (c) was obtained in conditions described in reference [0].

These schemes were also observed to generate much less uniform beams than QSS SXRL (see for example [0]). The far-field images of TCE or OFI x-ray lasers exhibit complex patterns with small-scale and highlycontrasted structures. Figure 1 presents some examples of experimental far-field images of a Ni-like silver TCE x-ray laser [0] [0]. In some cases, strongly distorted interference fringes were observed as shown in figure 1c. In most cases however the observed far-field images have the appearance of a speckle pattern with a typical angular size of 0.1 to 0.5 mrad and randomly distributed over the beam section as illustrated in figure 1a and 1b. From classical theory we know that speckle patterns result from the diffraction of a spatially coherent beam by a random phase or transmission medium. This interpretation cannot be directly applied to SXRL. Although the amplifying plasma is probably not homogeneous and could indeed include small-scale dephasing structures, the spatial coherence of the SXRL beam in the plasma is far too low to induce any speckle pattern in the far field. We have recently developed a model explaining the formation of the two types of observed far-field structures [0]: fringes and speckles. We have showed that these structures are apparent as a result of the specific optical properties of TCE SXRL which were recently experimentally

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investigated: a low spatial coherence, a high longitudinal coherence associated with a short pulse duration. After a brief summary of the model, we will discuss the predictions of our model regarding the beam structure of TCE and OFI SXRL. Finally we will present simple formulas that relate the main features of the beam small-scale structures to spatial and temporal properties of the emitting source.

2 Model description 2.1 General We briefly describe in this section the main characteristics of our model. The notations used are presented in figure 2. The amplifying plasma is modeled by a cylindrical rod of length L along the axis z. The gain coefficient is assumed to be independent of z. The refraction of the SXRL beam induced by electron density gradients is not included. Hence, our model can only be used to investigate the spatial structure of the beam but is not appropriate to predict the overall shape or the deflection angle. Finally, the electromagnetic field associated to the SXRL radiation is described in the framework of the scalar approximation.

Fig. 2 (a) Geometry of the model. (b) Soft x-ray laser field modulus and phase on the exit plane. (c) far-field intensity distribution.

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The time-integrated intensity I(X,Y) detected at a distance D from the source can be deduced from the field instantaneous complex amplitude A(x, y,t) , on the exit aperture, by the Huygens-Fresnel principle: T /2

I (X ,Y ) =

∫

dt ∫∫ A( x, y, t ) e iϕ ( x , y ,t ) e

−i

2π ( ( x − X ) + ( y −Y )) λ D

dxdy (1)

−T / 2

where T is the integration time of the detector, much greater than the pulse duration τ XUV . To account for the ASE origin of the emitted field, we consider that the phase front ϕ ( x, y, t ) of the field at the exit aperture, and at a given time, is composed of small cells of uniform phase, randomly distributed as shown in figure 2b. The typical size of each cell is given by the spatial coherence length in the exit plane of the laser, and can have distinct values along x and y. An order of magnitude of the shape and size of the spatial coherence length can be deduced from the profile of spontaneous emission at the opposite end of the plasma rod, using the Van Cittert-Zernicke theorem. The field on the exit aperture is indeed the superposition of random phase fields initially emitted by the lasing ions through spontaneous decay, and amplified with propagation along the plasma rod. Because of the exponential growth of intensity with plasma length, only emitters at the opposite end of the plasma rod will significantly contribute to the field emitted at the exit aperture. To simplify the presentation the modulus of the field amplitude will be taken constant over the exit aperture (Figure 2b). The instantaneous far-field intensity pattern I(X,Y,t) at the detection plane will result from the interferences between the field amplitudes emitted by the numerous small regions of uniform phase at the exit aperture. It will thus exhibit properties similar to a speckle pattern that would have been produced by the diffraction of a spatially coherent beam through a random phase aperture analog to the one described by ϕ ( x, y , t ) . The experimental images being time-integrated, we shall now consider the evolution of the SXRL field over the whole pulse duration. To simplify 2

the presentation, the instantaneous intensity A(x, y,t) at the exit aperture is taken constant over the pulse duration. The phase front of the field ϕ ( x, y, t ) can be considered constant over a time shorter than τ C , the coherence time of the field. However, because of the chaotic nature of the

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ASE field, ϕ ( x, y, t ) randomly change over time scale greater than τ C . In summary, on a time interval of the order of τ C , the phase ϕ ( x, y, t ) and hence the far field instantaneous intensity I(X,Y,t) can be taken constant, but will change many times from one random distribution to a completely different one over the pulse duration. If we define N as the ratio between the pulse duration τ XUV and the coherence time τ C , then the integrated far-field intensity distribution can be approximated by an incoherent superposition of N different and independent instantaneous intensity farfield patterns.

3 Predictions of the model 3.1 Size of the far-field micro-structures In the previous section 2.2, we have emphasised the analogy existing between the instantaneous far-field intensity and classical speckles patterns. From this analogy we can deduce that the average shape and size of the micro-structures observed in the far-field are given by the diffraction pattern of the limiting diaphragm, namely here the exit aperture. If the emitting pupil of the SXRL source is elliptical, with ax and ay being its dimensions along the x and y axis respectively, an order of magnitude of the angular dimensions β X and β Y of a microstructure is thus given by:

β X ≈ λ a X and β Y ≈ λ aY .

3.2 Contrast of the far-field micro-structures A simple relation determining the contrast of the speckle structures can be derived from the temporal structure of the field considered in section 2.3. For N=1, The far-field integrated intensity I(X,Y) is a pure speckle pattern. It can be shown from classical theory of speckles that its spatial average

I

1

is equal to the spatial standard deviation σ 1 =

contrast of the speckles V = σ 1

I

1

I2

1

− I

2 1

. The

is thus equal to 1. For larger values

of N, the contrast V decreases as the inverse square root of N:

V =σN

I

N

= Nσ1 ( N I 1) = 1

N.

(2)

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The contrast of the far-field structures is inversely proportional to the squared root of N. In the framework of our model, this feature explains why contrasted structures are observed in TCE or OFI x-ray laser beams (N close to unity), whereas they are smoothed out in QSS lasers, which have a longer pulse duration (N>30).

4 Applications to TCE soft x-ray lasers We have applied the model to three particular cases where the near field intensity distribution is supposed to be a) almost circular, b) strongly elliptic, c) composed of two sources. In the three cases, we have taken N=3, in order to be as close as possible of the Ni-like silver TCE x-ray laser properties measured in [0]: τ XUV ~ 5 ps and τ C ~2 ps.

Fig. 3. Simulated far-field patterns. N=3. Near-field intensity distribution is shown in the insert of each image.

The simulated far-field patterns are displayed in figure 3. The corresponding near field intensity distribution is shown in the insert of each figure. Figure 3a presents a contrasted and randomly distributed pattern of circular microstructures. This pattern is similar to the intensity distribution observed for some TCE x-ray lasers shots (see for example figure 1a). It presents also some dramatic similarity with some OFI x-ray laser footprint [0]. The more elongated near-field distribution considered in the insert of figure 3b, reproduces more precisely the general exit aperture shape of a TCE x-ray lasers. The far-field distribution resulting from this hypothesis presents evident similarity with figure 3a except in the general shape of the micro-structures. This comparison illustrates the relation derived in section 3.1 establishing a link between the shape of the exit aperture and the shape

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of the microstructure. Moreover the kind of structures obtained in figure 3b is often observed in TCE x-ray laser footprint as presented in figure 1b. Finally, we have performed simulations assuming a near-field structure composed of two separated sources. This type of near field shape has been experimentally observed in TCE x-ray lasers by Tanaka et al. [0] and by Guilbaud et al. [0] The numerical result is displayed in figure 2c. The beam profile is covered by distorted fringes of constant interfringe. This type of pattern is similar to the experimental images observed by Klisnick et al. [0] on a Ni-like silver TCE x-ray laser and displayed in figure 1a. Note that in the simulations, we did not assume any particular phase relation between the two sources, i.e, no mutual coherence. We have also performed different simulations for different values of N. We observed that for high N values, the structure vanishes, as expected from equation (2).

5 Conclusions In summary, we have presented model calculations that account qualitatively and quantitatively for the complex patterns observed in the beam cross-section of transient and OFI X-ray lasers. We show that the presence of the highly contrasted structures, speckles or fringes, is controlled by the specific optical properties of these sources: a low spatial coherence, a high longitudinal coherence, and above all, a short pulse duration. Our model reveals simple relationships between the main features of the far-field structures and the source characteristics. The contrast of the structures is inversely proportional to the square root of N, the ratio of the pulse duration to the coherence time. Moreover, the size and shape of the speckles is related by diffraction to the spatial characteristics of the source ones through a Fourier transform. This hence means that the size and shape of the XRL exit aperture on the one hand, and the proximity of the pulse to the Fourier transform limit on the other hand, can be extracted from the experimental far-field images of the beam. Finally, our model predicts that small-scale structures will affect the beam even though the amplifying plasma is perfectly homogeneous. As a result, a better uniformity of the beam, which is of great importance for future applications, can only be obtained by improving the spatial coherence at the source plane, e.g. by the injection of high order harmonics at the entrance of the plasma amplifier rod [0,0].

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Acknowledgements We would like to thank Gilles Maynard (LPGP), Stéphane Sebban and Islam Bettaibi (LOA) for fruitful discussions on this work.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

Lemoff B.E. et al., Phys. Rev. Lett. 74, 1995, 1995 Nickles P.V. et al., Phys. Rev. Lett. 78, 2743, 1997 Keenan R. et al, Phys. Rev. Lett. 94, 103901, 2005 Smith R.F. et al., Opt. Lett. 28, 1, 2003 Guilbaud O. et al., Eur. Phys. J. D 40, 125, 2006 Rus B. et al., Phys. Rev. A 55, 3858, 1997 Klisnick A. et al., in soft x-ray laser and application IV, Proc. SPIE Vol 4505, 75, 2001 Guilbaud O. et al., Euro. Phys. Lett. 74, 823, 2006 Bettaibi I. et al., private communication Tanaka M. et al., in Proceedings of the international conference on VUV radiation physics, Surface Rev. Lett. 9, 641, 2002 Guilbaud O. et al., in soft X-ray laser and applications V, Proc. of SPIE Vol. 5197, 17, , 2003 Zeitoun P. et al., Nature 431, 426, 2004 Wang Y. et al., Phys. Rev. Lett., In press, 2006

Focusing System for a Non-Normal Incidence Pumped, Sub-10 nm TCE XRL D. Ursescua, C. Bischoffa,b, T. Kühla,c and B. Zielbauera,c,d a

Gesellschaft für Schwerionenforschung mbH, Darmstadt, Germany; Fachhochschule Friedberg, Friedberg, Germany; cMainz University, Mainz, Germany; dMax Born Institute, Berlin, Germany b

Summary. An extended ray-tracing study of the main pumping pulse (MP) focusing optics was made in order to develop a transient collisionally excited (TCE) x-ray laser (XRL) set-up for sub 10 nm wavelength by using non-normal incidence pumping. The study takes into account limitations determined by the large beam dimensions of the high energy MP. A setup using two off-the-shelf spherical mirrors is proposed, corresponding to a possible realization at the PHELIX laser facility.

1 Motivation Development of the x-ray lasers requires the generation of a well defined line-focus with a high aspect ratio. With the development of TCE systems, one more parameter became essential, the travelling wave speed (TW) of the focusing system. Several methods were proposed, including "misalignment" of the optical pulse compressor, echelons, and combinations of spherical and parabolic mirrors. A simple set-up using the aberrations (astigmatism and wave-front tilt) from a single spherical mirror can be used to generate an appropriate set-up (e.g. [1]) as first demonstrated experimentally in [2]. With the GRIP scheme [3], the incidence angle of the pulse on the target comes into play. This parameter produces important changes in the behaviour of the XRL [2-7]. The basic analytical relations describing the properties of this setup are presented in section 2. However, with the development of XRL toward shorter wavelengths, such a GRIP set-up is no more useful for two reasons: on one side the pumping beams are more energetic and, as a consequence of the damage threshold of the optics, the beams have larger radii thus generating significantly longer line foci. On the other hand the incidence angle of the pumping pulses are no more favourable in the GRIP case for sub 10 nm XRL,

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smaller incidence angles for the pumping pulses on target being more appropriate [6,7]. As a consequence, other focusing systems have to be developed taking into account the TW, the incidence angle of the pulse on the target and also very important, the price of the optical components. This paper reports in section 3 a possible choice for the focusing system using low-price optics, as needed for future experiments at PHELIX laser facility [8].

2 Line focus with one spherical mirror Analytical relations can be obtained for line focus length and travelling wave speed in the case of a single focusing spherical mirror. The focusing system is represented in the fig. 1. A parallel laser beam is coming along lines L1M1 and L2M2 to the spherical mirror with the centre in O and radius OA = OM1 = OM2 = R = 2f. Using the notations in the picture one can write the line focus length:

Fig. 1. Representation of the main pulse focusing system used for deriving the analytical formula of the travelling wave and for the line focus length

and the average TW speed as:

The local TW can then be obtained as a limit of the above relation:

Focusing System for a Non-Normal Incidence Pumped, Sub-10 nm TCE XRL 71

3 Line focus generation using two spherical mirrors As it is clear from the relations above, one cannot control the line focus length and the incidence angle in an independent way by using only one spherical mirror for a given beam diameter. One way to do that is to use one off-axis parabolic mirror and one spherical mirror as reported in [9]. However, this approach is expensive when the beam diameter of the optics in use increases. This happens when one pumps shorter wavelengths XRL using picosecond pulses as it is prepared now at PHELIX facility. The alternative we analyse here is to use two off-the-shelf spherical mirrors, introducing in this way the additional degrees of freedom needed. The analytical approach becomes in this case difficult and an ray tracing program (Optica package for Mathematica) was used to analyse the optimal setup, taking into account the geometrical constraints. The pump laser beam has a beam diameter of 200 up to 250 mm and a target chamber with a diameter of 1600 mm. The optimal angle searched is 45°, as predicted in [6] for Sm. To check all possible geometrical setups, a simulation with Mathematica was programmed to scan the complete parameter space and to find the according parameters as a function of the angles of the mirrors, their focal lengths, diameters and distance (see fig. 2).

Fig. 2. Set-up with two spherical mirrors

The results obtained for a variation of the angle of the second spherical mirror are presented in fig. 3 for values between 0° and 60°. One can

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identify two regions of interest, separated by an interval where the parameters are producing clipping of the focused beam on the first mirror. The TW obtained in this way is below 2 c, and the incidence angle on the target can be varied between 20° and 60°. The parameter which has to be mastered in this case is the line-focus length which varies from 5 mm to 55 mm.

Fig. 3. Variation of the second angle, with first angle (between first mirror and first reflection) of 190 degree.

After optimization of the incidence angles on the mirrors, of the distance between the mirrors and of the focal lengths an optimal focusing system was obtained with the following parameters: focal length1=2054 mm, first angle=193°, distance=540 mm, focal length2=1524 mm, second angle 2=36.5°. In this case the TW =1.47 c, length of line focus=10.44 mm, incidence angle on target=42. 9° and the line focus width= 40 microns. In conclusion there were presented here focusing systems needed for obtaining TW at a given angle using one and two spherical mirrors. Optimal parameters for a sub-10 nm XRL are in reach with the two spherical mirrors system. The method to generate a line-focus with a given TW and incidence angle proposed in this paper is general and can be used to obtain other combinations of parameters as requested by the experiments.

Focusing System for a Non-Normal Incidence Pumped, Sub-10 nm TCE XRL 73

References 1. Neumayer, P.; Alvarez, J.; Mos, B.B.; Borneis, S.; Brück, K.; Gaul, E.W.; Häfner, C.; Janulewicz, K.A.; Kuehl, T.; Marx, D.; Reinhard, I.; Tomaselli, M.; Nickles, P.V.; Sandner, W.; Seelig, W.: 'X-ray laser spectroscopy on lithium-like ions', Soft X-Ray Lasers and Applications IV, SPIE, 4505, 236242, 2001 2. Neumayer, P.; Seelig, W.; Cassou, K.; Klisnick, A.; Ros, D.; Ursescu, D.; Kuehl, T.; Borneis, S.; Gaul, E.; Geithner, W.; Haefner, C. & Wiewior, P. 'Transient collisionally excited X-ray laser in nickel-like zirconium pumped with the PHELIX laser facility', Appl. Phys. B, 78, 957-959, 2004 3. Keenan, R.; Dunn, J.; Patel, P.K.; Price, D.F.; Smith, R.F. & Shlyaptsev, V.N.: 'High-Repetition-Rate Grazing-Incidence Pumped X-Ray Laser Operating at 18.9 nm', Phys. Rev. Lett., 94, 103901, 2005 4. Kühl, Th.; Ursescu, D.; Bagnoud, V.; Javorkova, D.; Rosmej, O.; Zimmer, D.; Ros, D.; Cassou, K.; Kazamias, S.; Klisnick, A.; Zielbauer, B.; Janulewicz, K.; Nickles, P.; Pert, G.; Neumayer, P.; Dunn, J. : 'A Non-Normal Incidence Pumped Ni-like Zr XRL for Spectroscopy of Li-like Heavy Ions at GSI/FAIR', these proceedings 5. Kazamias, S.; Cassou, K.; Ros, D.; Plé, F.; Jamelot, G.; Klisnick, A.; Lundh, O.; Lindau, F.; Persson, A.; Wahlström, C. G.; de Rossi, S.; Joyeux, D.; Zielbauer, B.; Ursescu, D.; Kühl, Th.: 'A 10 Hz, 3 µJ transient X-ray laser pumped in grazing incidence geometry', these proceedings 6. Pert, G. J.: 'Optimizing the performance of nickel-like collisionally pumped xray lasers', Phys. Rev. A, 73, 033809, 2006 7. Ursescu , D.; Zimmer, D.; Kühl, Th.; Zielbauer, B.; Pert, G. J.: 'Gain generation in the critical density region of a TCE XRL', these proceedings 8. Neumayer, P.; Bock, R.; Borneis, S.; Brambrink, E.; Brand, H.; Caird, J.; Campbell, E.; Gaul, E.; Götte, S.; Häfner, C.; Hahn, T.; Heuck, H.; Hoffmann, D.; Javorkova, D.; Kluge, H.; Kühl, T.; Kunzer, S.; Merz, T.; Onkels, E.; Perry, M.; Reemts, D.; Roth, M.; Samek, S.; Schaumann, G.; Schrader, F.; Seelig, W.; Tauschwitz, A.; Thiel, R.; Ursescu, D.; Wiewior, P.; Wittrock, U. & Zielbauer, B.: 'Status of PHELIX laser and first experiments', Laser and Particle Beams, 23, 385-389, 2005 9. King, R.E.; Pert, G. J.; McCabe, S. P.; Simms, P.A.; MacPhee, A.G.; Lewis, C.L.S.; Keenan, R.; O'Rourke, R.M.N.; Tallents, G.J.; Pestehe, S.J.; Strati, F.; Neely, D. & Allott, R.: 'Saturated x-ray lasers at 196 and 73 Ǻ pumped by a picosecond travelling-wave excitation', Phys. Rev. A, 64, 053810, 2001

X-Ray Imaging of the Heating Zone of Non-Normal Incidence Pumped XRL Plasma B. Zielbauer1,2,3, D. Ursescu2,3, T. Kühl2,3, S. Kazamias4, K. Cassou4, D.Ros4, A. Klisnick4, F. Plé4, S. de Rossi5, D. Joyeux5, O. Lundh6, F. Lindau6, A. Persson6 and C.-G. Wahlström6 1Max Born Insitut, Berlin, Germany; 2Gesellschaft für Schwerionenforschung (GSI), Darmstadt, Germany; 3Universität Mainz, Mainz, Germany; 4Université Paris XI, Paris, France; 5Laboratiore Charles Fabry (IOTA), France; 6Lund Institute of Technology, Lund, Sweden

Summary. Soft x-ray emission, above 600 eV, from a grazing incidence pumped Ni-like Mo x-ray laser (GRIP-XRL) [1] plasma was investigated. Using a pinhole camera looking along the target surface, perpendicular to the direction of the XRL emission, spatially-resolved information was obtained with a resolution which was limited only by the pinhole size of 10 µm. The relative distance from the target surface to the plasma zone heated by the picosecond pulse was investigated for different GRIP angles, energy ratios and delays between the plasma producing and the plasma heating pulses.

1 Motivation The optimization of the absorption of the compressed pump pulse within the plasma created by the long pulse is an important way to improve the performance of a plasma-based x-ray laser. One significant recent development following this idea is the so-called GRIP scheme [2]. It yields control of the depth in which the main pulse is absorbed within the plasma by varying its incidence angle in a strongly non-normal (“grazing”) regime. To learn more about the influence of various setup parameters on the position of the absorption region, a pinhole-type camera system with suitable parameters was developed and used as part of an extensive x-ray laser campaign. Under the assumption that the position of the strongest absorption is linked to the area of the strongest soft x-ray emission within the plasma, the changes of this position can be studied.

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2 Setup The pinhole camera was positioned directly above the target, to achieve the highest sensitivity for the distance between the target and the plasma, see figure 1. The keV emission from the plasma was coming upwards along the target surface through a 1.4 mm opening in the target holder. Since the entire target and its holder could be moved up and down by 40 mm to change the target surface, also the pinhole height had to be changeable under vacuum in order to make use of the highest possible magnification. To facilitate the alignment under vacuum, the pinhole was located on a changer which in turn could be moved in the horizontal plane to compensate for movements resulting from changes of the pinhole height. For the position measurements, a pinhole diameter of 10 µm was used together with a filter consisting of 1 µm polypropylene and 200 nm aluminum positioned about one millimeter above the pinhole, blocking radiation below about 600 eV. The magnification of the imaging system was determined by the distances plasma/pinhole and pinhole/CCD chip and was about 19 for the 17 degree measurements and about 17 for the higher angles. From these parameters, a position sensitivity of less than two microns can be expected. The x-ray laser setup was based on a 4 mm wide Mo slab target which was hit perpendicularly by two uncompressed pulses (300 ps each, 480 mJ in total) after which the plasma was pumped by the main pulse (5 ps, 500 mJ) under various incidence angles. For a detailed description, see ref. [1].

Fig. 1. Schematic side view of the pinhole camera setup.

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3 Experimental results Each x-ray laser shot produced a CCD image similar to the one given in figure 2. After several steps of smoothing and averaging, vertical cross section lines were extracted, showing the averaged intensity distribution along an axis perpendicular to the target surface. An example of these plots is given in figure 3 for a GRIP angle of 17°, showing the averaged intensity over the distance to the target surface for all measured delays. The distances are to be taken only relative within each separate GRIP angle series since the setup used here did not allow for an absolute reference of the distance to the target and thus the position reference was lost due to magnification changes between different GRIP angle series. +150 µm

Prepulse Main pulse

pos. of long pulse only line (0 µm)

Plasma XRL

Target

-250 µm -750 µm

+750 µm

approx. center of plasma line (0 µm)

Fig. 2. Typical CCD image showing a field of view of about 1.5 mm around the center of the plasma line. 60

delay [ps]

200 300 400 500 600 700 800

50

40

intensity [a.u.]

30

20

10

0

-10 60

40

20

0

-20

-40

-60

distance from target surface relative to long pulse only line [µm]

Fig. 3. Vertical cross section plot for the 17° GRIP angle delay scan series.

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One interesting feature can be seen by plotting the positions of the intensity peaks of the cross section lines over the respective delay times: linear fits (see figure 4) for each GRIP angle show clearly a decreasing slope with increasing GRIP angle. Based on the assumption that with increasing delay between the plasma-forming long pulse and the main pulse, the plasma is hit by the main pulse at a later stage in its development, one can interpret the slopes as expansion velocities. These velocities are plotted in figure 5, showing a clear decrease with increasing GRIP angle. This can be seen as an indirect demonstration that increasing the GRIP angle leads to absorption at higher electron density, closer to the target surface. 20 17° 19°

15

20° 21° distance 10 from target surface, referred to 5 long-pulseonly shots [µm] 0

-5

-10

200

300

400 500 600 delay long pulse/short pulse [ps]

700

800

Fig. 4. Emission peak positions for the measured delays of each GRIP scan. The linear fit lines are only given for 17° and 21°.

4 Comparison to simulation The measurement described above can be interpreted as a pump/probe experiment from which the dynamics of the hottest plasma region can be deduced as a function of the main pulse incidence angle. To analyze the effects, XRL plasma hydrodynamics modelling was performed using the EHYBRID code with inclusion of the short pulse incidence angle as in [3]. The simulation provides the temperature, average charge state, plasma expansion velocity and density distributions as functions of the distance to the target for different time instances. Since the turning point electron density can be estimated as being proportional to ncsin2α, a velocity can be deduced by evaluation the movement of points of equal density with increasing time. As expected, the turning point density expansion velocity

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is relatively high as presented in figure 5 using squares. The expansion velocity increases with decreasing electron density. The velocities predicted by EHYBRID are higher than the velocities of the x-ray emission peak measured in the experiment presented in figure 5 using circles. One possible interpretation for this could be that the timeintegrated x-ray emission peak is not placed at the turning point density region, but rather in the denser part of the plasma. speed from linear fits simulation (density)

50

4

simulation (nT )

40 speed 30 [km/s] 20 10 0

17°

18°

19° GRIP angle

20°

21°

Fig. 5. Comparison of the velocities derived from the keV emission peak measurements and the two modeling approaches

To support this assumption, the time-integrated plasma emission was simulated using the output of the EHYBRID code. The plasma emission was evaluated as being proportional with the electron density and with the electron temperature at power 4, as for the case of black body radiation. The simulated speed of the x-ray emission peak in this case (see figure 5, triangles) is much closer to the experimental result and qualitatively reproduces the measurements for the higher GRIP angles within a factor of 2. The result indicates, however, that the plasma is heated at densities higher than the turning point density which corresponds to a given incidence angle.

5 Conclusion The x-ray plasma emission of a GRIP Mo XRL was investigated using a versatile pinhole camera with variable magnification and adequate resolution. The x-ray plasma emission was studied in the plane along the plasma line focus and perpendicular to the target. Different main pulse angles were used and the delay of the pre-pulse to main pulse was varied

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over several hundreds of picoseconds. In this way, the influence of the incidence angle on the heating of the plasma was studied. In addition, plasma modelling performed with the EHYBRID code was used to analyse the experimental results using a black body approximation of the plasma emission. The comparison shows good qualitative agreement between simulation and experiment. Furthermore, the measured velocities inferred from the data indicate that the absorption density increases with the GRIP angle, as expected from theory.

References 1. K. Cassou et al.: "A 10 Hz, 3 µJ transient x-ray laser pumped in grazing incidence geometry", this conference 2. Keenan, R.; Dunn, J.; Patel, P. K.; Price, D. F.; Smith, R. F.; Shlyaptsev, V. N.: 'High-Repetition-Rate Grazing-Incidence Pumped X-Ray Laser Operating at 18.9 nm", Phys. Rev. Lett., 94, 103901, 2005 3. Pert, G. J.: ′Optimizing the performance of nickel-like collisionally pumped xray lasers′, Phys. Rev. A, 73, 033809, 2006.

Formation of an Elongated Plasma Column From a Gas Puff Target Irradiated With a Laser Beam Focused Using an Axicon H. Fiedorowicz, A. Bartnik, R. Jarocki, R. Rakowski and M. Szczurek Institute of Optoelectronics, Military University of Technology, Warsaw, Poland

Summary. Elongated plasma columns can be formed by irradiation a gas puff target with a laser beam focused in line using an axicon. The plasma columns created from high-density gas puff targets based on a double-stream approach have been studied. The results of investigations with the use of optical and X-ray imaging and X-ray spectroscopy are presented.

1 Introduction There is a considerable interest in formation of elongated plasma columns in gases that could be used for guiding high-intensity laser pulses. The propagation of high-power laser pulses in plasmas may have widespread importance in a number of areas including X-ray lasers, high-harmonic generation, laser fusion, and laser plasma acceleration of charged particles. Relativistic and charge-displacement self-channeling in an under-dense plasma require of using intense ultra-short laser pulses. Another approach that uses a breakdown laser spark in a gas target can be realized using low intensity nanosecond laser pulses. It was demonstrated that plasma columns can be formed by irradiation elongated gas puff targets with nanosecond laser pulses focused to a line with an axicon [1]. This paper reports investigations on formation of an plasma column in a new high-density gas puff target [2] by focusing of nanosecond laser pulses from a Nd:glass laser using an axicon. The plasma columns have been studied with optical and X-ray imaging and X-ray spectroscopy techniques.

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2 High-density gas puff target The target is based on a double-stream gas puff target approach [3]. It is formed by pulsed injection of working gas through a nozzle in a form of a slit, which is surrounded with two additional outer slit nozzles. The nozzles are supplied with gases from two separate electromagnetic valves mounted in the common body. Schematics of the nozzle setup and the valve system are presented in Fig. 1.

a)

b)

Fig. 1. Schematic of the double nozzle setup (a) and the valve system (b).

The stream of working gas injected through the central nozzle is confined by the outer stream of gas (helium), thus the central stream poses high density of gas at relatively large distance from the nozzle output. It allows efficient absorption of laser radiation in the plasma. Moreover, the central stream has a steep density gradient.

a)

b)

Fig. 2. Typical X-ray shadowgrams of the ordinary xenon gas puff target (a) and the double-stream xenon/helium gas puff target (b).

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3 Gas puff target characteristics The targets were characterized with the use of the X-ray backlighting technique. Laser plasma X-ray source based on a gas puff target was used for backlighting. Typical X-ray shadowgrams of the ordinary xenon gas puff target (without helium) and the double-stream xenon/helium gas puff target are presented in Fig. 2. The corresponding target characteristics (gas density spatial profiles) for the ordinary xenon target and the double-stream xenon/helium gas puff target have been evaluated. The profiles obtained from the presented shadowgrams are shown in Fig. 3.

a)

b)

Fig. 3. Gas density profiles for the ordinary xenon gas puff target (a) and the double-stream xenon/helium gas puff target (b).

Fig. 4. Schematic of the experimental setup to study plasma columns produced from elongated high-density gas puff targets.

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4 Experimental arrangements Schematic of the experimental setup to study plasma columns produced from elongated high-density gas puff targets is presented in Fig. 4. Laser pulses with energies up to 10 J in 1 ns FWHM from a Nd:glass laser were focused onto the target using an axicon. The axicon axis was parallel to the nozzle and placed at the distance of about 1 mm from the nozzle. The gas puff valve and the axicon mounted in the experimental chamber are shown in Fig. 5.

Fig. 5. The gas puff valve and the axicon mounted in the experimental chamber.

Fig. 6. Typical images of the plasma columns produced from 9-mm-long xenon gas puff targets.

5 Experimental results Typical images of the plasma columns produced from 9-mm-long xenon gas puff targets taken with a CCD photo-camera are presented in Fig. 6. X-

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ray images of the plasma columns obtained with the use of a pinhole camera coupled to the X-ray CCD camera and the X-ray intensity distributions along the images are shown in Fig. 7. Uniform plasma columns were formed from 9 mm-long and 4 mm-long xenon targets. In the case of other gases (krypton, argon, oxygen) the columns were formed for 4 mm targets.

Fig. 7. X-ray images of the plasma columns obtained with the use of a pinhole camera coupled to the X-ray CCD camera and the X-ray intensity distributions for the xenon and krypton targets.

X-ray spectra measurements performed with the use of a transmission grating spectrograph made possible to estimate the electron temperature of the plasma. Typical spectra for the xenon and oxygen targets are presented in Fig. 8. The temperature of about 100 eV was obtained in the case of the oxygen target.

Fig. 8. Typical X-ray spectra for the xenon and oxygen gas puff targets

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6 Conclusions Preliminary experiments on formation of elongated plasma columns from a high-density gas puff target irradiated with a nanosecond laser pulse focused to a line using an axicon were performed. Uniform plasma columns up a length of 9 mm could be produced.

References 1. Bartnik, A., Fiedorowicz, H., Kostecki, J., Szczurek, M., Morozov, A., Suckewer, S., Formation of elongated laser sparks in gas puff targets by nanosecond laser pulses, Proceedings of SPIE vol. 3156 Soft X-ray Lasers and Applications II (SPIE Press, Bellingham, 1997) 2. Fiedorowicz, H., Bartnik, A., Jarocki, R., Rakowski, R., Szczurek, M., Enhanced x-ray emission in the 1-keV range from a laser-irradiated gas puff target produced using the double-nozzle setup, Appl.Phys.B 70, 305-309, 2000 3. Fiedorowicz, H., Bartnik, A., Jarocki, R., Kostecki, J., Rakowski, R., Szczurek, M., Inst. Phys. Conf. Ser. No 186 Paper presented at 9th Int. Conf. X-ray Lasers, Beijing China, May 24-28, 2004©2005 IOP Publishing Ltd.

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Observation of Density Dip in a Pre-Formed Plasma: Toward Axial Pumping X-Ray Laser T. Kawachi, N. Hasegawa, M. Nishikino, Y. Ochi, M. Tanaka, T. Utsumi, and A. Sasaki X-ray Laser Group, Quantum Beam Science Directoratee, Japan Atomic Energy Agency (JAEA) Summary. We report the observation of electron density dip in a laser-produced molybdenum plasma pumped by double laser pulses which are linearly focused on the molybdenum slab target. Interferometer based on Wollaston prism was employed to diagnose the plasma, and we obtained interference pattern together with backlighting image of the plasma. The electron density dip was clearly formed at the time of 1~1.5 ns after the second pulse, and the electron density of the dip was estimated to be around 2x1018 cm-3 ~ 4x1018 cm-3. The existence of the density dip was also verified by the backlighting image, which showed that the probe beam was guided in the plasma column with the plasma length of up to 4.3 mm. The experimental result implies that the present plasma can be used as the pre-formed plasma for the axial pumping x-ray laser.

1 Introduction Ozaki et al. [1]. reported several years ago demonstration of directional xray laser beam at a wavelength of 18.9 nm of the nickel-like molybdenum ions, in which a molybdenum slab target was irradiated by line-focused pre-pulse of the laser in the normal direction, and the following main (heating) pulse with 150 fs-duration, an energy of 150 mJ was injected into the plasma column in the direction of longitudinal axis. Their explanation of the experimental result was that an electron density dip (or flat region) could be generated in the pre-formed plasma, and the main (heating) pulse in the longitudinal direction was guided in the pre-plasma to achieve substantial gain-length product. However, the existence of the density dip or flat region was not verified experimentally yet. Since the axial pumping scheme extends the possibility of x-ray lasers with very narrow beam divergence and improves the pumping efficiency of the GRIP (grazing incidence pumping) scheme [2], it is valuable to investigate the possibility of generating electron density dip in a pre-formed plasma. In this report, we employed the methods of interferometer and back lighting imaging

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technique to diagnose the pre-formed plasma, and found the electron density dip could be generated under double-pulse irradiation. Before the description of the details of the experiment, the related former works are described. The waveguiding of the pumping pulse has been studied before in the research fields of x-ray lasers and laser acceleration: In the laser-driven plasmas, Milchberg et al. found “light pipe” was generated in the gas target irradiated by double pulses irradiation. In this experiment, the first pulse makes density gradient in the radial direction, and the following second pulse was guided in the electron density structure [3,4]. In the discharge plasmas, Hosokai et al. demonstrated waveguiding of the terawatt laser pulse in the capillary discharge plasma column [5]. In the x-ray laser research, quite recently, Tommasini et al., measured density profile of the pre-formed plasma pumped by line-focused single pulse of TiSa laser. However, no density dip could be observed under the single pulse irradiation [6]. Therefore this work is located to the following attempt by use of double pulses irradiation.

2 Experiment and Discussion Experiment was conducted by use of JAEA CPA Nd:glass laser. The maximum total output energy of this laser is 20 J with 1 ps duration, however, since our objective was to diagnose the pre-formed plasma, we used only the pre-amplifier of this system to control the output energy to be 200 mJ ~ 500 mJ. The output consisted of two pulses. The duration of the first- and the second pulse was 10 ps, separated by 1.3 ns, and the energy ratio of the first pulse to the second pulse was 1:3.3. A portion of the uncompressed laser pulse was used as the probe beam: the duration was ~ 450 ps (bandwidth of 1.8 nm), and the energy was ~ 2 mJ. The probe beam was injected into the plasma in the longitudinal direction. The diameter of the probe beam was adjusted to be 5 mm at the position of the plasma. Then the probe beam went through the imaging lens, changed the polarization direction to 45 degree with respect to the horizontal axis by the first polarizer, was divided into two polarization components by Wollaston prism, WP, and changed the polarization direction again to the horizontal direction by the second polarizer. Finally the two components were merged by the steering mirrors at the focal position of the imaging lens, where the portion of the probe beam including the information of the plasma and that went through the vacuum region made interference pattern, and we could obtain the phase information of the probe beam at the edge of the pre-formed plasma. In this set up, the magnification factor

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was around 9, which was assured by use of 120 µm in diameter copper wire as the test sample. The spatial resolution was ~ 10 µm. We set the delay line in the optical path of the probe beam, and adjust the timing of the probe beam with respect to the pumping pulse. It should be noted that by cutting one of the probe beam of the interferometer, we could obtain the backlighting image of the plasma. In the following context, the time of the probe beam was measured from the peak of the second pumping pulse. Figure 1 shows the interferometer patterns together with the backlighting image of the pre-formed plasma at the timing of t = -300 ps; (a), t = +1000 ps; (b) and t = +1500 ps; (c), respectively. The total pumping laser energy was set to be 190-210 mJ, i.e., the pre-pulse energy and main-pulse energy was ~ 45-53 mJ and 145-157 mJ, respectively, which corresponds to the intensity on the target of 4x1012 W/cm2 and 1.2x1013 W/cm2, respectively.

(a)

(b)

(c)

Fig.1. Image of the plasma taken with an interferometer. Upper column is the interference pattern and the lower is the back lighting image.

In Fig.1 (a), the plasma image is the same with that pumped by single pulse (See ref. [6]). The interference pattern shows no unique feature in the density gradient, whereas at t=-1000 ps ~1500 ps, complicated patterns is shown in the interference patterns. The backlighting images at the same timing show the probe beam is guided in the plasma with the length of 1 mm. In order to assure the waveguiding, we change the thickness of the target from 1 mm to 4.3 mm, and the probe beam was clearly guided in the plasma as shown in Fig. 2. We tried to estimate the spatial profile of the electron density in Fig. 1. In the present experimental condition, the wavelength of the probe beam is 1 µm, and the thickness of the target or plasma is ~ 1 mm. This implies

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that one phase shift corresponds to the 2x1018 cm-3 of the electron density. We compare the interference pattern in Fig. 1 (c) with that without plasma, and the spatial profiles of the phase shift are derived. The data analysis showed that at t = +1500 ps, the density dip is generated: the electron density of the bottom of the dip is ~ 2x1018 cm-3, and that of the outer region was around 4x1018 cm-3. The interference patterns at t = +1000 ps is more complicated than that at t = + 1500 ps, which indicates that the density dip may be generated in higher density region by at least one-phase shift ( > 4x1018 cm-3), however, the density is higher than the range of the present interferometer. We estimate the possibility of axial pumping x-ray laser by using this pre-formed plasma. Consider the situation that the circularly polarized axial pumping (heating) laser pulse is injected into the pre-formed plasma. If the intensity is sufficiently high, the ions increase their ionization stage up to the nickel-like (z = 14). Our 1D hydrodynamics simulation (HYADES) shows the average of the charge state of the ions in the preformed plasma at the time of t = +1500 ps is z ~ 3, therefore the after the axial pumping pulse, the electron density of the pre-formed plasma is increased up to around ~ 1x1019 cm-3. This electron density is not so high compared with optimum electron density for the nickel-like molybdenum laser (> 5x1019 cm-3), however is enough to obtain substantial lasing in this scheme. In order to obtain the strong lasing in this scheme, the axial pumping pulse should be injected in earlier timing: Indeed hydrodynamics simulation shows that after the second (heating) pulse, plasma expands in the vacuum with keeping its spatial profile, therefore in earlier time region, electron density of the dip is expected much higher than at t =+1500 ps.

Fig. 2. The backlighting image of the plasma column. The probe beam was guided in the plasma with the length of up to 4.3 mm.

This tendency is consistent with present result, at t = 1000 ps, the electron density of the dip is higher than that at t = +1500 ps. In order to use earlier

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time region, it is required that the precise control of the intensity of the pumping pulses and their homogeneity on the target. In summary, we have demonstrated to generate electron density dip in the pre-formed plasma by use of double pulses irradiation. The plasma parameter at the time of t = 1.5 ns measured from the second pre-pulse timing, i.e. electron density and the ionization stage of the ions, indicate that the axial pumping x-ray laser in the nickel-like molybdenum ions is possible by use of this pre-formed plasma. This work is auspices by Japan Society for the Promotion of Science (JSPS).

References 1. T. Ozaki, R. A. Ganeev, A. Ishizawa, T. Kanai, and H. Kuroda, Phys. Rev. Lett. 89, 253902 (2002). 2. B. M. Luther et al., Opt. Lett. 30, 165 (2005). 3. C. G. Durfee III and H. M. Milchberg, Phys. Rev. Lett. 71, 2409-2412 (1993). 4. T.R. Clark and H. M. Milchberg, Phys. Rev. Lett. 78, 2373 (1997). 5. T. Hosokai, M. Kando, H. Dewa, H. Kotaki, S. K. N. Hasegawa, K. Nakajima and K. Horioka, Opt. Lett., 25, 10 (2000). 6. R. Tommasini, K. Eidmann, T. Kawachi and E. E. Fill, Phys. Rev. E 69, 066404 (2004).

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Experimental Studies on Transient Ni-Like Ag X-Ray Laser Pumped With the Picosecond Pulsed Laser Facility at NLHPLP J. R. Sun1) , Ch. Wang1) , Z. H. Fang1) , W. Wang1) , J. Xiong1) , J. Wu1) , S. Z. Fu1) , Y. Gu1) , S. J. Wang1) , G. P. Zhang2) , W. D. Zheng2) , G. L. Huang3) , F. Y. Guan3) , X. L. Xie3) 1)

Shanghai Institute of Laser Plasma, Shanghai, 201800, P. R. China Beijing Institute of Applied Physics and Computational Mathematics , Beijing, 100088, P. R. China 3) Shanghai Institute of Optics and Fine Mechanics, Shanghai, 201800, P. R. China 2)

Summary. The results of experimental studies on transient Ni-like Ag soft X-ray laser with the picosecond pulsed laser facility at the National Laboratory of High Power Laser and Physics (NLHPLP), China, has been reported in this paper. An somewhat intense Ni-like Ag X-ray laser beam at 13.9 nm with output energy 5~10 nJ was obtained from the solid flat targets under the joint irradiation of a long pulse laser beam of several hundred picosecond duration and another 1ps ultra-short pulsed laser.

1 Introduction Since X-ray laser has widespread application prospects in physics, biology, chemistry, materials science and initial confinement fusion (ICF), X-ray laser research has been intensively pursued by the community in recent years. Many laboratories have got the saturated output of X-ray laser from 3.5 nm to 50 nm [1-7] and try to demonstrate the soft X-ray laser amplification [8-15]. In order to find an approach to the table top X-ray laser devices of high efficiency and intense output in the short wavelength region, the most important issue in this X-ray laser development is to employ a proper compact pumping system. Recently, several experiments carried out in various laboratories have confirmed that saturated X-ray lasers pumped by transient collisional excitation (TCE) may be obtained with moderated pump laser energy requirements [16-22].

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In the generation of transient X-ray laser, the double-pulsed pumping scheme is often be used, where a long laser pre-pulse of nano- or subnanosecond duration forms the plasma on the target before the arriving of another short main pulse of pico- or sub-picosecond duration. To regulate properly the delay between two pumping pulses, the short main pulse can rapidly heat the pre-plasma and generate high gain output of the transient X-ray laser. In this paper we report the experimental demonstration of a Ni-like Ag X-ray laser at wavelength of 13.9 nm with a pumping energy ~15 J only. The experiments in this paper were characterized by employing a pre-prepulse before the pre-pulse to optimize the pre-plasma behavior, where the intensity ratio of the two pulses was 5~10 % and the time interval between them ranged 1 ~ 4 ns. A somewhat intense Ni-like Ag X-ray laser at 13.9 nm with output energy 5~10 nJ has been obtained under the irradiation on the solid flat targets with a long pulsed laser beam of 102 ps duration and an 1 ps ultra-short pulsed one jointly.

2 Experiments The experiments have been performed on the picosecond laser facility at the National Laboratory of High Power Laser and Physics (NLHPLP), Shanghai, China. This laser facility outputs two laser beams, in which the maximum energy of laser beam output from the compressor is ~15 J and with pulse duration ~1 ps, another long-pulse laser beam is of ~300 ps duration and ~25 J maximum output energy. The two beam lines provide respectively the pre-pulse and the main pulse with adjustable delay between them. The experimental setup is shown in Fig. 1. The long pre-pulse through the right window enters the chamber to irradiate the target. The horizontal line-focusing system for the pre-pulse consists of protruding cylindrical lens, glass windows and principle focus lens. On the other hand, the short main pulse passes the left window into the chamber to irradiate the target after a delay time. Its horizontal line-focusing system consists of plane reflector, concave cylindrical lens and the off-axial parabolic reflector. Two horizontal focus lines overlap after the off-axial non-spherical mirror and are with an incident angle of 25 degree towards the target. The both horizontal line-focusing systems are shown in Fig 1 (b) in detail. The linear spot size for the two focus lines is about 50 μm×10 mm. The laser intensity distribution along the line focus is asymmetry because of the single cylinder line focus system used. Therefore only the

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central part of line focus could be available. The slab targets were prepared with sliver coating of thickness 1 μm on polished glass substrates. The maximum length of sliver targets was 6 mm to assure the laser ablation plasma to cover the symmetrical central part of the line focus. The spectral composition of the X-ray output was observed with a flat field grating spectrometer consisting of a concave varied-spacing diffraction grating of 1200 grooves/mm and with an acceptance angle 12 mrad in the vertical direction. The detector was a back-illuminated X-ray charge-coupled device (CCD). The position of spectrometer and CCD detector in the horizontal direction could be changed to detect the X-ray output from different locations on the target. A Mo filament of 75 μm in diameter set at the spectrometer split was used to determine the refraction angle of X-ray laser beam.

Fig. 1. Experimental setup of (a) schematics (b) optical path

two

laser

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3 Results and Conclusion Fig. 2 shows the image recorded by the CCD detector in an experiment where the 6 mm-long silver target was irradiated by two laser pulses separated by 120 ps. The pre-pulse duration was 414 ps, energy ~1.3 J, the energy ratio of pre-pre-pulse to that of pre-pulse ~ 7.3 % and the interval of them 2.95 ns. The main pulse duration was equal to 1 ps and energy ~ 4.1 J. The irradiances of pre-pulse and main pulse on the target were 5.0×1011 Wcm-2 and 7.0×1014 Wcm-2, respectively.

Fig. 2 CCD detector recorded radiation image from the silver coating target

The X-ray output spectrum was measured and treated, and is shown in Fig. 3, whereas its spatial angle distribution in the horizontal direction is shown Fig. 4. Considering the reflective angle was ~10 mrad and the divergence angle ~4 mrad, this spectrum has a certain dependence upon the angle off the target normal, hence a high intensity and a well directed behaviour. In order to measure the spectral wavelength, an Al pass filter with central wavelength of 17.04 nm was placed in the beam path. The spectral line wavelength of 13.9±0.1 nm was measured by the spectrometer. It can be concluded that this spectrum demonstrates the X4

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ray output to be Ni-like Ag X-ray laser. The estimated X-ray output energy was 5~10 nJ. In conclusion, the Ni-like Ag x-ray laser output at 13.9 nm with energy 5~10 nJ has been successfully obtained in the experiments employing

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silver coating targets irradiated with three laser beams consisting of a long pre-pulse (102 ps in duration) added a pre-pre-pulse and an 1 ps ultra-short main pulse. The total pump energy used in the experiment was about 5 J. The better X-ray laser output could be achieved if the experimental setup with a line-focusing system capable of quasi-travelling wave irradiation on the target is developed. This approach has been considered as an important step in the development of X-ray laser and its applications in China.

Acknowledgements The authors are greatly obliged to stuff of the SG-Ⅱgroup at NLHPLP for their excellent efforts and contributions in the experiments.

References 1. Matthews D L, Hagelstein P L, Rosen M D et al , Phys. Rev. Lett. 54, 110, 1985 2. Wang S J, Gu Y, Zhou G L et al, Chin. Phys. Lett. 8, 618, 1991 3. Carillon A, Chen H Z, Dhez P et al, Phys. Rev. Lett. 68, 2917, 1992 4. Koch J A, MacGowan B J, Da Silva L B et al, Phys. Rev. Lett. 68, 3291, 1992 5. Rocca J J, Clark D P, Chilla L A et al, Phys. Rev. Lett. 77, 1476, 1996 6. Zhang J, MacPhee A G, lin J et al, Science 276, 1097, 1997 7. Wang C, Wang W, Wu J et al, Acta Phys. Sin. 53, 3752, 2004 8. Trebes J E, Brown S B, Campbell E M et al, Science 238, 517, 1987 9. DaSilva L B, Trebes J E, Balhorn R et al, Science 258, 269, 1992 10. Ress D, DaSilva L B, London R A et al, Science 265, 514, 1994 11. DaSilva L B, Barbee T W, Cauble R et al, Phys. Rev. Lett. 74, 3991, 1995 12. Rocca J J, Moreno C H, Marconi M C et al, Opt. Lett. 24, 420, 1999 13. Wang C, Gu Y, Fu S Z et al, Acta Phys. Sin. 51, 847, 2002 14. Filevich J, Rocca J J, Jankowska E et al, Phys. Rev. E 67, 056409, 2003 15. Wang C, Wang W, Sun J R et al, Acta Phys. Sin. 54, 202, 2005 16. Nickles P, Shlyaptsev V N, Kalachnikov M et al, Phys. Rev. Lett. 78, 2748, 1997 17. Dunn J, Osterheld A L, Shepherd R et al, Phys. Rev. Lett. 80, 2825, 1998 18. Kalachnikov M.P., Nickles, P.V., Schnürer, M., et al, Phys.Rev. A 57, 4778, 1998 19. Dunn J, Li Y, Osterheld A L et al, Phys. Rev. Lett. 84, 4834, 2000 20. Kuba J, Klisnick A, Ros D et al, Phys. Rev. A 62, 043808, 2000 21. King R E, Pert G J, McCabe S P et al, Phys. Rev. A 64, 053810, 2001 22. Klisnick A, Kuba J, Ros D et al, Phys. Rev. A 65, 033810, 2002

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X-Ray Laser Source Using Ceramic Target Y.Takemura1, N.Yamaguchi2 and T.Hara1 1

X-ray Laser & Plasma Engineering Laboratory, Toyota Technological Institute, 2-12-1 Hisakata, Tempaku, Nagoya 468-8511, Japan 2 Physics lab., Liberal Arts and Science, Graduate School of Medicine and Pharmaceutical Sciences, University of Toyama, 2630 Sugitani, Toyama 930-0194, Japan

Summary. Ceramic plates (AlN and alumina) have been used as targets for laserplasma x-ray sources for the first time. Radiation intensity of soft x-ray spectra from Li-like ions (Al XI) for the AlN target was almost the same as in the case of pure aluminium target. It was found that the ceramic target can be irradiated at the same place up to 70 times or more, radiating x-rays with nearly the same intensity as in the case when a virgin surface was irradiated. Craters formed on the target surface after irradiations were measured 3-dimensionally and their hollow volumes below the initial surface were analyzed. The ablated mass for AlN or alumina target was less than 1/6 compared with that for pure Al target. We succeeded in development of the laser-plasma x-ray source for a long operating period, maintaining stable x-ray output.

1 Introduction We are investigating table-top x-ray lasers based on the recombination plasma scheme. In this scheme, the well-known lasing line is Al XI 3d-4f transition line at 15.47 nm [1]. For researches on x-ray lasers and also on laser-plasma x-ray sources, pure aluminum slab or tape target is often used. After laser irradiation, some craters are created on the target surface or a part of aluminum tape is ablated, giving much particle debris. It causes one of the technical issues for development of practical laser-plasma x-ray sources. On the other hand, ceramic materials containing Al like AlN would produce little debris because of its high sublimating decomposition temperature (2450 °C), whereas the melting point of Al metal is 660 °C. Though ceramic materials could be useful as target materials, there are no attempts to apply ceramics for laser-plasma x-ray sources. We have carried out experiments using a ceramic target, which is AlN or Al2O3. Soft x-ray spectra were measured and surface profiles after laser

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irradiation were observed. Characteristics of soft x-ray radiation and debris production will be described in this report.

2 Experimental Setup 2.1 Irradiation System and Target A 100 ps laser pulse from a mode-locked YAG oscillator, 1064 nm, was transformed into a linearly polarized 16-pulse-train through an optical stacker and a delay line component. The interval of each pulse was 200 ps. A YAG laser system with four-stage amplifiers delivered output energy of about 0.7 J. A Nd:Glass amplifier having a 25-mm-diameter rod was added to the YAG laser system, and the output laser energy was increased up to 2.1 J. In our experiments, line-shaped plasmas are produced on a target by using a line-focusing optics. Intense x-ray could be generated from the line-plasma, because the x-ray intensity is proportional to its plasma length for the optically thin radiation. Another merit of this type of source is that a very few debris could come along the surface of the target which is the direction of x-ray beam [2]. The line-focusing lens system consists of a five segmented prism array, a beam expander and a cylindrical lens assembly [3]. The prism splits the incident laser beam into five beamlets. Each beamlet is then separately focused on a line and all these individual line foci overlap at the same place, which forms a common-line focus. The intensity variations in the incident beam are averaged, causing an overall homogeneous illumination along the focal line. Besides the irradiation pattern has a small scale modulation due to interference between divided laser beams that results to form an array of micro-dot on a target [4]. The irradiation pattern has an irradiation area of 50 µm × 11 mm with microdots of 50 µm in diameter and 140 µm-pitch spacing. Because of the interference pattern in the focused beam, the power density was 1011− 1012 W/cm2. Targets used were aluminium (1 mm thick), sintered AlN (2 mm thick) and alumina (2 mm thick) plates. 2.2 Diagnostics X-ray emission from the plasma was analyzed using a space resolving flatfield grazing incidence soft x-ray spectrograph with a toroidal mirror as a

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pre-focusing optics. The detector was an x-ray CCD camera (SX-TE/CCD 512TKB, Princeton Instrum.) using a back-illuminated CCD of 512 × 512 pixels with 24 × 24 µm pixel size. This spectrograph was designed to image x-rays from a source with a 1× magnification in a horizontal direction at the entrance slit and with a 3× magnification in a sagittal direction at the flat-field output plane. Surface profiles after laser irradiation were measured by using a 3D digital optical microscope (VHX-200/100F, KEYENCE) and a laser confocal microscope (VK-9500, KEYENCE). (a)

(b)

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Fig. 1. Typical soft x-ray spectra from (a) Al, (b) AlN and (c) alumina plasmas. Emission lines of the Li-like Al ions, labeled as Al XI, are intense in the AlN plasma.

3. Soft X-ray spectra from Laser-produced Plasmas Soft x-ray spectra were observed for each target material in the wavelength region from 12 nm to 17 nm. Typical spectra are shown in Fig. 1. In each

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spectrum, line spectra have been originated from ions of composed materials of each target. Emission lines from highly ionized Al, especially Li-like Al, were still observed with about the same intensity in the AlN plasma as those in the pure-Al plasma. On the other hand, Al spectra were weak in the alumina plasma. We performed multiple shots irradiation experiments where the laser beam was focused on the same position of the target many times. When an Al slab target was used, craters were formed on the target surface aligning in the focused line. The depth of the craters was around 8 µm in a single shot, and then the crater became deeper as increase of times of irradiation. Therefore, Al targets cannot be used to produce x-ray radiation for multiple shots on the same place efficiently, because the effective power density decreases. On the other hand, ceramics suffered weak damage after a number of laser irradiations. This leads to capability of multiple use of the same target area. Figure 2 shows the trend of radiated intensity of the 15.47 nm line as a function of number of irradiations for AlN target and Al target. 8

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Fig. 2. The trend of the 15.47 nm line intensity as a function of the number of irradiations for the case of AlN target.

4 Surface Modifications by Laser Irradiation Surface profiles of the target were measured three dimensionally. Small craters were formed by multiple irradiations even on the ceramic targets. The depth of the crater was 8 µm/shot, 1.4 µm/shot or 0.9 µm/shot, for the

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pure Al, AlN or alumina target, respectively. It was clear that the rate of crater formation on the ceramic target is much lower than that on the Al slab target. 250

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Fig. 3. The amount of target mass evaluated from the crater volumes as a function of the number of irradiations. Those give the maximum value of the ablated mass from the target.

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The above results lead that the amount of debris would be small in the case of ceramic target. The volume of craters was calculated from the 3D data of surface profile with respect to the initial flat surface. This gives us

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the maximum mass of the target material ablated. The amount of target mass evaluated from the hollow volume of the craters is plotted as a function of the number of irradiations in Fig. 3. Though the ablated mass for the ceramic targets is estimated to be in the order of several µg/shot, which is seemed to be rather large, it can be considered that the amount of debris from the ceramic target is 1/6~1/7 as that from Al slab target.

5 Laser-Plasma X-ray Source using Ceramic target In order to use laser-plasma x-ray source for a long operating period, we have constructed a target stage which holds a ceramic target. The ceramic plate can be moved back and forth along one axis on the stage, where the pitch of translation and the timing can be programmed by stepping motor controller. The target stage worked stably for 2 hours under 10 Hz-laserirradiation on the target surface. We have performed a test experiment on the stability of x-ray generation. X-ray pulses measured by a fast response x-ray detector (AXUV HS1) are shown in Fig. 4, where the signals show time behaviour of x-ray intensity generated at the different shot during continuous operation. The present results indicate that the stability of x-ray generation is fairly good.

6 Conclusions Ceramic targets containing Al, such as AlN and alumina, have been investigated as a target for soft x-ray source. In the case of AlN, emission lines from highly ionized Al, especially Li-like Al, were still observed with about the same intensity those in the pure-Al plasma. Moreover, it was found that 15.47 nm x-ray intensity for each laser shot was almost constant for 70 shots and more in the multiple shots irradiation experiments. It would be possible to construct a long-lived and compact laser-plasma xray source with less debris using a peace of AlN plate.

References 1. N. Yamaguchi, T. Hara T. Ohchi, C. Fujikawa and T. Sata: Jpn. J. Appl.Phys. 36, 51, 1999.

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2. P. Abraha, Y. Hisada, K. Takamoto, N. Yamaguchi, and T. Hara: Jpn.J. Appl. Phys,. 42, 1491, 2003. 3. N. Yamaguchi, T. Ohchi, C. Fujikawa, A. Ogata, Y. Hisada, K. Okasaka, T. Hara, T. Tsunashima and Y. Iizuka: Rev. Sci. Instrum. 70, 1285, 1999. 4. N. Yamaguchi, C. Fujikawa, T. Ohchi and T. Hara: Jpn. J. Appl. Phys,.39 5268, 2000

The Generation of X-Ray Laser Radiation on SOKOLP Laser Facility A.V. Andriyash, O.V. Chefonov, D.A. Dmitrov, D.S. Gavrilov, A.G. Kakshin, E.A. Loboda, V.A. Lykov, E.P. Magda, V. Yu. Politov, A.V. Potapov, V.A. Pronin, G.N. Rykovanov, V.N. Sukhanov, A.S. Tischenko, A.A. Ugodenko, D.A. Vikhlyaev and A.L. Zapysov Russian Federal Nuclear Center – named after academician E.N.Zababakhin All-Russia Research Institute of Technical Physics (RFNC-VNIITF, Snezhinsk, Russia)

Summary. The transient collisional excitation (TCE) scheme was used to obtain generation of X-ray laser radiation on the 3p-3s transitions of the Ne-like Ti-ions at 10 TW SOKOL-P laser developed at RFNC-VNIITF. The Nd-laser light was focused in a line with length from 2 up to 8 mm and width of 30 microns. Two successive pulses irradiated the polished Ti-slab. The duration of prepulse was equal to 400 ps and a pumping pulse had duration of 4 ps; the delay between pulses equals to 1.5 ns. The Nd-laser energy was about of 10 J and the ratio of energy in prepulse and basic pulses was equal to 1:2. The grating spectrometer equipped with a focusing mirror and CCD detector was used for measurement of the X-ray laser line at 32.6 nm. A small signal gain about of 30 cm-1 was obtained in experiments with target length from 2 up to 4 mm. The 32.6 nm line radiation with energy about of 1 μJ and divergence of 9 mrad were registered in SOKOL-P experiments with target length of 8 mm.

Introduction The transient collisional excitation (TCE) scheme of X-ray laser (XRL) makes it possible to attain extra-high peak gain factors gmax≥100 cm-1 [1]. This is promising for the development of tabletop XRL as well as progress in shorter wavelengths. X-ray lasing on 3p-3s transition of Ne-like titanium ions with TCE was first demonstrated at Max Born Institute [2]. In those experiments the flat titanium targets were irradiated by a combination of a 1.5 ns prepulse (energy up to 7 J) and a main pulse of 0.7 ps (energy up to 4 J). The experimental value of XRL gain was measured to be g=19±1.4 cm-1. Similar experimental results, but with the higher gain factor (g=24 cm-1) were obtained at LLNL on the “Janus” facility [3].

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A numerical simulation of hydrodynamics and level-by-level ion kinetics for the XRL active media under powerful picoseconds heating has been carried out [4]. This simulation shows that the active media length dependence of output XRL energy is determined, first of all, not by the peak value of the gain, but by the refraction of XRL beam in the strong density-gradient amplifying region, and by the effect of radiation lag. This dependence results in obtaining of certain effective gain factor that does not reflect the g values really attainable in the XRL plasma. The gain value g ~ 50 cm-1 was estimated in [4] for the XRL on 3p-3s transitions of Nelike Ti ion.

1 Experimental Setup The experiments were conducted on the laser facility SOKOL-P [5]. The facility is a picosecond chirped pulse amplification laser whose maximum power is about 10 TW. In these TCE experiments, a portion of energy of the chirp-modulated amplified pulse tch=400 ÷ 440 ps long was used as a prepulse creating the laser active medium. The duration of the basic pumping pulse tp is varied with a base compressor adjustment. The compressor was set for pulse duration tp=4 ps. The picosecond pulse lag relative to prepulse was maintained constant and equal to 1.5 ns. The ratio of prepulse and main pulse energies was 1:2. This ratio was also maintained constant; the prepulse energy was 2.5±0.3 J, the main pumping pulse energy was 6.3±1.0 J. The accuracy of position coincidence of prepulse and main pulse beams focused into a thin line on the target is no worse than ±3 μm. The focusing optics consists of a toroidal mirror mounted in a vacuum target chamber and a meniscus lens located in the air in front of the LiF input window. This system ensures the laser beam focusing into a thin line with a maximum length of 10 mm. To eliminate the non-uniform irradiation of the target, the parallel beam was blinded and the target length was no longer than 8 mm. In this case the droop of intensity on the target edges was below than 15% of its value in the center of the focal line. X-ray images from the pinhole-camera enabled the control of the focal line width and irradiation uniformity as well. The target position in the pumping laser beam was not changed in experiments and the focal line was equal to 35-40 μm in width. The laser light intensity on the target surface was 2⋅1012 W/cm2 in prepulse and 6⋅1014 W/cm2 in the main ps pulse. The grazing incidence spectrograph with flat diffraction grating

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(600 mm-1) was used to register spectra in the wavelength region 120÷400 Å (see Fig.1).

Fig. 1. Layout of grazing incidence spectrograph: 1 – target, 2 – focusing mirror, 3 –spectral slot, 4 – diffraction grating, 5 – CCD-matrix

A focusing spherical mirror was mounted between the target and the grating. The mirror collected the target radiation in a plane perpendicular to the target surface in an angle of 0.035 radians. The target center was in the meridional focal plane of the mirror, which formed almost parallel beam of x-rays. The width of this beam for x-ray laser radiation is determined by XRL divergence and by the collection angle of the mirror for all other registered spectral lines. Thus, this diagnostic allows analysis of XRL beam divergence in the plane perpendicular to the target surface. The spectrum is recorded with PI-SX: 400 x-ray CCD-camera. The spectral resolution λ/Δλ for the XRL wavelength λg=326 Å was about 140. Special attention was given to the thorough adjustment of the spectrograph relative to the axis of the x-ray laser beam. The error of the spectrograph slot alignment about the beam axis was approximately ±3 mrads.

2 Experimental Results Figure 2 shows a spectrogram obtained in the experiment with the 6-mm target. The bright spectral line with wavelength λ=326 Å dominates in the spectrogram. The target length was varied from 2 to 8 mm. Figure 3 shows the dependence of x-ray laser intensity on the target length. As far as

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pumping energy during the experiments was not strictly constant (experimental scattering ±16%), the experimental points on the plot are

Fig. 2. Spectrogram of the shot with 6 mm target length

Fig. 3. Dependence of XRL intensity on target length

arrow-accompanied to point trends in the variation of the recorded spectra in the case where the pumping energy would be of a nominal value of 6.3 J. For 2 mm targets, the XRL output was founded out to be below the diagnostic threshold sensitivity. The downward direction of the arrow means that the given experimental point is actually the upper limit of XRL output.

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Fitting our data for target lengths of 2-4 mm with the Linford formula and taking into account the above mentioned corrections due to pumping energy instability, gives a gain value of 30±5 cm-1, that is somewhat lower than the simulation gain value of ~ 50 cm-1 [4]. The calculated results seem to be overestimated because of the imperfect model that was used for the XRL radiation transport under strong influence of refraction. The maximum energy of the X-ray laser beam was registered about of 1 μJ and its divergence was 9±3 mrads in experiments with target length of 8 mm.

Conclusion The X-ray laser generation on the 3p-3s transitions of the Ne-like Ti-ions has been studied in experiments performed on 10 TW SOKOL-P laser facility developed at RFNC-VNIITF. The TCE scheme was implemented through the sequential irradiation of polished Ti-slab with 0.4 ns and 4 ps laser pulses focused into a line. Pumping laser energy density per unit line length was about of 0.7 J/mm. The experimental small signal gain of the 32.6 nm line radiation was 30±5 cm-1. The maximum energy of the XRLradiation about of 1 μJ and its divergence of 9±3 mrads were registered in experiments with the Ti- target length of 8 mm.

References 1. Afanasiev, Yu. V., Shlyaptsev, V.N.: Quantum Electronics, 16, 2499, 1989. 2. Nickles, P. V., Shlyaptsev, V. N. et al.: Phys. Rev. Lett., 78, 2748, 1997. 3. Dunn, J., Osterheld A. L., Sheperd R. et al.: In: Proc. SPIE Meeting (San Diego, California), 1997; Dunn J. et al.: Phys. Rev. Lett., 80, 2825, 1998. 4. Politov V. Yu., Lykov V. A., Shinkarev M. K.: Quantum Electronics, 30, 1037, 2000. 5. Dmitrov D. A., Fomichev L. A., Kakshin A. G. et al.: Proc. 28th European Conference on Laser Interaction with Matter, 591-599, 2004.

Electron Temperature Measurements of Model NeLike X-Ray Laser Plasmas From Resonance keV Spectra J. Nejdl*, B. Rus, J. Kuba*, T. Mocek, M. Kozlová, J. Polan and P. Homer *Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Czech Republic Department of X-ray Lasers, Institute of Physics/ PALS Centre, Prague 8, Czech Republic

Summary. We present results of temperature measurements of Ne-like Zn plasmas created by an intense laser pulse, using slab targets. Pulses with typical energy of 50 J in 300 ps were focused to a line or point foci, in which the pumping pulse energy was varied from shot to shot. The electron temperature in dependence on the pulse energy and irradiation intensity is studied. The temperature is inferred spectroscopically from a set of selected Ne-like spectral lines. The experimental results are compared with the numerical simulations made by the hydrodynamic code EHYBRID.

1 Introduction Electron temperature is one of the crucial parameters of plasma based X-ray lasers, especially of those using collisional excitation pumping. Therefore, the knowledge of the dependence of temperature on various pumping conditions could bring us better understanding of the processes involved in setting up optimal conditions for the lasing action, and to help us increasing pump efficiency of these devices. During the experimental campaign at PALS Centre in 2006, we obtained time-averaged values of the electron temperature. These were measured from time integrated resonance spectra in the range of 8 to 12 Å yielded by KAP spectrometers using X-ray CCD camera as the detector.

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2 Experimental setup

Pumping beam

We used two nearly identical KAP crystal 2d=26.6Å spectrometers, equipped with a narrow slit covered by 6 or 18 µm Al filter, and a 16-bit X-ray CCD camera Andor DX440 with 2048×512 pixel resolution, cooled down to 10°C. The configuration of both spectrometers is outlined in Fig.1. An do

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Fig. 1. Setup of the spectrometers: a) short line plasma – the spectrometer slit is covered by 6µm Al filter, b) X-ray laser plasma– the slit is covered by 18µm thick Al filter. The line focus is orientated horizontally in both cases.

3 Examples of the obtained spectra

2p53d-2p6

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Fig. 2. Spectrum of the Ne-like Zn laser plasma and its lineout with calibrated wavelength axis, with some Ne-like lines labeled. The plasma is generated by a prepulse and the main pulse, the latter producing irradiance ~3x1013 Wcm-2.

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Figure 2 shows a spectrum of a ~16-mm long section the zinc X-ray laser plasma (geometry corresponding to Fig.1b), created on a 3 cm long target by a weak prepulse and the main pulse separated by 10 ns; the intensity contrast of these pulses is ~7x10-4. Figure 3 shows examples of spectra generated by the second type of plasmas, produced using narrow slab targets (see Fig.1b) and different foci. a)

b) c) Fig. 3. Spectra of short zinc plasmas serving as testing system for X-ray laser amplifiers, produced by: a) Spot focus with 800µm diameter; b) 150µm wide line focus on 3mm long target; c) 150µm wide line focus on 1mm long target.

4 Technique of data analysis The electron temperature was estimated from the intensity ratio of two Nelike lines whose upper level populations are assumed to be mutually in thermodynamic equilibrium, while reabsorption of these lines in the plasma is similar. In this case, the intensity ratio of such lines is given by:

⎛ E − E1u I 2 A2 λ1 g 2 = exp⎜⎜ − 2u I1 A1 λ 2 g1 kTe ⎝

⎞ ⎟⎟ , ⎠

where A1, λ1, g1, E1u and A2, λ2, g2, E2u are the spontaneous emission probabilities, the wavelengths, statistical weights, and the energies of the upper level of each transition, respectively. In the below analysis, the Al filter transmissions and CCD spectral efficiency was further accounted for.

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5 Results We analysed the intensity ratio between the following spectral line pairs: 2s22p53s(3/2,1/2)J=1 → 2s22p6J=0 (λ=11.77Å)

(1)

2s22p53s(1/2,1/2)J=1 → 2s22p6J=0 (λ=11.52Å)

(2)

2s22p53d(3/2,5/2)J=1 → 2s22p6J=0 (λ=10.66Å)

(3)

and 2

5

2

2s 2p 3d(1/2,3/2)J=1 → 2s

2p6J=0

(λ=10.46Å)

(4)

Since the first pair of lines (3s-2p) is assumed to have non-negligible reabsorption, the intensity ratio I2/I1 of these lines is multiplied by a constant in order to adjust the deduced temperature to that obtained from the lines (3d-2p). For the X-ray laser plasma, this constant is 3/5, whereas for the plasma of test amplifier it amounts to 5/7. 5.1 Investigation of the plasma of the zinc X-ray laser Figures 4 and 5 show the electron temperature dependence on the prepulse energy, and the temperature along the ~16-mm section of the line focus. 60 50

T e [eV]

40 30

estimated from 3s-2p lines estimated from 3d-2p lines

20 10 0 1.7

1.9

2.1 2.3 2.5 Energy of prepulse [J]

2.7

2.9

Fig. 4. Electron temperature of the X-ray laser plasma as a function of the prepulse energy, estimated both from the 3s-2p and 3d-2p lines.

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70 60

Te [eV]

50 40 30 20 10 0 0

2

4

6

8

10

12

14

16

Distance along the line focus z [mm]

Fig. 5. Electron temperature distribution along the line focus of the X-ray laser plasma, estimated from the 3d-2p lines.

5.2 Investigation of short plasmas relevant to X-ray laser amplifiers The temperature of 3-mm long zinc plasmas, produced by sequence of a weak prepulse (contrast 7x10-3) followed after 5.5 ns by the main pulse, is ~4 eV higher than in plasmas produced by the main pulse alone. Figure 6 shows lateral distribution of the temperature for both the prepulse-main pulse sequence and for single pulse pumping. 40

Te [eV]

30

20

3s-2p, main pulse only 10

3d-2p, main pulse only 3s-2p, prepulse + main pulse

0 1.0E+13

1.5E+13

2.0E+13

2.5E+13

3.0E+13

Main pulse intensity [Wcm-2]

Fig. 6. Electron temperature of the 3mm zinc plasmas depending on the main pulse intensity; the data include both prepulse and prepulse-free shots.

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Fig. 7. Lateral electron temperature distribution (across the line focus) of short line plasmas, estimated from the 3d-2p lines. Shown are cases of prepulse pumping (#27_0804, 3mm plasma) and single pulse pumping (#13_0713, 1mm plasma).

6 Discussion The higher electron temperature of plasmas when using prepulse (see Fig. 6) is likely to be attributed to more efficient absorption of the main pulse. The upper level of line 2 of our analysis, 2s22p53s(1/2,1/2)J=1, is the lower level of the lasing transition 2s22p53p(1/2,1/2)J=0 → 2s22p53s(1/2,1/2)J=1. In consequence, the thermodynamic equilibrium between the upper levels of line 1 and 2 could be perturbed, resulting in higher electron temperature deduced than the actual value; however, this effect is assumed to be negligible. It turns out that the experimentally estimated values of time-integrated electron temperature correspond fairly well to the electron temperature of the corona, given by simulations done by the EHYBRID code and followed by a special postcode. The compared time-integrated value is calculated by

T ( x) =

∫ T ( x, t ) ⋅ n ( x, t )dt , ∫ n ( x, t )dt e

e

e

where Te and ne are the electron temperature and the electron density.

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Acknowledgments This work benefited from support of the Czech Science Foundation grant No. 202/05/2316, from the Centers of Fundamental Research project LC528 of the Czech Ministry of Education, and from NEST Specific Targeted Research Project of the EU, contract No. 12843. We are grateful to G. J. Pert (University of York) for providing us the EHYBRID code.

References 1. Rus, B. et al: Investigation of Zn and Cu prepulse plasmas relevant to collisional excitation x-ray lasers, Physical Review A 56, 4229, 1997 2. Zhang, H. et al: Collision Strengths and Oscillator Strengths for Excitation to the n=3 and 4 Levels of Neon-like Ions, Atomic Data and Nuclear Data Tables, Vol. 37, p. 17, 1987.

Development of Plasma X-Ray Amplifiers Based on Solid Targets for the Injector-Amplifier Scheme M. Kozlová1, B. Rus1, T. Mocek1, J. Polan1, P. Homer1, M. Stupka1, M. Fajardo2, D. De Lazzari2 and P. Zeitoun3 1 - Department of X-ray Lasers, Institute of Physics/ PALS Centre, Prague 8, Czech Republic 2 - Centro de Física dos Plasmas, Instituto Superior Técnico, Lisbon, Portugal 3 - Laboratoire d'Optique Appliquée, ENSTA - Ecole Polytechnique, Palaiseau, France

Summary. Results of experimental studies aimed at generation and diagnostics of advanced soft X-ray amplifiers, produced from solid targets, are presented. 2D profiles of electron density of short plasma columns, generated by ~300-ps laser pulses under various illuminating conditions, were investigated by near-field distribution of the plasma self-emission, and by X-ray laser backlighting at 21 nm, accessing in the given geometry electron densities of 1022 cm-3. The obtained data indicate that by employing line focus with concave intensity profile it is possible to generate laterally highly uniform plasma columns of width ~500 µm, potentially suitable as amplifiers with negligible lateral refraction. By X-ray laser backlighting we further probed the morphology and gain region of test Zn plasmas, pumped by a sequence of a loosely focused weak prepulse and tightly focused main pulse, separated by 5.5 ns. The data clearly show the beneficial role of the prepulse in lateral homogenization of the plasma, and reveal narrow ~50-µm gain region.

1 Introduction The scheme in which HHG seed is strongly amplified in a separated amplifier was demonstrated using gas-cell OFI plasmas, at the wavelength 41.8 nm [1]. In this approach, the energy extractable from the amplifier is limited by the saturation intensity, and therefore boosting the output beyond µJ level requires denser plasmas produced from solid targets [2]. Feasibility of this approach was recently demonstrated by amplification of HHG seed in Ne-like Ti plasma at 32.6 nm [3]. In this work, we studied 2D transverse density profile of line plasmas potentially exploitable as X-ray amplifiers, at conditions relevant to the

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pedestal pulse in transient X-ray lasers. Plasmas produced using conventional “flat top” line focus, as well as using laterally modulated illumination profile, were examined. The density profiles were investigated by high-resolution imaging of the XUV self-emission, and by backlighting with X-ray laser at 21.2 nm [4]; the latter technique is able accessing ne up to 2.4×1024 cm-3, though in practice this value is lower due to refraction of the X-ray beam. The ionization balance and electron temperature of the plasmas was measured by resonance keV spectroscopy, the results of which are presented elsewhere in these Proceedings [5]. In order to probe dense and emissive plasma by X-ray laser backlighting, spatial filtering in the X-ray beam surrogate focal plane was employed. This technique allows exploiting the directionality of the X-ray laser beam and largely reduces contribution of self-emission of the probed plasma into the detected signal.

2 Experimental setup The experiment was conducted at the PALS Centre, benefiting for the backlighting purposes from availability of the neon-like zinc X-ray laser at 21.2 nm. The investigated plasmas were produced by the auxiliary 148-mm

Fig. 1. Experimental scheme. Targets consisting of 1- or 3-mm wide slabs are irradiated either by a single pulse or by sequence prepulse / main pulse produced in the dogleg. The pulses are focused down to a ~150 µm × 4 mm line by f=120 cm spherical / f=400 cm cylindrical lens doublet; the prepulse is separately defocused by additional f=3000 cm lens. The X-ray laser at 21.2 nm, upon probing the plasma, is reflected by f=253 mm off-axis MoSi multilayer parabolic mirror and passes though a pinhole located at the focal plane of the mirror.

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diameter beam, delivering 80 J at the fundamental wavelength (1.315 µm) in 300 ps (FWHM) pulses. A doublet of spherical f=120 cm and cylindrical f=400 cm lenses is employed to produce 4-mm long line focus (with minimal lateral size ~150 µm) overfilling 1 or 3 mm slab targets. The investigated plasmas are produced either by a single pulse or by sequence of a weak prepulse followed by the main pulse. In the latter case, dogleg arrangement (see Fig. 1) was employed: the incident beam is split by a 10/90 % (T/R) beamsplitter into two beams that are recombined back by a 20/80 % beamsplitter. The dogleg makes it possible changing the delay between the prepulse and the main beam from 2 to 10 ns. Additional lens in the optical path of the prepulse is employed to produce prepulse focus larger than the focus of the main pulse. The studied plasmas were further monitored by a keV spectrometer [5] and their dimensions were measured by means of VIS emission using an optical telemicroscope. The output plane of the plasma was imaged to a back-illuminated X-ray CCD camera PI-MTE (2048×2048, 13.5 µm pixels). The imaging was carried out by off-axis parabolic (f=253 mm) MoSi multilayer mirror, with magnification 8. A small pinhole (100 µm to 1 mm) was placed in the focal plane of the X-ray laser, acting effectively as spatial filter strongly improving the contrast of the plasma self-emission to the X-ray laser probe.

3 Experimental results In chapter 3.1, we show the effect of spatial filtering on the resolution of the imaged object, and demonstrate its ability to attenuate plasma emission. Results of probing plasmas that were produced comparatively by narrow line focus and by a “hollow” line focus are shown in chapter 3.2. In chapter 3.3, zinc plasmas produced with and without weak prepulse are investigated, and from local amplification/absorption information about the gain region is obtained. 3.1 Spatial filtering in X-ray laser plasma probing A simplified principle of this technique is shown in Figure 2a. Its use needs appropriately selected pinhole size, adequate to the interval of spatial frequencies pertinent to the details at the object to be imaged. The required pinhole size may be estimated using equation 1 (assuming paraxial approximation), adopting here an arbitrary criterion of at least three

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Fig. 2a. Principle of spatial filtering: rays of a (near) parallel beam pass freely through a pinhole, located in the focal plane of the lens/mirror, while majority of (near) isotropic emission from the probed object is stopped by the pinhole.

Fig. 2b. Intensity distribution in the focal plane of the probing 21.2-nm beam backlighting a rectangular obstacle of width D=1 mm.

maxima transmitted. In this experiment, D=1 mm, f =253 mm, λ=21.2 nm, which gives intensity distribution displayed in Figure 2b. I(y) = I0 sinc2(πDy/λf)

(1)

The first minimum corresponding to y =50 µm, the target edge appears blurred when 100-µm diameter pinhole is employed (Fig. 3a). When the pinhole size is increased to 300 µm so as to pass three diffraction maxima, sharp image of the target edge is produced (Fig. 3b). Reduction of the plasma self-emission, resulting in dramatic improvement of the contrast probe /plasma emission at the detector, is demonstrated in Figure 4. Here, a 300-µm pinhole placed in the focus of the imaging parabola, removes completely the plasma self-emission. The presence of the plasma is apparent only by the bent contours of the filtering mesh that acts here as a casual sensor of wavefront distortion of the probing X-ray beam.

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Fig. 3. Effect of spatial filtering on the image of the target backlighted by X-ray laser at 21.2 nm: (a) 100 μm hole removes high-frequency details of the target edge, (b) 300 μm hole appropriately bandpassing target edge details (the chequered pattern is due to the mesh supporting thin Al filter in front of the CCD).

Fig. 4. Plasma column with length of 1 mm, produced with ~30 J and probed by the X-ray laser at 21.2 nm (the chequered pattern corresponds to a fine mesh supporting the Al filter located ~50 cm in front of the CCD camera): (a) shot taken without spatial filtering; (b) shot with spatial filtering, using a 300-µm diameter pinhole. The distorted contours of the mesh near the target are due to refraction of the XRL beam in the probed plasma; the contours are redrawn in the bottom image.

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3.2 Shaping the lateral plasma profile of the amplifier In searching for generation of laterally uniform line plasmas with width much larger than 100 µm, we studied comparatively target irradiation by the “conventional” narrow line focus, and by laterally concave (with intensity dip on the axis) line focus. The data, obtained with Fe targets, are shown in Figure 5. For the narrow focus, producing 4×1013 Wcm-2 along a single ~150 µm line, the coronal plasma XUV emission roughly reproduces the lateral profile of the driving intensity. For the concave focus, producing two 13 -2 ~1.6×10 Wcm peaks ~500 µm apart with intensity modulation axis/peak of ~3, the modulation of the XUV intensity, and hence modulation of the coronal plasma, is smaller than modulation of the driving intensity.

Fig. 5. Lateral profiles of the XUV self-emission of a 1-mm long Fe plasma produced by (a) narrow line focus, and (b) hollow focus. The bottom images show the front VIS plasma emission visualizing spatial distribution of the driving intensity (note different scales in the lateral and axial directions).

Both plasmas were axially probed by the X-ray laser, accessing large electron densities near the target. The obtained data are shown in Figure 6. The probed plasmas appear here as thin dark regions from which the X-ray laser is “pushed out”, and which extend beyond both sides of the target edge original position. These dark regions extend for the narrow and for the concave focus respectively 18 µm and 13 µm above the target surface. Most importantly, the data reveal that the concave focus produces laterally very homogeneous plasma of width ~500 µm, in stark contrast to the narrow

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focus geometry resulting in laterally rapidly varying density profile. This indicates that plasmas employing concave line focus represent a promising approach for producing laterally refraction-free X-ray laser amplifiers.

Fig. 6. Images of the 1-mm long Fe plasmas, backlighted along their axis by the 21.2-nm X-ray laser: (a) plasma produced by the narrow focus, (b) plasma produced by the hollow focus. Both images were obtained using a 1-mm pinhole. The images are shown with different horizontal and vertical scale to improve the data visibility.

As Fe plasma is highly transparent at 21.2 nm even at low temperatures [6], we attribute the dark region to refraction of the X-ray beam. To assess the electron density, we used ray tracing to follow rays propagating near the target. This tracing assumes exponential electron density fall-off, ne=ne0exp(-x/L), where ne0 is density to be inferred, and L is adopted to have a value compatible with the extent of the detected plasma (<20 µm). The result, shown in Figure 7, indicates that the plasma density in the region close to the target surface is ~1.2×1022 cm-3. Transverse distance (microns)

20

RAY 1 L = 4 microns

18

RAY 1 L = 8 microns

16

RAY 1 L=10 microns

14

Measured

12

RAY 2 L = 4 microns

10

RAY 2 L= 8 microns RAY 2 L = 10 microns

8 6 4

ne0 = 1.2×1022 cm-3

2 0 0

0.2

0.4

0.6

Longitudinal distance (mm)

0.8

1

Fig. 7. Trajectories of the probing X-rays, down the axis of the 1-mm long line plasma. The rays are injected parallel to the target and are refracted away, which results into a dark region near the surface at the output plasma plane (at 1 mm). The density ne0 = 1.2×1022 cm-3 at x=0 is adjusted so as the shadow size equals to the experimentally found value and to be nearly insensitive to the scale length L.

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3.3 Gain probing, amplification of X-ray laser in a 3-mm zinc plasma The plasmas were produced on Zn target by sequence of a weak prepulse and the main pulse arriving 5.5 ns later. They were focused down to respectively ~600 μm and ~150 μm wide lines, producing target irradiance contrast 7x10-4 (same as prepulse contrast in the X-ray laser at PALS [4]).

Fig. 6. XUV self-emission of the Zn plasmas: (a) single main pulse; (b) sequence of prepulse and the main pulse. The same plasmas backlighted by the 21.2-nm X-ray laser, arriving 200 ps before the peak of the main pulse: (c) single main pulse; (d) sequence of prepulse and the main pulse. The irradiance produced by the prepulse and the main pulse is ~2×1010 Wcm-2 and ~3×1013 Wcm-2, respectively.

The data reveal that the weak prepulse (0.1 J) leads to appreciable lateral smoothing of the emitting region in the vicinity of the target surface (see Figs 6a,b), as well as to widening of the lateral extent of the plasma (see width of the dark region in Figs 6c,d). This indicates that a weak prepulse applied a few nanoseconds before the pedestal pulse in transient X-ray laser systems may (besides impacting the density profile in the direction perpendicular to the target) improve lateral uniformity of the plasma.

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(b)

Fig. 7. Images obtained by removing contribution of the self-emission from the backlight records of Fig.6: (a) 6a subtracted from 6c, and (b) 6b subtracted from 6d.

Improvement of lateral uniformity of the plasma in presence of the prepulse is clearly seen in Figure 7, showing the difference between signals from the plasmas backlighted by the X-ray laser and from the corresponding self-emissions. Moreover, Fig.7b reveals that in the presence of the prepulse the probing X-ray laser is locally amplified in a narrow region of width of ~50 µm, located ~40 µm from the target surface. 4 Conclusions Prototype line plasmas for X-ray amplifiers, produced under various irradiating conditions by 300 ps IR pulses, were studied by high-resolution XUV imaging and by X-ray laser backlighting. The experimental setup, in conjunction with the technique of spatial filtering, allows to reveal details ~2 µm and to obtain insight into electron densities 1022 cm-3 near the target, providing important testbed data for hydrodynamic codes. It is found out that shaping the intensity distribution of the line focus, namely using a concave profile, is a promising technique to produce laterally homogeneous X-ray amplifiers. Secondly, the irradiation scheme using hollow focus may offer prospects for generation of near refractionfree amplifiers without excessive pumping energy, compared to that required to produce “top-hat” focus of the same width. The data also indicate that the lateral uniformity of the pedestal plasmas for TCE lasers may be improved by applying a weak prepulse prior the “main” pedestal pulse. Although studies of plasmas produced by a prepulse followed by the main pulse delivered in a concave focus were not undertaken on this occasion, it will be carried out in next experiments.

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5 Acknowledgments This work benefited from support of the Czech Science Foundation grant No. 202/05/2316, from the Centers of Fundamental Research project LC528 of the Czech Ministry of Education, and from the NEST Specific Targeted Research Project of the EU “TUIXS”, contract No. 12843.

Reference 1. Zeitoun, P., et al. A high-intensity highly coherent soft X-ray femtosecond laser seeded by a high harmonic beam, Nature 431, 426, 2004 2. Zeitoun, P.: Paving the way towards 1 mJ, 100 fs soft X-ray lasers, in this Proceeding 3. Wang, Y., et al.: High-brightness injection-seeded soft-X-ray-laser amplifier using a solid target, Phys. Rev. Lett. 97, 123901, 2006 4. Rus, B., et al., Multimillijoule, highly coherent X-ray laser at 21 nm operating in deep saturation through double pass amplification, Phys. Rev. A 66, 063806, 2002 5. Nejdl, J., et al.: Electron temperature measurements of model Ne-like X-ray laser plasmas from resonance keV spectra, in this Proceeding 6. Tallents, G.J., private communication

X-Ray Laser Beam Shape Control: High-Res VIS and keV Imaging of the Amplifying Plasma P. Homer, M. Kozlová, T. Mocek, J. Polan, B. Rus and M. Stupka Department of X-ray Lasers, Institute of Physics / PALS Centre, Prague 8, Czech Republic

Summary. We describe results of an experimental study aimed to control the single-pass far-field profile of the X-ray laser beam at 21.2 nm emitted by a QSS neon-like zinc amplifier. The plasma is produced by a prepulse followed after 10 ns by the main pump pulse, both with duration of ~300 ps, focused down to a 3-cm long line by a composite smoothing optics. This optics involves a matrix of 10 cylindrical lenses and an aspherical lens, and produces 10 individual line foci which are superimposed in the focal plane of the aspherical lens. In this work, we study the dependence of distribution of the pump intensity across the focal line and the spatial profile of the emitted X-ray laser beam. The intensity distribution of the pump emission is monitored by a high-resolution VIS camera, providing details <5 µm. The results show that the best X-ray laser beam profile is obtained when the partial line foci are not ideally superimposed, while for the “ideal” (=narrow) focus of the optical system the X-ray laser beam is split vertically into two characteristic lobes.

1 Introduction The motivation of the presented study was to understand and control the beam quality of the neonlike zinc X-ray laser beam, generated in nominal configuration for user applications at PALS. From the past campaigns it turned out that the beam quality of this laser changes from one experimental session to another, although the available diagnostics of the lasing plasma, most notably the survey X-ray cross-slit camera (see [1]), did not reveal any significant differences. Similarly, the X-ray laser beam shape was found to be fairly insensitive on the prepulse energy – despite dramatic dependence of the X-ray laser output on this parameter. To understand this issue we implemented high-resolution diagnostics of the visible and X-ray emission produced by the amplifying plasma, viewing a short section (few mm) along the 3-cm long amplifier.

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2 Instrumentation The principal diagnostics was a high-resolution VIS camera (see Fig. 1a), consisting of a CMOS head (1280x1024 pixels), and zoom (magnification 2.1 to 13.5). The resolution of whole system could be varied between 4.9 and 1.6 µm. The plasma light entering the objective was heavily attenuated by set of ND filters. The X-ray laser beam was examined by the footprint monitor (Fig. 1b). This employs a Tb-doped phosphor screen, converting soft X-ray radiation to visible light, and a fix focal-length objective (magnification 1x) relaying the image onto an off-shelf CCD camera based on 768x576 pixels.

a)

b)

c) Fig. 1. a) High-resolution VIS imaging system; .b) Footprint monitor; .c) Composite X-ray pinhole camera: the X-ray emission is imaged (magnification 2.5) by pinhole to a thin phosphor pellicle, which is imaged using a 4x objective to a high-resolution CMOS head.

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The plasma was also monitored by a composite high-resolution X-ray pinhole, see Fig. 1c. The overall resolution (phosphor resolution is ~1 µm) of this camera depends on the imaging optics; here it was ~3 µm. The system has coaxially integrated laser diode for alignment.

2 Experimental setup The VIS imaging camera and the X-ray pinhole were located sideways of the pump laser beam, inside the vacuum chamber, and were viewing ends of the line focus, see Fig. 2a. The phosphor screen of the footprint monitor sits inside the chamber, and is viewed through a glass vacuum window by the imaging system and the camera, both mounted outside.

a)

b) Fig. 2. a) Experimental setup. The driving IR beam (1.3 µm) is focused to 3-cm long line by a matrix of 10 cylindrical segments and by an aspherical lens; b) Focus geometry of the driving IR laser beam (vertical plane, to scale), assuming caustic 130 µm. Three indicated positions of the focus were investigated.

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3 Profile of the pump intensity and the X-ray laser beam shape The VIS emission profiles of the plasma were studied for three positions of the focus with respect to the target, as indicated in Fig.2b. When the 10 partial line foci, produced by the composite optics, are best superimposed, narrow ~140-µm amplifier is generated (Fig. 3). However, the X-ray beam (Fig. 4) is split into two lobes, indicating that density gradient is such narrow amplifier leads to significant lateral refraction of the X-ray laser beam.

a)

b) Fig. 3. a) Plasma VIS emission for the “best” focus position; b) Vertical lineout of the image 3a): the emission FWHM is 138 µm.

Fig. 4. The X-ray laser beam produced at the best focus as in Fig. 2.

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When the focusing optics is moved 0.5 mm out of the “best” focus, we obtain ~50% wider plasma, with slightly asymmetric lateral profile (Fig. 5). The X-ray laser beam, however, has a single maximum and also higher intensity, as seen in Figure 6. Finally, Fig. 7 shows the plasma shape for the lens 1 mm away from the “ideal” focus. Here, the plasma is ~30% wider than in the previous case and is rather inhomogeneous; it is already possible to recognize individual foci of the composite optics. Despite this lateral inhomogeneity, the X-ray laser beam in this configuration, Fig. 8, is narrowly collimated (it has least divergence of the three positions), though its shape is slightly asymmetric in vertical direction indicating asymmetric local gain conditions across the plasma. In comparison with the “0.5-mm” case, the X-ray laser has for this “1-mm” focus position also slightly lower intensity.

a)

b) Fig. 5. a) Plasma VIS emission for the lens 0.5 mm off the best focus (see Fig.2b); b) Vertical lineout of the image 5a): the emission FWHM is 198µm

Fig. 6.. The X-ray laser beam shape for the lens shifted 0.5 mm away from the ideal focus.

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It is to note that the near-field emission pattern of the 3-cm long amplifier exhibits at these pump conditions (prepulse 10 ns ahead of the main pulse) relatively weak dependence on the focus position, see [2].

a)

b) Fig. 7. a) Plasma VIS emission for the lens 1 mm off the best focus (see Fig.2b); b) Vertical lineout of the image 7a): the emission FWHM is = 253 µm

Fig. 8. The X-ray laser beam shape for the lens shifted 1 mm away from the ideal focus

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4 Summary By using high-resolution imaging diagnostics, we were able to correlate the lateral distribution of intensity in the driving laser focus with the spatial profile of the 21.2-nm X-ray laser beam. We found that, under the given pump conditions, the X-ray beam shape and its intensity are optimized for the width of the line focus of ~200 µm, which corresponds to the lens “defocused” by 0.5 mm. For the narrowest ~140 µm focus, the X-ray emission suffers lateral refraction in the amplifying plasma, and the X-ray beam is split into two lobes. The results point out at the importance of the lateral profile of the pump intensity in generating and/or amplifying X-ray beams, and demonstrate that lateral refraction may be efficiently controlled.

References 1. Rus, B., et al: Multimillijoule, highly coherent X-ray laser at 21 nm operating in deep saturation through double pass amplification, Phys. Rev. A 66, 0638061-063806112, 2002. 2. Polan, J., et al: This Proceedings

Spatial and Temporal Profiles of the 21.2-nm Saturated X-Ray Laser Output J. Polan, T. Mocek, M. Kozlová, P. Homer and B. Rus Department of X-ray Lasers, Institute of Physics / PALS Centre, Prague 8, Czech Republic

Summary. Results of experimental investigation of near-field spatial distribution and time history of the emission produced by the saturated Ne-line zinc laser are presented. We compare the near-field 2D profiles of the 21.2-nm emission at the output of a 3-cm long amplifier for the prepulse pumping involving the delay between the pulses of 10 and 50 ns, as a function of focusing conditions and prepulse contrast. For selected pump parameters, temporal profiles of the X-ray laser output produced in the 10- and 50-ns prepulse delay regimes were also measured. It is found out that the near-field profiles of the emitted X-ray laser are considerably different for the two prepulse delays, and exhibit strongly different behavior with respect to intensity distribution of the focused pump laser. On the other hand, the X-ray pulse lengths in the two prepulse regimes are similar (~150 ps), suggesting comparable time history of the ionisation and atomic levels kinetics. The data indicate that, under well-defined conditions, the 50-ns prepulse pumping produces gain over larger region and in less refractive plasma than the 10-ns prepulse regime.

1 Introduction The soft X-ray zinc laser, delivering in the double-pass regime up to 4 mJ at 21.2 nm, is routinely exploited at PALS for user applications. The laser is pumped by sequence of a weak prepulse followed after 10 ns by the main pulse [1]. Recent studies aimed at searching possibilities for boosting the output of this laser showed that by using a prepulse applied 50 ns ahead of the main pulse it is possible, in the double-pass regime, to generate 10 mJ in a narrowly collimated beam [2]. It was also found that functioning of the laser with 50-ns prepulse is sensitive to the main beam focus conditions. To understand different regimes of prepulse pumping, we measured the pattern of the X-ray laser emission at the plasma exit plane and the temporal profile of the pulse. These data provide important insight into the

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plasma hydrodynamics, its refraction properties, and gain evolution (see e.g. [3,4]).

2 Experiment The experimental arrangement, shown in Figure 1, employs MoSi multilayer mirrors sending the X-ray laser beam to either the near-field monitor or the streak camera. The near-field emission profiles were obtained using an imaging system including three mirrors, where the first two ones relay the plasma output to the object plane of an off-axis parabola (f=254 mm), providing magnification of ~8, see Figure 2. The images are detected by the X-ray CCD camera (Roper Scientific MTE 2048x2048 13.5-µm pixels). The X-ray laser temporal profiles are obtained by retracting the spherical mirror and sending the X-ray laser beam by additional plane mirror towards an X-ray streak camera (Kentech lowmagnification with CsI photocathode). By small displacements of the individual mirrors, the setup allows simple switching between near-field and streak camera shots, and imaging applications in which the probed object sits in the object plane of the parabola.

Fig. 1. Experimental setup. The output plane of the zinc X-ray laser is relayed with magnification ~1 by tandem of f=800 mm spherical and plane mirror to the object plane of f=254 mm off-axis parabola producing image with magnification ~8 on the X-ray CCD camera. A flat mirror is employed alternatively to send the X-ray laser output to streak camera for temporal measurements.

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Fig. 2. Calibration image of the near field monitor, using a test 100×100 µm pitch SEM transmission grid placed at the XRL output plane and illuminated by HeNe laser. One CCD pixel corresponds to ~2 µm. The target surface position is determined with accuracy of ±20 µm.

The zinc X-ray laser is produced by irradiating 3-cm long slab targets with sequence of a prepulse focused down to a ~800 µm wide line, and with the main pulse focused more tightly to ~150 µm × 3 cm line. The delay between the pulses was 10 and 50 ns; both pulses were 300 ps FWHM of 1.315 µm laser light. In the nominal configuration using 10 ns delay, these pulses produced respectively 2×1010 Wcm-2 and 3.5×1013 W cm-2 (contrast ~6×104 ). The main laser beam is focused by matrix of 2×5 cylindrical lenses and one aspherical lens (f# = 3.5), ensuring smooth distribution of intensity along the line focus. Figure 3 illustrates the geometry of the near-focus region, showing dependence of the focus width with respect to the target position. Displacement of the lens by 0.5 and 1 mm from the best focus thus results in enlargement of the focus width from 130 µm to respectively 195 and 280 µm; these values agree very well with focus width measurements [5].

Fig. 3. Focus geometry of the main laser beam in the vertical plane (to scale, assuming caustic 130 µm). The line focus is produced by matrix of ten cylindrical lenses arranged in two rows; the lens mount involves a horizontal central rib effectively splitting the incoming beam into two halves. D=0 corresponds to the nominal lens position optimizing the X-ray laser beam shape for 10 ns (see [5]).

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2 Results of the near-field measurements The near-field patterns of the “nominal prepulse” configuration (10 ns, 2×1010 Wcm-2), as a function of the focus position, are shown in Fig.4. It is Double pass

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Fig. 4. Single- and double-pass near-field X-ray laser profiles for the prepulse arriving 10 ns before the main pulse, as a function of the distance of the main lens from the target (cf. Fig. 2). The laser is incident from the left, see Fig. 3. With respect to its nominal position D=0, cf. Fig.3, the main lens is (a) 0.5 mm closer to the target, (b),(c) at the nominal position, (d) 0.5 mm away from the target.

seen that neither spatial extent nor intensity as well as morphology of the emission are significantly varied. This corresponds to our former observation that at the given 10-ns pumping regime, the X-ray laser intensity is fairly insensitive to the focusing conditions (although the pump intensity drops by ~30% when moving the lens 0.5 mm away from the best focus). When changing the prepulse delay to 50 ns, the dependence of the nearfield pattern on the focus position is dramatically different, which is shown in Figure 5 (the prepulse energy in these shots is ~3× higher than for 10 ns, see dependence of the X-ray laser output on this parameter below). For the lens position corresponding to the optimum for 10 ns prepulse, the X-ray laser is much weaker and is emitted from a region 2.5× narrower in the lateral direction. The emission exhibits strong maximum when the focus is shifted 1 mm away from the nominal position, and its profile is significantly larger in both lateral and perpendicular direction. Compared to 10 ns case, the pattern is laterally much less modulated, indicating that the amplifying plasma is laterally less refractive and/or that its density profile is laterally smoother likely due to larger thermal conduction. The lineouts of the near-field patterns showing the X-ray laser emission profiles perpendicularly to the target are in Figure 6. It is seen that the 50-ns prepulse regime makes it possible generating the same X-ray laser intensity at the plasma output, but over larger region. This corresponds to saturated

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Fig. 5. Single-pass near-field X-ray laser profiles for the prepulse arriving 50 ns before the main pulse, as a function of the distance of the main lens from the target. The lens is (a) at the nominal position D=0, then with respect the nominal position (b) 0.5 mm closer to the target, (c) 1 mm closer to the target, (d) 1.5 mm closer to the target. The signal level in (a) and (b) is enhanced for better visibility.

emission in both cases, and indicates that for 50 ns the gain region is larger than for 10 ns, and/or that for 50 ns the trajectories of amplified rays are less defined by refraction than for 10 ns.

Fig. 6. Near-field profiles in the direction perpendicular to the target (integrated over lateral FWHM width) for the 10 ns (left) and 50 ns (right) pumping.

Figure 7 shows the 21.2-nm output as a function of the focus position, displaying the stark difference between the two prepulse regimes. The single-pass X-ray laser emission for 50 ns prepulse exhibits a strong peak for the lens position D=-1 mm, at which the pump intensity is identical to that for D=0 (symmetrically placed at the other side of the best focus), but where the 21.2-nm output is ~10× weaker. Reasons for this behaviour are not understood, though it is likely connected to 2D coupling of the converging / diverging laser beam into the expanded prepulse plasma having a fairly complex spatial profile [6]. Comparison of the dimensions of the near-field patterns for both prepulse regimes, obtained from the data in Figs. 4 and 5, is shown in Figure 8. It is evident that generation of the gain region and/or the plasma hydrodynamics in these two pumping regimes are qualitatively different.

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Fig. 7. Near-field pattern signal (spatially integrated output) in the 10- and 50-ns prepulse regime, as a function of the focusing lens position from the target.

Fig. 8. FWHM size of the near-field patterns in the direction perpendicular (left) and lateral, along the target (right), depending on the distance of the lens from the target. The brightest emission in the 50-ns prepulse regime is produced at -1 mm.

Figure 9 shows dependence of the X-ray laser output on the prepulse energy for the 50-ns regime. While the prepulse level optimizing the 21.2-nm emission is ~4× higher than that for 10-ns pumping, the strong sensitivity of the X-ray laser on the prepulse level for 50 ns is similar to that for 10 ns (the latter dependence was repeatedly measured in earlier experiments using far-field beam diagnostics). (a)

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Fig. 9. Single-pass near-field profiles for the prepulse arriving 50 ns before the main pulse, as a function of the prepulse energy: (a) Epp=0 (no prepulse; image contrast enhanced 20x), (b) Epp=1.6 J (nominal for 10 ns), (c) Epp=3 J, (d) Epp=7 J.

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4 Measurements of the X-ray laser time profiles Temporal profiles of the single- and double-pass X-ray laser emission, produced in the 10-ns prepulse regime, are displayed in Figure 10; Figure 11 shows single-pass profiles for the 50-ns pumping. The streak camera was set up according to Fig. 1 identically for both configurations, with 1.5-µm Al foil placed in front of the photocathode to block visible light. The received signal represents therefore soft X-ray emission in the spectral interval of ~1 nm, centered on the design wavelength of 21.2 nm of the multilayer mirror relaying the X-ray laser into the streak camera. (a)

(b)

Fig. 10. Temporal profiles of the X-ray laser using 10-ns prepulse delay: (a) single-pass regime, for three different positions of the main lens (D=0, -0.5, and 1 mm), (b) double pass regime (main lens at nominal position D=0).

(a)

(b)

Fig. 11. Single-pass temporal profiles of the X-ray laser using 50-ns prepulse delay, with the main lens at D=-1 mm (position of the strongest 21.2-nm emission, see Fig.5c). The full line corresponds to the X-ray laser produced by nominal ~300 ps pump pulse, the broken line to ~420 ps pump pulse; (b) displays these profiles over 2 ns window, additionally including continuum emission recorded in a shot fired in absence of prepulse (dotted line).

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The single-pass X-ray laser pulse length in the 10-ns regime is ~150 ps, which is very close to the (single-pass) pulse duration generated for the 50-ns prepulse (solid line in Fig. 11). From the data available (only a limited number of streak-camera shots with 50-ns prepulse could be fired), the X-ray laser pulse profiles in the 50- and 10-ns regimes are similar. On the other hand, as seen from Fig. 11, the long-lasting continuum emission generated with 50-ns prepulse is much stronger than for 10-ns prepulse, where the continuum does not become visible within the streak camera dynamic range. This indicates that the 50-ns regime generates a large volume of the emitting plasma. It is to note that the continuum emission signature is weak in the near-field measurements, which use three multilayer mirrors and are therefore more wavelength selective (>2× narrower bandpass) than the streak camera measurements. Finally, Figure 11 also shows the X-ray laser pulse emitted when a ~50% longer IR pump pulse is used (broken line). The X-ray emission emerges in this case as a short ~50-ps outburst preceding a very intense continuum (which is stronger than the continuum for the nominal 300-ps pump pulse). Although analogous shot for 10-ns prepulse was not fired, we know from previous experiments that the X-ray laser is not in such configuration critically sensitive to the pump pulse duration. This further strengthens the conclusion that the X-ray laser in the 50-ns prepulse regime may be efficiently generated only over a narrow interval in the pumping parameter space.

5 Conclusions We studied comparative characteristics of the 21.2-nm X-ray laser emission produced by prepulse pumping using 10 and 50 ns prepulse delays, motivated by the possibility to generate 10 mJ pulses on a routine basis. The results show that besides sensitivity of both regimes on the prepulse level, the 50-ns regime is additionally very sensitive to coupling of the focused pump laser into the plasma produced by prepulse. While the streak camera records indicate comparable kinetics of the excited levels for both regimes, from the near-field data it is found out that the 50-ns prepulse delay makes it possible to generate 2× larger (in the direction perpendicular to the target) amplification region than in the 10-ns regime. This suggests that very long prepulse delays give prospects for significant and yet unexploited alleviation of refraction in this type of X-ray lasers, and for boosting their output to 10-mJ level or beyond.

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6 Acknowledgments We thank P. Zeitoun of LOA for providing us the X-ray CCD camera for the near-field measurements. This work benefited from support of the Czech Science Foundation grant No. 202/05/2316 and from the Centers of Fundamental Research project LC528 of the Czech Ministry of Education.

References 1. Rus, B., et al: Multimillijoule, highly coherent X-ray laser at 21 nm operating in deep saturation through double pass amplification, Phys. Rev. A 66, 0638061-063806112, 2002. 2. Rus, B., et al: Generation and applications of 10-mJ XRL pulses near 20 nm using long scale length plasmas, in X-ray Lasers 2004, Proc. 9th Int. Conf. on X-ray Lasers, ed. J Zhang, Institute of Physics Conference Series, IOP Publishing Ltd, Bristol, 2005 3. Smith, R.F., et al: Plasma conditions for improved energy coupling into the region of the Ni-like Pd transient collisional x-ray laser, Phys. Rev. E, 72, 0364041-0364044, 2005. 4. Nilsen, J., et al: Two-dimensional imaging and modeling of the 14.7 nm Ni-like Pd x-ray laser, J. Opt. Soc. Am. B 20, 191-194, 2003. 5. Homer, P., et al: X-ray laser beam shape control: high-resolution VIS and keV imaging of amplifying plasma, this Proceedings 6. Rus, B., et al, Investigation of Zn and Cu prepulse plasmas relevant to collisional excitation x-ray lasers, Phys. Rev. A 56, 4229-4241, 1997

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Advances in High Repetition Rate Soft X-Ray Lasers: Lasing Down to 10.9 nm and High Brightness Operation of a Seeded Soft X-Ray Amplifier Using a Solid Target J.J. Rocca1,2, Y. Wang1,2, M. Larotonda1,2, B. Luther1,2, M. Berrill1,2, D. Alessi1,2, A. Weith1,2, M. Marconi1,2, D. Patel1,2, C.S. Menoni1,2, V.N. Shlyaptsev3, J. Dunn6 ,Y. Liu2,5 and D. T. Attwood2,4,5 1

NSF ERC for Extreme Ultraviolet Science and Technology Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO 80523 3 University of California Davis at Livermore 4 Lawrence Livermore National Laboratory 5 University of California at Berkeley 6 Lawrence Berkeley National Laboratory 2

Summary. We have demonstrated saturated tabletop lasers operating at 5 Hz repetition rate with microwatt average powers at wavelengths between 18.9 nm and 13.2 nm in the 4d 1P1-4p 1S0 transitions of Ni-like ions. Lasing was also observed on transitions of the same isolectronic sequence for wavelengths as low as 10.9 nm in Ni-like Te, and on transitions near 30 nm in Ne-like ions. The results were obtained using picosecond laser heating pulses with an energy of only 1J by optimizing the grazing incidence angle of the pump beam for maximum energy deposition. As a further step in the development of these lasers we also realized the first demonstration of saturated amplification of a high harmonic seed in a transient collisional soft x-ray laser amplifier created by heating a solid target. A 32.6 nm Ne-like Ti amplifier was used to amplify a seed pulse from the 25th harmonic of Ti:Sa into the gain saturation regime. The amplified beam was measured to approach full spatial coherence. The peak spectral brightness is estimated to be ~ 2×1026 photons/(s.mm2.mrad2 0.01% bandwidth). The scheme is scalable to produce extremely bright lasers at very short wavelength.

1. High repetition rate lasers with saturated output at wavelengths down to 13.9 nm and gain down to 10.9 nm There is significant interest in the development of compact high average power soft x-ray lasers for a variety of applications. Fast discharge excita-

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tion of capillary plasmas has produced extremely compact saturated lasers emitting at 46.9 nm in Ne-like Ar at repetition rates up to 10 Hz [1]. Laserdriven optical field ionization lasers have produced saturated operation at 41.8 and 32.8 nm in Pd-like Xe and in Ni-like Kr respectively [2]. However, until recently gain-saturated laser operation at shorter wavelengths have required picosecond optical laser pump pulses with an energy of ~ 7 J, which limited their repetition rate to one shot every several minutes [3,4]. Recently it was shown that the energy required to pump collisional soft x-ray lasers can be significantly decreased by directing the short pulse pump beam onto the target at a grazing angle, which increases the absorption efficiency of the pump pulse into the gain region of the plasma [5-9]. We have extended these results to shorter wavelengths, demonstrating for the first time high repetition rate saturated laser operation (5 Hz) of a tabletop laser at wavelengths as short as 13.2 nm in Ni-like Cd [10], a wavelength that is within of the bandwidth of the Mo-Si multilayer coatings for EUV lithography. We also demonstrated the isolectronic scaling of this high repetition rate laser scheme to shorter wavelengths with the observation of amplification at wavelengths of 11.4 and 10.9 nm in Ni-like Sb and Ni-like Te [9], respectively. The results were obtained heating a precreated plasma with an 6-8 ps laser pulse of only 1 J energy impinging at a grazing incidence angle of 23 degrees. The experiments were conducted using a table-top 5 Hz repetition rate 800 nm Ti:Sapphire pump laser system, consisting of a mode-locked oscillator and three stages of chirped pulse amplification. The soft x-ray laser amplifier consisted of a line focus plasma of up to 4 mm in length generated by exciting polished slab targets with a sequence of an early prepulse of 120 ps duration and 10-15 mJ energy, followed after about 5 ns by a main prepulse of the same duration and ~350 mJ energy, which in turn was followed after a variable delay –typically 100 ps to a few 100s ps- by a 8 ps duration, ~ 1 J energy heating pulse that rapidly heats the plasma creating a transient population inversion and gain in transitions of Ni-like ions. Overlapping line foci of 30 µm × 4.1 mm FWHM were generated for the pre-pulse beam and short pulse pump beams that impinged onto the target at near normal incidence and at a selected grazing incidence angle of 23 degrees, respectively. The on-axis plasma emission was spectrally resolved using a variably spaced spherical grating and recorded with a backilluminated CCD detector. Figure 1 shows on-axis spectra corresponding to 4 mm long targets of Ru (Z=44), Pd (Z=46), Ag (Z=47), Cd (Z=48), Sn (Z=50), Sb (Z=51) and Te (Z=52) that are dominated by the 4d1S0 – 4p1P1 laser line of the corresponding Ni-like ions at wavelengths between 16.9 nm and 10.9 nm respectively. Gain measurements were performed on Ni-like Cd plasmas by

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Fig. 1. Single shot on-axis spectra of 4 mm line focus plasmas showing lasing in the 4d1S0- 4p1P1 transition of the Ni-like ions at wavelengths ranging from 16.5 to 10.9 nm. The laser lines completely dominate the spectrum except in the case of Ni-like Te. Lasers down to 13.2 nm are saturated.

monitoring the variation of the 13.2 nm laser line intensity as a function of target length. The results are shown in Fig. 2. The laser line intensity is observed to increase exponentially with an small signal gain coefficient of69 cm-1, until it rolls off into saturation. A fit of the data yields a gainlength product of g×l =17.6, value for which collisionally excited soft xray laser systems are normally in the gain-saturated regime. The laser pulse energy was estimated from the counts on the CCD taking into account the quantum efficiency of the detector and the losses. The energy of the most intense 13.2 nm shots obtained with a 4 mm target are estimated to exceed 430 nJ. The intensity of the Ni-like Cd laser is estimated to be about 1.6×1010 W/cm2, a value that exceeds the computed saturation inten-

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Fig. 2. Intensity versus target length for the 13.2 nm line of Ni-like Cd. The solid triangles represent the average of the points shown. The fit corresponds to a small signal gain of 69 cm-1 and a gain-length product of 17.6. The dark triangles are the average of about 10 laser shots.

sity of 0.6-0.8×1010 W/cm2 for this laser line at the plasma conditions of this experiment. Figure 3 illustrates continuous 5Hz repetition rate operation of the Nilike 13.9 nm Ag laser for 250 shots. The data was obtained moving the target at a velocity of 0.2 mm/s. Lasing is observed in all shots, with an intensity variation characterized by a standard deviation of ~ 30% of the mean. The 13.9 nm laser average power approaches 2 µW. Measurements for Ni-like Ag at a grazing incidence pumping angle of 23 degrees for the optimum delay of 300 ps have yielded further increases in the laser output intensity, generating pulses with an energy up to 0.85 µJ. The shortest wavelength line for which amplification to gain-saturation levels was achieved was the 11.9 nm line of Ni-like Sn. The variation of the 11.9 nm laser line intensity as a function of plasma column length was measured using a main pre-pulse energy of ~ 350 mJ and a short pulse energy of ~ 1 J at a grazing incidence angle of 23 degrees. For an optimum delay of 125 ps the gain coefficient was measured to be 50 cm-1, and a gain length product of g×l=14.3, value for which the onset of gain saturation effects was observed. The most intense 11.9 nm laser pulses were measured to have an energy of ~ 230 nJ. To demonstrate lasing in Ni-like Sb and Nilike Te we reduced the FWHM length of the short pulse line focus to 3.5 mm, to increase the irradiation intensity up to 1.2×1014 W/cm2. While the main focus of the work reported herein is the high repetition rate generation of gain-saturated soft x-ray laser radiation at wavelength shorter than 16.5 nm, we also re-visited the generation of 18.9 nm laser light from Ni-

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like Mo ions by grazing incidence pumping. We conducted a new Ni-like Mo laser experiment at a grazing incidence pumping angle of 20 degrees using 1 J of short pulse (~8 ps duration) excitation and the calibrated filters.A series of shots made using a 4 mm long Mo slab target yielded an average 18.9 nm laser pulse energy of 1 µJ, with the most intense pulses reaching 1.4 µJ. Saturated laser operation at 5 Hz repetition rate with gainlength products of about 20 was also obtained for transition of Ne-like Ti and V with wavelength near 30 nm [11], with resulting average powers of about 1.5 to 2.5 µW.

2 Demonstration of high brightness soft x-ray beam by high harmonic seeding of a solid target transient collisional amplifier The output beam characteristics and peak spectral brightness of these lasers can be greatly improved by seeding of the amplifiers with high harmonic pulses. The high coherence, short pulse duration, low divergence, and defined polarization of the seed pulse can be imprinted in the amplifier output. In addition, the seeding can shorten the soft x-ray laser output pulse width to values approaching the limit set by the amplifier linewidth. This short pulse duration combined with the high energy stored in this type of soft x-ray amplifiers can result in table-top sources of unprecedented brightness. Saturated amplification of the 25th harmonic of a Ti:Sa laser was recently demonstrated in a 32.8 nm Ni-like Kr optical field ionization (OFI) soft x-ray laser amplifier [12]. However, the relatively low plasma density at which optimum lasing occurs in these OFI lasers results in a

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relatively low saturation intensity, that will ultimately limit the maximum brightness. The high electron density of soft x-ray laser amplifiers based on solid targets results in a higher saturation intensity and a broader laser linewidth, opening a route to higher soft x-ray laser pulse intensities and shorter pulsewidths. An early experiment performed in a Ne-like Ga plasma amplifier pumped by overlapping three 200 J optical laser beams onto a solid gallium target demonstrated the amplification of the harmonic seed, but only by a factor of about 3× [13]. More recently, a Ne-like Mn soft x-ray laser amplifier was reported to amplify a high harmonics seed from 4.7 pJ to 3 nJ [14]; We report the first demonstration of saturated amplification of a high harmonic seed in the high density plasma of a transient collisional soft xray laser created by heating a solid target. A 32.6 nm table-top soft x-ray laser amplifier operating in the 3p1S0→3s1P1 line of Ne-like Ti at 5 Hz repetition rate [11] was used to amplify a seed pulse from the 25th harmonic of Ti:Sa laser into the gain saturation regime. The 27th harmonic of Ti:Sa was simultaneously amplified in the 30.1 nm 3d1P1→3p1P1 line of Ne-like Ti in the same plasma. This seeding is scalable to produce extremely bright lasers at very short wavelength. We demonstrated that the resulting soft x-ray beam is essentially fully spatially coherent. Below we discuss the measurements in comparison with modelling results that describe the dynamics of seeded amplification in a dense collisionally pumped soft x-ray laser amplifier. The model simulations indicate the soft x-ray laser pulses are sub-picosecond in duration. The results were obtained with a table-top laser operating at a repetition rate of 5 Hz, showing this is a practical scheme to produce extremely high brightness soft x-ray beams for applications in a small laboratory environment. The experimental set up is schematically illustrated in Fig. 4. A single table-top Ti:Sa laser chirped pulse amplification laser system (λ = 800 nm) driver was used both to create the harmonic seed pulse, and the soft x-ray laser amplifier. High harmonic pulses of a few nJ energy are generated using 20 mJ drive pulses compressed to ~ 50 fs. These pulses were focused by a 5 m focal length lens into an 8.8 cm long gas cell filled with 5 Torr of argon. The center wavelength of the 25th harmonic was matched to the 32.6 nm wavelength of the highest gain laser line in the Ti amplifier by adjust ing the compressor. The 0.5-1 nJ harmonic seed pulses exiting the gas cell were relay imaged onto a ~ 100 µm diameter spot at the entrance of the soft x-ray plasma amplifier using a toroidal mirror. Figure 5 illustrates the dramatic increase in the output of a 3 mm long

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Fig. 5. Spectra illustrating the relative intensity and beam divergence for; a) unseeded 32.6 nm soft x-ray laser amplifier; b) high harmonic seed pulse; c) seeded soft x-ray laser amplifier. The length of the plasma amplifier is 3 mm. The intensity scale of the seed pulse is magnified by 10 times.

32.6 nm Ne-like Ti amplifier and the large decrease in the beam diver gence achieved by seeding the amplifier. The top frame (5a) shows the spectra of the un-seeded Ti soft x- ray laser amplifier, and the corresponding intensity distribution in the direction parallel to the target. The laser line at 32.6 nm dominates the spectra and has a divergence of about 10 mrad. Fig. 5b shows the much lower divergence, about 1 mrad, but significantly broader spectra of the harmonic seed. The seeded ampli-

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fier output shown in Fig. 5c consists of a highly monochromatic spectral line with an energy that is ~ 64 times larger that of the seed pulse. The FWHM beam divergence is observed to be about 2.2 mrad, much smaller than that of the un-seeded laser. We also observed that it is possible to simultaneously inject seed the 32.6 nm and 30.1 nm lines of Ne-like Ti with the 25th and 27th harmonics. Figure 6 illustrates the measured increase of the energy of the 32.6 nm seed pulse as a function of amplifier length for a time delay of 4 ps. The data was obtained by varying the length of the target between 0 and 4 mm while maintaining both the seed pulse and the amplifier pump excitation conditions constant. The measurements are compared with the results of

Fig. 6. Measured and computed (continuous line) variation of the intensity of the amplified seed pulse as a function of plasma amplifier length for the 32.6 nm line of Ne-like Ti. The measured beam reaches the saturation intensity after ~ 2.5 mm into the plasma

model simulations in the same figure. The simulations were conducted using a 1½ dimension hydrodynamic/atomic physics code with multi-cell radiation transport to compute the evolution of the gain and plasma density profile of the Ne-like Ti amplifier [16]. The propagation and amplification of a 0.7 nJ seed pulse was computed using a ray tracing post processor code taking into account the effects of gain narrowing and gain saturation. The experimentally measured amplification behaviour is very similar to that predicted by the code, and can be divided into three distinct phases. The first phase, which takes place in the first ~1 mm of the amplifier, is dominated by the gain narrowing of the seed pulse which initial 0.1 nm spectral bandwidth greatly exceeds that of the laser line. This leads to the amplification of only a fraction of its bandwidth, resulting in the observed

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slow initial seed pulse energy increase. When the seed pulse bandwidth narrows sufficiently to approach the laser linewidth, a second amplification phase starts in which a quasi-exponential increase in the energy of the seed pulse takes place. This rapid increase ends after about 2.5 mm into the amplifier, when the amplified seed pulse reaches the saturation intensity of the 32.6 nm Ne-like Ti line. The third amplification phase corresponds to the gain saturated regime in which efficient energy extraction occurs. The a)

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Fig. 7. Results of Young’s slit pair interference experiment for the output of the seeded 32.6 nm laser amplifier. a-d) Interferograms and their lineouts for the slit separation indicated. e) Plot of the degree of coherence as a function of the slit separation

maximum measured amplified seed pulse energy, 50-60 nJ, is similar to that predicted by the model. The model simulation of the pulse propagation in the amplifier predicts a pulse duration of 0.5-0.8 ps determined by the gain-narrowed bandwidth of the amplified laser transition, which is an order of magnitude shorter than the amplifier gain lifetime.

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We have measured the variation of the intensity of the amplified seed pulse as a function of delay between the 6.7 ps pump pulse and the arrival of the harmonic seed pulse. The time span during which the seed pulse is amplified is determined by the duration of the gain in the amplifier [15], and is about 5 ps. The maximum amplification is observed at delays between 2 and 4 ps. Measurements in grazing incidence transient collisional lasers have shown that the spatial coherence length is nearly an order of magnitude smaller than the beam diameter [8]. The results of a Young’s slit interference experiment illustrated in Fig. 7 show the degree of spatial coherence improves dramatically when the amplifier is seeded. Pairs of 5 µm wide slits separated by 30, 75, 150 and 200 µm were placed at 10 cm from the exit of the amplifier, a location at which the FWHM beam diameter is about 200 µm. The measured fringe visibility as a function of slit separation is illustrated in Fig. 7e. A fit of the data with a Gaussian profile yields a coherent length of Lc = 150 µm. The measurement shows the beam approaches full spatial coherence as the majority of beam energy falls within a coherent length. The equivalent incoherent source diameter of this laser is about 6.9 µm. Using the measured beam parameters mentioned above, and assuming a pulse duration of 0.5-0.8 ps and a horizontal divergence equal to half the vertical divergence, the peak spectral brightness of this source can be estimated to be 1.7-2.8×1026 photons/(s.mm2.mrad2 0.1% bandwidth). Moreover, it should be noticed that the linewidth of this laser is about 20 times narrower than the 0.1 % bandwidth used to specify the brightness of synchrotrons and free electron lasers, an advantage in applications requiring high photon flux in a narrow bandwidth. In conclusion, we have demonstrated a seeded solid target laser amplifier with high spatial and temporal coherence that is readily scalable to significantly shorter wavelengths and higher plasma densities, leading towards table-top soft xray sources of extremely high peak brightness.

Acknowledgments We would like to thank Henry Kapteyn, and Margaret Murnane for their contributions. This work was supported by the NSF ERC for Extreme Ultraviolet Science and Technology under NSF Award EEC-0310717

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References 1. B.R. Benware, et al., Phys. Rev. Lett. 81. 5804 (1998) 2. S. Sebban, et al, Phys. Rev. Lett. 86, 3004 (2001), and S. Sebban, et al., Phys. Rev. Lett. 89, 253901 (2002). 3. P.V. Nickles et al., Phys. Rev. Lett. 78, 2748 (1997). 4. J. Dunn, et al, Phys. Rev. Lett. 84, 4834 (2000). 5. V.N. Shlyaptsev, et al, Proc. of SPIE 5197, 221 (2003). 6. R. Keenan et al., Phys. Rev. Lett. 94, 103901, (2005) 7. B.M. Luther et al, Opt. Lett. 30, 165 (2005). 8. M. A. Larotonda et al, IEEE J. Sel. Top. Quantum Electr. 10, 1363, (2004); Y. Liu et al, unpublished. 9. Y. Wang et al., Phys. Rev. A, 72, 053807, (2005). 10. J.J. Rocca et al., Optics Letters 30, 2581, (2005). 11. D. Alessi et al, Opt. Express 13, 2093, (2005). 12. P. Zeitoun, et al, Nature 431, 426, (2004). 13. T. Ditmire et al, Phys. Rev. A 51, R4337, (1995). 14. T. Kawachi et al, SPIE Vol. 5919, 155, (2005). 15. T. Mocek et al, Phys. Rev. Lett. 95, 173902, (2005). 16. M. Berrill and J. J. Rocca, unpublished

On the Way Towards a High Repetition Rate X-Ray Laser K. A. Janulewicz1, J. Tümmler1, H.Stiel1, W. Sandner1, P.-V. Nickles1, H.T. Kim2, I.W. Choi2, N. Hafz2, J.H. Sung2, T.J. Yu2, K.-H. Hong2, T.M. Jeong2, D.- K. Ko2, J Lee2, I. J. Kim3 and C. H. Nam3 1

Max Born Institute, Max-Born_Str. 2A, D-12489 Berlin, Germany Advanced Photonics Research Institute of Gwangju Institute of Science and Technology, Gwangju, Republic of Korea 3 Korean Advanced Institute of Science and Technology, Deajon, Republic of Korea 2

Summary. A way towards a high repetition rate X-ray laser (XRL) is proposed. The proposal consists of analysis of the existing pump schemes for collisional Xray lasers and their development prospects. Most of the attention is devoted to a new laser driver working at a repetition rate of 100 Hz, being developed now at the Max Born Institute. The most important output parameters expected to be available from this laser system are discussed in detail. It is expected that such a laser could increase the average brightness of XRLs by about two orders of magnitude.

1 Introduction Present X-ray lasers offer the peak brightness between 1025 and 1027 photons×s-1×mm-2×mrad-2 contained in 0.1% of the bandwidth Bw. This makes them one of the brightest sources of short-wavelength radiation and places them in the lower range of the brightness of free-electron-lasers (FELs) working in the amplified spontaneous emission regime. While the peak brightness is at a high level the average brightness lags behind the values typical for radiation from synchrotrons of fourth generation. This results from the fact that until the appearance of the grazing incidence pumping (GRIP) geometry X-ray lasers worked dominantly as single-shot devices. The X-ray lasers pumped in the GRIP geometry achieved an average brightness of 1014 photons×s-1×mm-2×mrad-2/0.1%Bw [1]. It is expected that this value can increase in high-repetition rate XRLs up to 1016-1017 photons×s-1×mm-2×mrad-2/0.1%Bw

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Recent developments in the field of X-ray lasers caused reduction in the pump energy needed for saturation of Ni-like ions of moderate Z elements down to 1-2 J [2-5]. This energy is at the moment available from commercial lasers working at a repetition rate of 10 Hz and is sufficient to saturate most of the XRLs emitting between 10 and 60 nm. Deliberately modified commercial lasers systems based on Ti:sapphire technology can deliver the required energy in two pump pulses. At the moment there are only two XRL schemes working stably in saturation. Optical-field-ionized (OFI) X-ray lasers need rather high intensity than energy and a very short single pump pulse. Saturation in this scheme has been demonstrated at two wavelengths of 41.8 nm and 32.8 nm [6,7]. As low density gases used to be applied as an active medium the saturation parameter deciding about the energy extraction is very low (usually two orders of magnitude if compared to that of solid targets). Additionally, ionization induced refraction limits the length of the active medium and guiding is needed to overcome this limitation.

Fig. 1. The spatio-temporal distribution of the local again coefficient for two geometrical variants of irradiation: a) the heating pulse incident normally to the target surface, b) grazing incidence of the same pulse.

The second very robust pump scheme is the transient inversion scheme in the traditional and GRIP pump geometries. In this scheme two pulses irradiate a slab target. The first long (nanosecond) pulse creates a preformed (with ionization stage close to that required) plasma plume. The second one of picosecond length falls on the target either normally (traditional scheme) or obliquely under grazing angle 15° - 30° (GRIP) [8,9]. This incidence angle enables control over the energy deposition area in the plasma. This is exactly the advantage of this irradiation geometry. This is clearly seen in Fig.1 where the spatio-temporal distribution of the local gain coefficient is plotted for the normally (Fig.1a) and obliquely (Fig.1b)

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incident heating pulses of the same energy. The obliquely incident heating pulse generates a significantly larger area of a high local gain factor than this is the case for the normally incident laser beam. This pump arrangement, however, shows low energy extraction efficiency typical to all mirrorless lasers. The extraction process, to be effective, requires an input (to be amplified) signal at the level of the saturation factor (fluence or intensity). In XRLs a significant part of the amplifying medium has to be used to achieve this signal level and only a small part of the stored energy will be extracted by the pulse. This disadvantage can be removed in a scheme most frequently called injector-amplifier system. Such a scheme was investigated more than a decade ago using two X-ray lasers one as an injector and another one as an amplifying medium. Using such an arrangement a full spatial coherence has been demonstrated recently [10]. A very interested method has been proposed in 1996 [11]. It was suggested, that the use of easily applicable high harmonics as a seeding source could solve the injector problem The accompanying experiment succeed only partly. The same idea has revived and irrefutable amplification with a significant gain factor of the seeding signal was demonstrated by using OFI XRL as the amplifying medium at 32.8 nm [12]. The amplification system working with seeding by a single high harmonic is a very challenging task. The essential problem is a mismatch between the broad bandwidth of the seeder and a limited bandwidth of the amplifying medium. In the best case this is a difference by a factor of 10. This means that a lot of the energy contained in the seeding pulse will be not amplified during the transition through an amplifier. Moreover, such a relation suggests that the polarisation decay time in the amplifying medium can be much longer than the seeding pulse. It is well known that then we can deal with a specific, so called, coherent amplification of the seeded pulse. This process, in contrast to the classic incoherent amplification, is related rather to intensity than to energy. The difference and consequences are described in [13]. In a nutshell, in the coherent amplification the very short seeding pulse can be split into many lobes (in the extreme case intoquasi-pulses) and the strongest of them will increase significantly its intensity but only in a limited way its energy. The extraction efficiency will be heavily reduced in comparison to that of the incoherent process, i.e. when the seed pulse is longer than the polarization decay time of the amplifying medium. All experiments conducted so far suggest exactly the coherent amplification scenario. Even in the saturated regime the output energy was at least one order of magnitude lower than those obtained from a

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Fig. 2. The idea of seeding with high harmonics an amplifying medium pumped in the GRIP geometry.

laser in the standard ASE regime. The extraction limitations in the incoherent regime are easily derivable from the known formula describing output energy fluence as a function of the input one:

E OUT = E S ln{1 + exp( g 0 l )[exp(E IN / E S ) − 1]}

If E IN >> E S then we obtain the maximum energy available in the extraction process E AVAIL = g 0VE S , where V is a volume of the active/amplifying medium. This means, that the saturation fluence and its relation to the input energy fluence determine the energy extractable from the medium. Simple estimates, assuming an amplifying medium with the dimensions 5 mm×20 µm×20µm and a volume of 2×10-6 cm3, show that the input energy fluence necessary for efficient energy extraction should correspond to the total energy about 100 nJ. This is at the moment not achievable in the spectral range of our interest between 10 and 20 nm.

2. MBI project Analysis of the situation and the development prospects caused the MBIgroup to pursue its own way towards a beamline-like facility available to external users. It was decided to focus the attention on Ni-like soft X-ray laser working at 13.9 nm. The expected output parameters are collected in Table 1. The work towards this final goal is organized in two topics. The first one is experimental work on the dynamics and kinetics of XRL active medium irradiated in

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Table 1 Output parameters of the 100 Hz XRL planned at MBI

Parameter Pulse length/repetition rate Wavelength Coherence (spat./longit.)

Energy Peak/average brightness/ ph/(s*mrad*mm2*0.1%Bw Linewidth

Injector - amplifier project ≤ 1 ps/ 100 Hz 10 - 20 nm full/~0.5 mm 0.1 mW ~ 5 - 10 µJ 1026 /1015 <10-4λ

the GRIP geometry, as well as preparation of a short-wavelength seeder. The second topic concentrates on construction of a new diode-laser pumped CPA Yb:YAG laser system with a repetition rate of 100 Hz as a pump device for a new class of high-repetition X-ray lasers. 2.1 MBI-APRI experiment The experimental part of the project was performed in a joint experiment of MBI-group and the group from Advanced Photonics Research Institute in Gwangju (South Korea) and the Korean Advanced Institute of Technology in Daejon (South Korea).

Fig. 3. Dependence of the local gain coefficient on the medium length. Two different variants of the estimate are shown demonstrating how critical is the choice of the points included in the approximation if a significant jitter of the measurement points exists.

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A nominally 100 TW Ti:sapphire laser delivered pump energy on the slab target in two pulses. The first, long pulse with a length of 350 ps irradiated the target normally to its surface, focused into a line of 7 mm length and 30-40 µm width. The energy of the pulse was equal to 500 mJ. This laser pulse created pre-plasma which was subsequently irradiated after some optimized delay (here 300 ps) by a short, 8 ps long heating pulse focused to a line of similar dimensions but falling onto the target under a grazing angle of 18 degrees. These values give linear fluence on the target of 70 and 200 mJ in long and short pulses, respectively. These values are lower than those reported for the normally incident beams but one should bear in mind that the irradiated surface is also significantly smaller. The local gain coefficients as a function of the target length are shown in Fig.3 and Fig.4. The latter has been obtained under irradiation with only single

Fig. 4. Local gain coefficient as a function of the medium length. Two different choices of the measurement point are shown and the corresponding estimates of the small-signal gain coefficients are given.

short pulse using the spontaneous emission of the laser system and a parasitic pre-pulse to create the pre-plasma. It is seen from Fig.3 und Fig. 4 that the medium irradiated (pumped) with a single pulse gives more smooth dependence of the gain coefficient on the target length. This is not surprising as the pointing effect disturbing overlapping of both pump beams is in this case eliminated. The same effect can be responsible for the reduced gain in the case of double-pulse irradiation. In contrast, the output energy is equal to 1.2 µJ and 1.5 µJ for the single- and double-pulse irradiation, respectively. The pre-forming laser pulse of the double scheme is more energetic than background of the single pulse and it gives for this reason larger emitting volume.

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Trying to understand the physics behind the processes leading to the effects described, we have modelled the interaction of the pump radiation with a slab silver target. The results for the case of double-pass irradiation are shown in Fig.5.

Fig. 5. 3D plot showing distribution of the local gain coefficient in spatiotemporal coordinates.

The local (without correction due to refraction) gain coefficient is very high but limited to a narrow strip close to the original target surface. The significant gain factor lasts only about 20 ps. An area of very strong absorption is created directly in the neighborhood of the target after 40 ps from the arrival of the heating pulse. This is caused by a high plasma density and low electron temperature in this area. The latter is a result of very efficient cooling by thermal conduction to the bulk material of a massive target. The narrow area of the significant gain could be a problem in beam propagation and the energy extraction. However, the 1.5D numerical code used in modelling is less exact for the focusing conditions applied in the experiment. The footprint recorded in the experiment indicated rather good propagation conditions showing a regular round profile.

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Fig. 6. Harmonic spectrum obtained by irradiation with a Ti:sapphire laser of a gas-puff ejecting Ne from a round nozzle of 1 mm diameter

Fig. 7. Harmonic spectrum obtained by irradiation with a Ti:sapphire laser of a gas-puff ejecting Ne from a slit-nozzle of 5 mm length.

One of the fundamental problems in seeding of such an amplifying medium is matching of the seeder radiation to the conditions of the amplifier. There is a big bandwidth mismatch which can be reduced but not fully removed. Some hope for improvement is connected with strong gain narrowing during unsaturated amplification. However, then the energy extraction efficiency will decrease dramatically. The extraction efficiency needs, to be maximized, a seeding signal at the level of the saturation fluence, i.e.

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with an energy about 100 nJ. This is a serious challenge at the spectral range below 20 nm. On the other hand, a precise control over the central wavelength of the injected seeder radiation has to assure overlapping of the peaks of the seeder and gain spectrums. To check such a possibility we generated high harmonics in neon using a gas-puff valve delivered by IOP MUT Warsaw. There was possible to use either a round nozzle or a slit with a length of 5 mm. The backing pressure was changed between 1.5 and 6 bar and the valve was mounted in a vacuum chamber and positioned with a 4-axis (XYZ+angle) manipulator. This mechanics, positioning of the focusing mirror and changing the distance between the compressor diffraction gratings enabled a reasonable control over the chirp of the pump radiation and the same over the spectral characteristics of the generated high harmonics. The results, in a form of the spectrums of generated high harmonics for the round and slit nozzles are shown in Fig.6 and Fig.7, respectively. The recorded spectra have a limited resolution as a combination of a multi-channel plate and a CCD camera was used as a detector. Rough estimates gave seed energy lower than 1 nJ but perfectly matching the centre of the gain spectral bandwidth. It was also clearly observed that elongated gas medium is much more efficient in the production of higher harmonics. The nozzle position relative to the focus of the pump beam seems to be equally important for the conversion efficiency as the shift of the compressor gratings. Changing the former parameter it was possible to obtain an uniform (over a length of many millimeters) source of high harmonics. This was recorded by lateral observation of the breakdown in the gas medium irradiated with a pump laser pulses. 2.2 New high-repetition-rate laser driver for XRL While the peak brightness of an XRL situates it among the brightest XUV sources, there is some need to improve the XRL position regarding the average brightness. This goal requires a new high-repetition-rate laser sources working with output energies at least about 1 J and pulse lengths between 1 and 10 ps. Such a parameter set requires the newest technology and no laser of these energetic parameters has been demonstrated with a repetition rate higher than 10 Hz. Our aim is to build such a laser working with a repetition rate of 100 Hz. The project is supported within the EU EFRE Program and funded by the government of Berlin in a form of ProFIT Project. Ferdinand Braun Institute in Berlin is a project partner and develops new efficient diode lasers to pump active material of the new laser driver. The laser

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itself will be built in collaboration with IFSW (Institut für Strahlwerkzeuge) from the University of Stuttgart. It was decided that the thin disk technology with Yb:YAG as an active material will be applied in the amplifier heads. This technology developed originally for high power and

Fig. 8. Top view of a laser amplifier head based on the thin disk technology. (Courtesy of A. Giesen, IFSW Stuttgart)

continuous-wave lasers [14] will be adopted for the first time to the lasers with less frequent but much more energetic pulses. An example of such a diode-laser-pumped amplifier module is presented in Fig.8. The thin disk technology takes the advantage of a very efficient heat sink as the temperature gradients are directed along the propagation direction of the amplified pulse. Thus, a very destructive thermal lens effect can be dramatically reduced. This advantage is realised at the cost of a low gain during a single radiation transit through the medium. In spite of this, due to very efficient spectrally matched pumping the conversion efficiency from the pump into the output radiation is very high and achieves 30 %. It is expected that the developed laser will achieve after the first part of the project an energy of 200 mJ in a long (200 ps) laser pulse and an energy of 500 mJ in a short (5 – 6 ps) laser pulse. The output energies of both beams will be doubled in the second phase of the project, foreseen for 2008.

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Acknowledgments This work was supported by a ProFIT project of Berlin government within the EU EFREM Program, by the governmental German-Korean bilateral Collaboration Program and by the Ministry of Commerce, Industry and Energy of Korea through the Industrial Technology Infrastructure Building Program.

References 1. Y. Wang et al., Phys. Rev. A, 72, 053807, (2005). 2. R. Keenan, J. Dunn, P.K. Patel, D.F. Price, R.F. Smith, and V.N. Shlyaptsev, Phys. Rev. Lett., 94, 103901, 2005 3. J. Dunn and Y. Li and A. L. Osterheld and J. Nilsen, J. R. Hunter and V. N. Shlyaptsev, Phys. Rev. Lett., 84, 4834, 2000. 4. B. M. Luther, Y. Wang, M. A. Larotonda, D. Alessi, M. Berrill, M. C. Marconi, J. J. Rocca, and V. N. Shlyaptsev, Opt. Lett., 30, 165-167 (2005) 5. J. Tümmler, K.A. Janulewicz, G. Priebe, P.V. Nickles, Phys. Rev. E, 72, 037401, 2005. 6. S. Sebban, R. Haroutunian, Ph. Balcou, G. Grillon, A. Rousse, S. Kazamias, T. Marin, J. P. Rousseau, L. Notebaert, M. Pittman, J. P. Chambaret, A. Antonetti, D. Hulin, D. Ros, A. Klisnick, A. Carillon, P. Jaeglé, G. Jamelot, and J. F. Wyart, Phys. Rev. Lett., 86, 3004, 2001 7. S. Sebban, T. Mocek, D. Ros, L. Upcraft, Ph. Balcou, R. Haroutunian, G. Grillon, B. Rus, A. Klisnick, A. Carillon, G. Jamelot, C. Valentin, A. Rousse, J. P. Rousseau, L. Notebaert, M. Pittman, and D. Hulin, Phys. Rev. Lett., 89, 253901, 2002 8. V.N. Shlyaptsev, J. Dunn, S. Moon, R. Smith, R. Keenan, J. Nilsen, K.B.Fournier, J. Kuba, A.L. Osterheld, J.J. Rocca, B. Luther, Y. Wang, and M. Marconi, Proc. SPIE, 5197, 221, 2003 9. R. Keenan, J. Dunn, V.N. Shlyaptsev, R.F. Smith, P.K. Patel, and D.F. Price, Proc. SPIE, 5197, 213, 2003. 10. M. Nishikino, M. Tanaka, K. Nagashima, M. Kishimoto, M. Kado, T. Kawachi, K. Sukegawa, Y. Ochi, N. Hasegawa, and Y. Kato , Phys. Rev. A, 68, 061802, 2003. 11. T. Ditmire et al., Phys. Rev. A, 51, R4337, 1995. 13. Ph. Zeitoun, G. Faivre, S. Sebban, T. Mocek, A. Hallou, M. Fajardo, D. Aubert, Ph. Balcou1, F. Burgy, D. Douillet, S. Kazamias, G. de Lache`ze-Murel, T. Lefrou, S. le Pape, P. Mercere, H. Merdji, A. S. Morlens, J. P. Rousseau, C. Valentin, Nature, 431, 426, 2004. 12. E. Armandillo and I. J. Spalding, J. Phys. D: Appl. Phys., 8, 2123, 1975 14. A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, H. Opower, Appl. Phys. B, 58, 365, 1994

A 10 Hz, 3 Microjoule Transient Soft X-Ray Laser Pumped in Grazing Incidence S. Kazamias, K. Cassou, D. Ros, F. Plé, G. Jamelot, A. Klisnick LIXAM, UMR 8624, Université Paris XI, F-91405 Orsay Cedex, France, O. Lundh, F. Lindau, A. Persson, C.-G. Wahlström Department of Physics, Lund University, S-22100 Lund, Sweden S. de Rossi, D. Joyeux Laboratoire Charles Fabry (IOTA), F-91405 Orsay Cedex, France B. Zielbauer, D. Ursescu, T. Kühl Gesellschaft für Schwerionenforschung (GSI), D-64291, Germany

Summary. We present recent results on the extensive investigation of a Ni-like Mo X-ray laser pumped in the transient regime and GRIP configuration (grazing incidence pumping). The pump laser was the 10 Hz, multiterawatt, Ti:Sa Lund University laser system in Sweden. The main diagnostic was a monochromatic near-field imaging system with a 1.7 micron spatial resolution. Intense lasing was observed routinely at 18.9 nm with up to 3 microJoule output energy and stable operation at 10 Hz was demonstrated in 100-shot sequences. We have investigated the role of several pumping parameters, in particular the relative energy and delay between the long and short pulse. A preliminary investigation was done on the effect of a low energy prepulse. Finally, the grazing angle of the pumping pulse was systematically varied between 13 and 21°, while keeping all parameters constant. We show that this multi-parameter scan leads to a well-defined optimal zone of operation and better understanding of the GRIP configuration.

1 Introduction The soft X-ray laser research field is currently experiencing a rapid development since the first demonstration of a transient soft X-ray laser from solid target by Keenan et al [1] who used a high repetition rate Ti:Sa laser as the pump laser. They also showed the advantage of the so-called GRIP

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configuration for which the plasma is pumped at grazing incidence and the pump laser is refracted in the plasma. This first demonstration was followed by the work of other groups [2], [3], [4], [5] who obtained the saturation of different kind of soft-X-ray lasers at various wavelengths down to 13 nm. The idea of the GRIP configuration has theoretically many advantages over the normal incidence pumping [6]: the grazing angle is a new parameter that can be adjusted to match the energy deposition and plasma heating to the optimum zone for gain. As the density at which the energy is absorbed is reduced following the equation: ne= ncsin2φ where nc is the critical density and φ the grazing angle. At this lower density the density gradient is reduced and this should improve the propagation of the soft-X ray beam in the amplifying medium. It is now of a great importance to precisely investigate the effect of GRIP angle on the plasma and soft X-ray laser characteristics and to compare the results with detailed quantitative simulations. This will improve the physical understanding of GRIP systems, which is crucial for their optimization and their use as a source for applications. During an experimental campaign on the 10 Hz multiterawatt Ti:Sa laser system of the Lund Laser Center in Sweden, we used the GRIP configuration to produce a saturated soft X-ray laser at 18.9 nm from a Ni-like molybdenum plasma generated by a 4 mm solid target [7]. Thanks to a high spatial resolution near-field imaging of the soft X-ray laser source, we especially investigated in detail the effect of the GRIP angle on the soft Xray laser output characteristics such as for example integrated energy, vertical and horizontal size and emission distance from target surface. This was done for a large set of parameters such as the delay between the long and short pulse and their relative energy but also the existence of a small prepulse before the long pulse.

2 Experimental set-up and diagnostics A schematic view of the experimental set-up is presented in fig. 1. After the last amplification stage, the CPA Ti:Sa laser system of the Lund University delivers an energy of 1.4 J at 800 nm in a chirped, 300 ps pulse. This energy was split into two beams before it entered the compressor. One beam remained uncompressed (the so-called long pulse) to create the plasma and the other beam (the so-called short pulse) was compressed down to 5 ps to heat the plasma and pump the soft X-ray laser transition. The splitting ratio between the two pulses was adjustable to optimize the

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soft X-ray laser output. We found that the best condition corresponded to 480 mJ and 500 mJ energy on target for the long and short pulse respectively. A low-energy pre-pulse generator was installed on the long pulse beam path. For most of the experiment, the pre-pulse preceded the long pulse by 1.3 ns and contained 7 % of its energy. All of those beams were line-focused in line on a 4 mm long molybdenum slab target.

Fig. 1. Experimental set-up showing the pump laser beamlines and diagnostics used to characterize the soft X-ray laser.

2.1 Focusing systems for the long and short pulses The focusing system for the long pulse was composed of the combination of one cylindrical (f = -4 m) and one spherical (f = 1 m) lens. The position of the latter was finely adjusted to control the width of the focal line. The length of the line focus was around 6 mm and led to irradiance on target of 5×1010 W/cm2 and 3.8×1011 W/cm2 for the pre-pulse and long pulse respectively. The focusing system for the short pulse incident on target at grazing incidence was simply composed of a spherical mirror (f = 650 mm) for which the incidence angle was adjustable under vacuum between 6.5 and 10.5° to lead to a GRIP angle range on target of 13 to 21°. This configuration produces automatically a travelling wave with a velocity very close to the speed of light c, for the angular range investigated. The

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focal line length increases linearly with the GRIP angle, between 5 to 9 mm in our case, whereas the width is approximately 40 microns. An important point is that the position of this mirror together with the one of the 45° mirror before it (see fig. 1) was also adjustable under vacuum to maintain the target position and direction always constant while changing the GRIP angle. The superposition and shape of the focused beams was controlled by an imaging microscope device with a resolution around 3 microns. The delay between the long and short pulses was adjustable under vacuum from 100 to 800 ps with 100 ps time steps, thanks to a delay line placed on the long pulse beam path. This set-up conception is different from the one presented for example in reference [2] where the GRIP angle was varied by rotating the target. We believe that our configuration leads to a better quality focusing and superposition of the focal lines but also allows the installation of more accurate diagnostics of the plasma and soft X-ray laser. 2.2 Soft X-ray laser near-field and plasma diagnostics The diagnostics shown in fig.1 consisted first of a 2D XUV near-field imaging system composed of a f= 500 mm multilayer spherical mirror coated for spectral selection at the soft X-ray laser wavelength (IOTA design and manufacturing). To get a very high spatial resolution with low astigmatism, the mirror is used at the minimum available incidence angle (0.7°) to allow the beam redirection by a flat mirror placed at the center of the vacuum chamber. After more than 4 meter propagation, the magnified image of the soft X-ray laser source placed at the exit plane of the plasma is detected on a calibrated 16-bit back thinned XUV charge coupled device (CCD) camera. The resolution given by the system is 1.7 µm and corresponds to a magnification factor of 7.6. A set of aluminum filters with different thicknesses between 1 and 6 µm is placed on the XUV path to adjust the signal level. The 6 µm filter was used in most of the experimental configurations, indicating in itself a high signal level for the soft X-ray laser output energy. The recorded images were carefully analyzed to get as much information as possible. The physical quantities that could be extracted were the integrated energy, the horizontal and vertical widths (FWHM) of the soft X-ray laser (SXRL) source, and its position to the target surface. The mean fluence of the SXRL in the emitting pupil can also be directly calculated. The second diagnostic is a pinhole imaging of the keV emission of the plasma, viewed from above. This diagnostic was developed by the GSI group and is described in detail in another paper in these proceedings [8].

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3 GRIP angle effect The 10 Hz operation of this soft X-ray laser is a unique opportunity to perform complete series of multidimensional parameter optimization. It also allows for a statistical analysis of the shot-to-shot fluctuations, which was impossible to carry out using lower repetition rate pump lasers. This will for sure lead to a better and faster understanding of this kind of physical systems.

Fig. 2. Mean soft X-ray laser fluence (solid line) and distance to target surface of the emission peak (dashed line), as a function of the GRIP angle φ.

Fig. 2 presents the most significant result concerning the effect of the grazing angle on the soft X-ray laser emission. Each data point plotted is an average over at least 10 shots acquired in the same experimental conditions. The delay between the long and short pulse was 400 ps which was observed to be optimum or close to optimum for all investigated GRIP angles. The mean output fluence shows a clear optimum for 19 ° GRIP angle and reaches 0.33 J/cm2, which corresponds to an integrated energy of 3 µJ. The distance of the source from the target surface also varies significantly with the GRIP angle: it decreases from 50 to 35 microns for small angles between 15 and 19°and then increases around 50 microns for larger ones. This trend is expected as the pump laser beam penetrates deeper in the

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plasma and is absorbed at a higher electron density for increasing GRIP angle. The absorption density is ~ 1.8. 1020 cm-3 for 19° following ne= ncsin2φ. Above the optimum value, the soft X-ray laser source aperture is shifted to larger distances. This can be understood by the existence of a steeper density gradient in the absorption region, leading to stronger refraction of the XUV beam. The GRIP angle optimization is thus a compromise between absorption at high electron density and low electron density gradient.

4 Influence of the delay between long and short pulse Fig. 3 shows the behavior of the soft X-ray laser source for a fixed GRIP angle of 19°, as a function of the delay between the short and long pulse.

Fig. 3. Soft X-ray laser output energy, fluence, vertical and horizontal size as a function of delay between the short and long pulse.

As was mentioned above, the soft X-ray laser output energy is optimized for a 400 ps delay but due to spatial effects, the SXRL fluence is optimized for a smaller delay. The horizontal and vertical sizes of the source behave differently with respect to the delay: whereas the horizontal width does not change significantly, the vertical one increases rapidly until 400 ps, then reaches a constant value close to the short pulse line focus width. This shows the importance of 2D plasma effects that have to be further analyzed and simulated quantitatively [9].

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5 Prepulse effect: preliminary results We set a pre-pulse generator in the long pulse delay line to vary both delay and balance between the pre-pulse and long pulse. The effect of using a double pulse to create the preplasma has already been studied by a large number of groups [10, 11] and is widely known to increase the soft X-ray laser emission and to reduce the electron density gradient in the gain region. As reported before [5], the GRIP optimization is very sensitive to the plasma density distribution in the subcritical region at which the short laser pulse energy is mainly absorbed and refracted. The images of fig. 4 show the dramatic effect of the low pre-pulse on the soft X-ray laser source energy and size.

Fig. 4. Near field images, φ = 19°: a) prepulse (PP)-long pulse (LP) delay 1.3 ns ;b) doubled energy in the PP and PP-LP delay 2.4 ns.

The reference case is shown in Fig. 4a and corresponds to the maximum output energy of 3 uJ at the 19° GRIP angle. The energy distribution in the SXRL near-field is relatively smooth with 21×42 micrometer FWHM size. Fig. 4b shows the dramatic effect of varying the PP-LP delay from 1.3 ns to 2.4 ns, and doubling the PP energy level. This leads to a very small, nearly circular source of approximately 10 micrometer FWHM in diameter, containing 1 uJ and reaching a mean fluence close to 1 Jcm−2. This size reduction was observed routinely for the given parameters, and over a wide LP-SP delay range. The corresponding maximum theoretical transverse coherence length at the exit aperture inferred from the amplifier ge-

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ometry [12] is estimated to 8 micrometers. This leads to a transverse coherence length similar to the size of the SXRL source. This important result needs further experimental investigation and detailed simulations to understand with more accuracy the effect of the pre-pulse parameter variation. .

6 Conclusion For the best conditions, a soft X-ray laser beam with a of 3 uJ output energy was obtained routinely at a 10 Hz repetition rate: this corresponds to a conversion efficiency of 3.10-6 and an average power of 30 microwatt. The brightness of this XUV source can be estimated by assuming usual values for the pulse duration and bandwidth [10]. It is of the order of 6. 1017 ph/s/mm2/mrd2/(0.1% bandwidth) for the average value and up to 1028 ph/s/mm2/mrd2/0.1% bandwidth for the peak one. Those values confirm that GRIP soft X-ray lasers can usefully complement third generation synchrotrons or X-ray free electron laser sources. The LASERIX facility of the Paris XI University (see Ros et al. in this proceedings [13]) will be based on soft X-ray lasers pumped in GRIP configuration. Following the users needs and the pump laser characteristics, this installation will be able to deliver either a 10 Hz multi-microjoule level XUV source, or a 0.1 Hz source with tens of uJ. In the next future, we plan to explore a larger wavelength range for the available soft X-ray sources and to perform the harmonic seeding of those amplifiers. We expect then shorter pulse duration and almost full spatial coherence that are very important characteristics for a large range of applications.

Acknowledgements This work was supported by the Swedish Research Council, the Knut and Alice Wallenberg Foundation and through the EU Access to Research Infrastructures activity (contract RII3-CT-2003-506350, Laserlab Europe)

References 1.Keenan R., et al. “High-Repetition-Rate Grazing-Incidence Pumped X-ray Laser Operating at 18.9 nm”, Phys. Rev Lett 94, 103901 (2005)

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2. Luther B.M., et al. “Saturated high-repetition-rate 18.9-nm tabletop laser in nickellike molybdenum”, Opt. Lett. 30, 165 (2005) 3. Wang Y., et al. “Demonstration of high-repetition-rate tabletop soft-X-ray lasers with saturated output at wavelengths down to 13.9 nm and gain down to 10.9 nm”, Phys Rev A 72, 053807 (2005) 4. Weith A., et al. “Continuous high-repetition-rate operation of collisional soft-Xray lasers with solid targets”, Opt. Lett. 31, 1994 (2006) 5. Tümmler J., et al. “10-Hz grazing–incidence pumped Ni-like Mo X-ray laser,“ Phys. Rev. E 72, 037401 (2005) 6. Pert G.J., “Optimizing the performance of nickel-like collisionally pumped Xray lasers”, Phys Rev A 73, 033809 (2006) 7. Cassou K, et al. Opt. Lett to be published (2006) 8. Zielbauer B., et al. proceeding in this book 9. Cassou K., et al. Phys Rev A to be published (2006) 10. Lu, P,. et al. “Spatial coherence of prepulse-induced neonlike X-ray lasers”, Phys. Rev. A, 58, 628 (1998) 11. Balmer, J.E. et al. “Saturation in Neon- and Nickel-Like Collisional Soft-Xray Lasers at Low Pump Energy” IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, 5, 1435 (1999) 12. Guilbaud O., et al. “Origin of microstructures in picosecond X-ray laser beams”, Europhys. Lett. 74, 823 (2006) 13. Ros D., et al. proceeding in this book

Generation of Ni-like Ag X-Ray Laser and High-Order Harmonics Forward Harmonic Seeded X-Ray Laser H. T. Kim1, I. W. Choi1, N. Hafz1, J. H. Sung1, T. J. Yu1, K. –H. Hong1, T. M. Jung1, J. –H. Kim1, Y. -C. Noh1, D. -K. Ko1, J. Tümmler2, P.V. Nickles2, K. A. Janulewicz2 and J. Lee1 1

Femtoscience Lab., Advanced Photonics Research Institute, GIST, Oryongdong 1, Bukgu, GwangJu, Korea. 2 Max Born Institute, Max-Born-Strasse 2A, D-12489 Berlin, Germany.

Summary. Harmonic seeded x-ray laser beccame a key issue in x-ray laser development to obtain a high-flux, short-pulse good-quality soft x-ray source. Recently, we succeeded in generation of coherent radiation from a Ni-like Ag x-ray laser and separately from high-order harmonics at the same wavelengths. In this proceeding, we report progress and the development lines of such an coherent X-ray source at APRI based on harmonic seeded x-ray laser.

1 Introduction Coherent soft x-rays in form of intense laser pulses have become an important source of short-wavelength radiation, which can be applied to interferometry/holography [1], ultrafast x-ray spectroscopy [2] and different metrological techniques with high spatial resolution. X-ray laser (XRL) [3] and high-order harmonic generation [4] are two different sources of coherent soft x-rays generated by interaction of intense laser pulses with matter. High-order harmonics have excellent properties such as ultrashort pulse duration [2], good coherence [1], and continuous wavelength tunability [5]. In spite of these unique features, high-order harmonics can not be applied to broad spectrum of applications in the wavelength region below 20 nm due to low conversion efficiency in this spectral range. On the other hand, x-ray lasers based on Ni-like ions of moderate Z and using transient collisional pumping scheme can generate sufficient number of XUV photons around 13 nm wavelengths. Recent progress in the x-ray laser research has caused reduction in the pump energy necessary for saturation of

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x-ray lasers and as a consequence, achieving the table-top scale of the devices. Specifically, high-repetition table-top x-ray lasers were demonstrated using the grazing-incidence pumping (GRIP) scheme [6], which can reduce necessary pumping energy for x-ray laser by optimizing absorption of laser energy in plasma medium. However, transient collisional x-ray lasers have not shown a beam quality good enough for many applications even if they have sufficient energy. Consequently, since x-ray lasers and high-order harmonics have their own advantages and disadvantages, combining advantages of these two techniques could be the best solution to obtaining high pulse energy and good beam quality for applications. In this proceeding, we report on the progress and plans of coherent soft x-ray radiation research in the Advanced Photonics Research Institute (APRI) based on x-ray laser development and high-order harmonic generation using a 100-TW Ti:sapphire laser. Recently, we obtained preliminary results on high-order harmonic generation and successfully developed Nilike silver x-ray laser. In sec 2, we describe 100-TW 10-Hz Ti:Sapphire laser system in APRI. The experimental results on x-ray laser development and high-order harmonic generation are described in sections 3 and 4, respectively. The summary is given in section 5. 2 100-TW 10-Hz Ti:Sapphire laser system in APRI The coherent x-ray generation using x-ray lasers and high-order harmonic generation was performed with a chirped-pulse amplification 100-TW Ti:sapphire laser operating at 10 Hz. Figure 1 shows the schematics of the 100-TW Ti:sapphire laser system in APRI. The laser system consisted of a femtosecond laser oscillator, a grating pulse stretcher, a regenerative amplifier, a pre-amplifier, two multi-pass power amplifiers and a grating pulse compressor. The laser oscillator generates 20-fs pulses with 6-nJ energy and laser pulses from the oscillator were stretched to about 350 ps by a grating pulse stretcher. The stretched pulse was then amplified in a regenerative amplifier with a 1-kHz repetition rate. The 0.8-mJ pulse from the regenerative amplifier was injected into a 4-pass pre-amplifier and its energy was boosted up to 50 mJ. The output pulse from the pre-amplifier was then injected into two multi-pass power amplifiers and reached an energy of 5.6 J. The amplified pulses were double-passed through two parallel gratings that have 1480 grooves/mm. After compression, the final laser output had an energy of 3.6 J and a pulse duration of 32 fs, reaching over 100 TW at 10 Hz. Recently, high-intense laser field interaction experiments are intensively being performed using this laser. The 100-TW 10-Hz laser system will be upgraded to PW-class laser system.

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Pump Laser 2

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3 Development of Ni-like Ag x-ray laser For x-ray laser development, we applied the GRIP geometry because it can maximize energy absorption using refraction on the density gradients in a plasma medium [6]. Both pump pulses, a 300-ps 0.5-J pre-pulse and a 5-ps 1.5-J main heating laser pulse, delivered its energies into a 7.5 mm-long line focus. The obliquely (~72 degrees to the target normal) incident heating pulse was delayed about 300ps relative to the pre-pulse. The pre-pulse irradiates target normally to its surface. X-ray laser signal was detected by a flat-field soft x-ray spectrometer [7] equipped with a back-illuminated xray CCD. The scattered IR/visible light were blocked by Zr metal filters of different thickness. We saturated Ni-like silver x-ray laser pumped in the GRIP geometry. Figure 2 (a) shows x-ray laser output signal of the Ni-like x-ray laser as a function of the target length. The small-signal gain coefficient was estimated to be about 61 cm-1 when Linford formula was used to fit the averaged data points. Figure 2 (b) shows the foot print of x-ray laser beam measured at 55 cm from the X-ray laser exit. The spatial distribution of x-ray laser beam shows non-uniform structure and the divergence of this x-ray laser was around 4 mrad. To measure coherence of the x-ray laser, Young’s two-slit interferogram was obtained by installing a stainless-steel plate with a sequence of double-slits of different separation. The slits were positioned 84 mm behind the X-ray laser exit. The size of the x-ray laser beam was about 300 μm (full width at half maximum) at the position of the plate. Young’s two-slit interferometry demonstrated clear intereference pattern of the xray laser beam as shown in Fig 2 (c). In this case, the two slit was separated as 100 μm and the visibility of fringe was about 0.6. Consequently,

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we obtained a high-quality x-ray laser beam from a 7-mm silver target by using the GRIP geometry. 10000

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In addition, we succeeded in saturation of Ni-like Ag x-ray laser pumped by only single composite laser pulse from 10-Hz Ti:Sapphire laser system irradiating the target under a grazing angle. In same setup in GRIP geometry, The 300-ps pre-pulse present in the traditional GRIP geometry was removed and a main heating pulse was modified in its strucrure by controlling amplification processes in Ti:Sapphire laser system to drive the X-ray laser. Figure 3 shows the profile of controlled laser pulses and output spectrum of x-ray laser with controlling amplification of the laser system. The laser profiles were measured by a fast photo diode in front of the compressor. After compression, the controlled pulse is composed of three parts: a weak 8-ps laser pulse at around 4.5 ns before the main pulse, nano-

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second background and main heating pulse. The x-ray laser signal increased rapidly as shown in Fig. 3 (b) with the increase of both the weak pre-pulse and the nanosecond background,. The X-ray laser output signal was measured as a function of the medium length and demonstrated clear saturation of amplification process. In this case, the small-signal gain coefficient was about 76 cm-1 and gain-length product was 15.6 for 2-mm target. Consequently, we succeeded in saturation of Ni-like Ag x-ray laser with very high gain pumped by only single pulse from Ti:Sapphire laser system.

4 High-order harmonic generation High-order harmonic generation is a well developed and understood method of coherent x-ray generation [3]. We obtained preliminary results of high-order harmonics from noble gases. For high-order harmonic generation, we focused 33-fs Ti:Sapphire laser pulses on a 1.2-mm gas jet with a spherical mirror having a focal length of 1 m. We attempted to find optimum condition for high-order harmonic generation by changing laser intensity and gas density. We obtained the harmonics up to more than 91th order from He as shown in Fig. 4 (a). In this case, the laser intensity was 8x1014 W/cm2 and the gas density was 1.4x1019 cm-3. In high-order harmonic generation, the maximum order of generated harmonics is limited by the depletion of neutral atoms. Hence, the highest order of harmonics was obtained with He due to its highest ionization potential. 1.0

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High-order harmonics around wavelength of 13 nm was obtained from Ne gas jet. Figure 4 (b) shows the harmonic spectra from Ne with a laser intensity of 6x1014 W/cm2 and the gas density of 5x1018 cm-3. High harmonics from Ne was optimized to generate bright harmonics around 13-

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nm wavelength. The bright harmonic generation around 13-nm wavelength can play an important role in a harmonic-seeded x-ray laser because the wavelength of Ni-like silver x-ray laser is 13.9 nm. Since we have successfully developed Ni-like silver x-ray laser using GRIP scheme as described earlier, this preliminary result on high-order harmonic generation shows the potential for harmonic seeded x-ray laser at the wavelengths below 16 nm in the nearest future.

4 Summary We have presented our recent results on the development of coherent x-ray sources based on high-order harmonic generation and x-ray laser technology. We succeeded in saturation of Ni-like Ag x-ray laser using GRIP geometry. In addition, we developed new pumping method using a single pulse from Ti:Sapphire laser system. The single pulse lasing technique with Ti:Sapphire laser system can simplify experimental setup of a harmonic seeded x-ray laser. Preliminary results of high-order harmonic generation have been obtained using He and Ne gases. Specifically, we obtained harmonics around the wavelength of Ni-like silver x-ray laser by using Ne gas. Since we have succeeded in developing high-order harmonics and x-ray laser, we will try to combine these two sources to achieve a high-flux and high-quality coherent x-ray beam.

Acknowledgement This work was supported by the Ministry of Commerce, Industry and Energy of Korea through the Industrial Technology Infrastructure Building Program. The participation of MBI group was funded by a ProFIT Project by the state Berlin within the frame of EU EFREM Program.

References 1. R. A. Bertels et al., Science 297, 376 (2002). 2. P. M. Paul et al., Science 292, 1689 (2002). 3. P. B. Corkum, Phys. Rev. Lett. 71, 1994 (1993). 4. D. L. Matthews et al., Phys. Rev. Lett 54, 110 (1985). 5. H. T. Kim et al., Phys. Rev. A 67, R051801 (2003).

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6. J. Tümmler et al., Phys. Rev. E 72, 037401 (2005); R. Keenan et al., Phys. Rev. Lett. 94, 103901 (2005); J.J. Rocca et al., Opt. Lett. 30, 2581 (2005); Y. Wang et al., Phys. Rev. A 72, 053807 (2005). 7. I. W. Choi et al., Appl. Optics. 36, 1457 (1997).

LASERIX : A Multi X-Ray/XUV Beamline High Repetition-Rate Facility D. Ros1,2, G. Jamelot1,2, M. Pittman1,2, F. Plé1,2,3, S. Kazamias1,2, A. Klisnick1,2, J-C. Lagron1,2, K. Cassou1,2, O. Guilbaud1,2, J-P. Chambaret4, S. Sebban4 and P. Zeitoun4 1

Univ. Paris-Sud, LIXAM, UMR n° 8624, Bâtiment 350, Orsay, F-91405 CNRS, LIXAM, Orsay, F-91405 3 Amplitude Technologies, CE2926, Evry, F-91029 4 LOA, UMR n° 7639, ENSTA / CNRS / Ecole Polytechnique, Chemin de la Hunière, 91761 Palaiseau cedex, France 2

Summary. LASERIX is a high-power laser facility intended to realize and use for applications transient collisional X-ray laser (XRL) beamlines at various wavelengths. In addition new types of XRL schemes giving rise to emission at short wavelengths will be developed using the high energy LASERIX driver. Thus, this laser facility will both offer Soft XRLs in the 30-7 nm range and auxiliary IR beam that could also be used to produce XUV sources. This experimental configuration highly enhances the scientific opportunities of the facility. Indeed it will be possible to realize both X-ray laser experiments and more generally pump/probe experiments, mixing IR and XUV sources. Then, this laser facility will be useful for the community, opening a large scale of XUV laser investigations.

1 Introduction Early X-ray laser actions were obtained in high-power laser facilities intended to inertial fusion studies. Since the first demonstration of the laboratory X-ray lasers 20 years ago [1], there has been significant progress in demonstration of X-ray amplification based on various pumping schemes, characterizing and improving their performances and developing XRL applications. Nevertheless, the low access and low repetition rate of the large laser facilities are not well adapted to improve the development of short wavelength lasers and those of their applications. Considering this context and the international experiment of the LIXAM team, we obtained a financial support (4.2 M€) to build a laser facility devoted to the development

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of XRL emitting in the 30-10 nm range and of their applications, particularly investigations on XRL interaction with matter. In this paper, we shortly describe XRL drivers before giving some details about the LASERIX driver. Then we will indicate the possibility of the beam-lines, available for applications, considering the present state of LASERIX.

2. X-ray lasers drivers Since more than 20 years, many inversion mechanisms have been considered to produce lasing effect in the XUV range. Among these, two were especially strongly studied, called recombination scheme [2] and collisional excitation scheme [3]. But, only the last one succeeded to produce large gain coefficient in laser-produced plasmas, leading to XRL emission. All these studies are based on line-shaped focalisation of IR laser on solid target. Indeed, to obtain strongly amplified XUV emission, it is necessary to achieve plasma conditions producing at the same time a large fraction of the lasing ions on one hand and on the other hand a large population of high-energy electrons, leading to a strong monopole collisionalexcitation rate from the ground state.

Fig. 1. Total pump energy for XRL (J) versus on X-ray laser wavelength for three different X-ray pumping scheme (QSS, TCE and GRIP).

Several scenarios using either a single or several successive driving pulses of duration comprised between ~ 500-ps and 30 fs may be employed to produce XRL actions [4]. Thus, different XRLs can be realized with different properties in term of number of photons or output energy, duration,

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optical quality (spatial and temporal coherence). Basically, the use of a long pulse leads to so-called Quasi-Steady Sate (QSS) XRLs [5], while ultra-short pulses, circularly polarized, are able to drive XRLs in plasmas produced by optical field ionization (OFI) [6]. Between these two extreme situations, “picosecond” pulses give rise to another class of X-ray lasers, so-called Transient Collision Excitation scheme (TCE) [7,8]. The figure 1 summarizes the pump energy that is needed to obtain X-ray lasers. We can observe that from QSS regime to GRIP one, the pump energy is considerably reduced. Taking into account all the previous work assumed by the LIXAM team, we planed to build a laser facility to mainly develop TCE and GRIP X-ray lasers in the 30-10 nm range.

3. The LASERIX driver The main technology of the LASERIX driver is based on Ti:Sa crystals [9]. Indeed, due to their large line width, Ti: Sa lasers may emit much shorter pulses (in the range of few tens of fs) than Nd-glass ones ( > 300 fs). The general architecture of the Ti:Sa laser is schematically represented in figure 2.

Fig. 2. Schematic view of the LASERIX driver architecture

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The front-end is designed as a customized laser based on standard modules, developed by French companies (THALES LASER and AMPLITUDE TECHNOLOGIES). It is composed by two parts, one for the shaping and pre-amplification of the oscillator pulse, the other for two cryogenic amplifiers. The output energy at the front-end is more than 2J at the 10Hz repetition rate. The front-end beam (2.5 J) is then injected in the main amplifier, which is composed by the large Ti:Sa crystal (diameter 100 mm), shown in figure 3. The crystal is pumped by a 4-module Nd:glass laser delivering 100 Joules of 2ω green light, developed by the French laser company QUANTEL. The energy deposition on each side of the crystal is homogenized using lens arrays. The crystal is held in a mount in which a special liquid is circulating all around to cool the crystal and limit the transverse lasing. After 4 successive passes through the crystal, the expected output before compression is ≅ 40 Joules at the repetition rate of 10 Hz. Basically, as shown in figure 2, the 40-joule beam is divided in two parts, respectively 20 Joules of 500 ps and 10 Joules of 50 fs-1 ps (after compression). Besides, two more beams are offered at the final stage. Thus, the zero-order rejected by the compressor may be itself compressed to give a beam of ≅ 1 J in 50 fs. Besides, a weak part of the energy at the exit of the front-end, ≅50 mJ in 50 fs at the repetition rate of 10Hz, can be offered to the users

Fig. 3. The large titanium-doped sapphire crystal (diameter : 100 mm) of the LASERIX driver amplifier is shown on the left. On the right image, we can see the crystal and its mount, including a liquid all around the mount.

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4 Description of the beam-lines possibility Owing to our choice of the Ti:Sa technology for the driver, LASERIX will offer the largest experimental possibilities. Thus, as shown in figure 4, the main beams represented in the part (a) give a long pulse and a short pulse leading to TCE X-ray lasers at 0.1 Hz repetition rate. Beside these two beams, several infrared beam-lines will be useable for applications in the IR range and/or for producing auxiliary XUV beamlines. For instance, the zero-order issuing from the compressor will be itself compressed to produce an auxiliary beam of 1 Joule in 50 fs, as shown in part (b) of figure 4. In addition the energy of the uncompressed beam will be generally larger than needed, so a part of it will be available. Finally, leaks taken in the front-end offer the possibility to have other auxiliary IR beam-lines, as shown in part (c) of the figure 4. Such beams can be used again for applications at 10Hz repetition rate. But, particularly they offer possibility to produce XUV beams by high-order harmonic generation (HHG). Such beams may be amplified in TCE plasmas to produce intense XRL beams of high optical quality [10]. All these beam-lines open a large field of applications, especially because they all are synchronized with the main beam

Fig. 4. Configuration of the main beam-lines in the experimental area.

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5 Applications of X-ray lasers and LASERIX project X-ray lasers can be employed to excite matter, to diagnose solid surfaces, or probe high-density plasmas. Indeed, the unique XRL properties (very large brightness, coherence, short duration) add to good beam collimation, and make XRLs attractive with respect to the other soft XUV sources. Owing to their high brightness, XRLs are well suited as diagnostic tools for various purposes, in particular in microscopy and interferometry [11,12,13]. As a widely used diagnosing tool in the research of laser-produced plasma, interferometry has many advantages in the accurate measurement of the plasma electron density because it directly gives refraction index mapping from the interference pattern processing. Indeed, due to the high intensity and short wavelength, X-ray lasers applied as a probing beam for the interferometry provides better penetration into high density plasma (1019–1022 cm-3) with small refraction, which is a main limitation of interferometry in the UV range for high-density gradient plasma diagnosis. In this paper, we just ullustrate the interest of X-ray lasers for laserproduced plasmas investigations from the results of an X-ray interference microscopy diagnosis using a wavefront-division imaging Fresnel bimirror interferometer [14] and a transient picosecond Ni-like Ag X-ray laser [15].

Fig. 5. Experimental set-up of the Fresnel bi-mirror X-ray interference microscopy.

The configuration of the experimental setup is shown in Figure 5. The X-ray laser illuminated the sample plasma and the bi-mirror separated the

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wave front after the plasma and produced an enlarged overlapped interference field. The diffraction-limited ellipsoidal imaging mirror gave a magnified image of the sample plasma onto the thinned backlighted CCD. The spatial resolution in the sample plasma plane was limited by the magnification and the pixel size to ~ 1.75 µm. The diagnosed plasma was formed by irradiating a 1 mm-long Al slab target with a 1 J, 1.2 ns IR (1053 nm) pulse. A line focus system produced a plasma column of ~ 100 µm in width and 6 mm in length (intensity within the line focus: 1.4×1011 Wcm-2). The X-ray laser probed the plasma along the column axis. The intense plasma self-emission was observed close to the target surface and mixed with the interference fringes. However this low frequency signal can be removed by using a Fourier filtering in order to let appear the interference field. The density map may be then easily deduced from the fringe pattern, as shown by figure 6, which describes the successive steps of the analysis leading from the raw data to the electron density map. For the plasma length of 1 mm, the electron density, ne, is related to the fringe shift as ne ≈1.583×1020 δfringe [cm-3]. Due to the limitation of the spatial resolution, the minimum detectable limit of the electron density is ~ 3×1019 cm-3.

Fig. 6. Main steps of results and analysis of laser-produced plasmas investigations. 1) Image of the sample plasma, reflected by the reference part of the bimirror, without X-ray laser. 2) Interference field with superimposed plasma image, recorded for the same shot. 3) Interference field after removing plasma emission by a Fourier treatment. 4) Electron density map deduced from 3.

Pictures of the figure 6 correspond to a delay of 1 ns between the plasma heating pulse and the X-ray laser. The peak electron density measured is 1020 cm−3 at the position comprised between 10 and 15 μm away from the target surface. In some zones of plasmas diagnosed later, typically 2 and 3 ns after the peak of the heating pulse, inverted fringe shifts were observed, leading to refraction index larger than 1. That means that the plasma is no more a classical dilute electron gas and that the refraction in-

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dex is not mainly governed by the electron density, but by free-bound and bound-bound transitions. Thus, these results will contribute to the validation of the 1D and 2D hydrodynamic codes and a better understanding of the physics of laserproduced plasma [16]. They could be performed in a near future using LASERIX facility.

6 Summary and perspectives. Thus, the LASERIX facility is now built. The laser driver is running and the choice of the Ti:Sa is experimentally successful confirmed. It will offer the possibility to highly increase the repetition rate of the X-ray lasers and then will be very useful for applications. A virtual (3D) of the experimental area is represented in Figure 7.

Fig. 7. 3D virtual view of the LASERIX facility. The main chamber producing TCE X-ray lasers is represented in the center of the room.

This laser facility will be located in a new building, available in November 2006, at the Laboratoire d’Optique Appliquée (Ecole Polytechnique, Palaiseau, France). Thus, the LASERIX facility will be installed during the first semester of 2007 and first applications investigations will be performed during the second semester of 2007. Among the different applications, we plane to purchase the density diagnostics of plasmas produced by the low-energy beam. The possibility to vary the duration of the IR beam producing the plasma, to vary the wavelength of the X-ray laser,

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and, above all, the large repetition rate (0.1 Hz) will be very useful to realize full-scale studies. That has been demonstrated at the 1st LASERIX Workshop [17], held in Orsay on 2-3 February 2006.

7 Acknowledgments LASERIX is an X-ray laser facility of the Université Paris-Sud. The financial support of the Conseil Général de l’Essonne and the Ministère de la Recherche under the Contrat de Plan Etat-Régions 2000-2006 is gratefully acknowledged. We are indebted to Patrick Georges (LCFIO), Pascal d’Oliveira (CEADRECAM) and Claude Rouyer (CEA-CESTA) for valuable discussions.

References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

D.L. Matthews et al, Phys. Rev. Lett. 54, 110, 1985 L.I. Gudzenko et al., Sov. Phys. Doklady 10, 147, 1965 R.C. Elton, Appl. Optics 14, 97, 1975 D. Ros et al, Laser ans Particle Beams Journal, 20, 23,.2002 B. Rus et al., Phys. Rev. A 55, 3858-73, (1997) S. Sebban et al., Phys. Rev. Letters, 86, 3004-7, (2001) P.V. Nickles et al., Phys. Rev. Lett. 78, 2748, 1997 A. Klisnick et al., J.O.S.A. B 17, 1093, 2000 G. Jamelot et al., in X-Ray Lasers 2004, IOP Conf Series N° 186, 677 (2005) P. Zeitoun et al., Nature 431, 426, (2004) D. Di Cicco et al., Opt. Lett. 17, 157, (1992). R.E. Burge, et al., Opt. Lett. 18, 66, (1993). D.H. Kalantar et al., Phys. Rev. Lett. 76, 3574, (1996). D. Joyeux et al., J. Phys IV France 11, Pr2, 511, (2001). A. Klisnick et al, J.O.S.A. B 17, 1093, (2000). H. Tang et al., Appl. Phys. B 78, 975, (2004). The CD ROM of contributions to the workshop is available : [email protected]

Seeding High Order Harmonic in a Transient X-Ray Laser Amplifier I. R. Al’Miev*, O. Larroche+, A. Klisnick*, C. Moller*, D. Benredjem*, S. Kazamias-Moucan*, O. Zabaydullin* and J. Dubau* *)

LIXAM, Laboratoire d’Interaction du rayonnement X Avec la Matiere, UMR 8624, Bat. 350, Universite Paris-Sud, 91405 Orsay, Cedex, France +) CEA-DIF, Boite postale 12, F-91680 Bruyeres-le-Chatel France

Summary. The seeding of high-order harmonic (HOH) radiation in a transient Xray laser amplifier was numerically investigated using the code COLAX. The code was recently modified to account (i) for the travelling-wave irradiation of a preformed plasma pumped in the transient regime, and (ii) for the injection of a HOH pulse at the X-ray laser wavelength, and at one boundary of the plasma amplifier. We show that the time-dependent description of the polarisation (TDP) leads to significantly different results in comparison to the widely used adiabatic description. Namely, with TDP, HOH produces a wake in the intensity distribution, which is not only amplified but lasts much longer than the HOH pulse. This could explain recent experimental observations in the spectral domain.

1 Context and motivation It is well known that a conventional optical laser exhibits few principal problems associated, firstly, with necessity of creating a high quality seed, secondly, with maintaining the quality over the amplification region, and, thirdly, with reducing the level of the self-emission of the amplifier. The area of X-ray lasers was investigated in a number of papers. Starting from the first successful demonstration of X-ray laser, the world has seen the lasing even at the wavelength 3.5 nm [2] that is just inside the waterwindow. One of new promising routes of the X-ray laser research is the amplification of HOH pulse inside the X-ray laser. The importance of this topic could be explained by the potential improvement of the properties of X-ray laser, for example, coherence. One of the first reports on the ampli-

202 I. R. Al’Miev et al.

fication of the HOH was published by Ditmire et al [3]. In their work they reported an amplification of the 21st harmonic of neodymium chirpedpulse-amplification laser pulse in Ne-like Ga laser plasma. Substantial progress has been made by Ph.Zeitoun et al [4] in 2004 with successful demonstration of seeding HOH in Ni-like Kr OFI amplifier at a wavelength of 32.8 nm. The authors claimed an amplification of 25th harmonic from Ar gas by a factor of 103. We note that the work in similar area has been made by Japanese scientists Kawachi et al [5], and Hasegawa et al [6]. They made an attempt to produce shorter wavelength radiation using transient collisional excitation (TCE) scheme. If one would like to obtain larger energy output and reach shorter lasing wavelengths then, indeed, TCE X-ray lasers, based on the use of solid target, is a valuable medium for the potential amplification. Our goal is to simulate propagation of short high-order harmonic pulse within Ni-like Ag laser-produced plasma created by the traveling wave irradiation. We note that the HOH pulse differs from X-ray laser pulse in that the spectral width of HOH is much broader than that of the X-ray laser pulse. That is why we have used and upgraded the code COLAX that is appropriate to resolve numerically short-, of order of 10 fs, and long-duration, of order of 10 ps, electric field amplitudes. Conditions of the simulations match the experimental ones reported by Klisnick et al [7].

2 Simulated experiment To perform the simulations we considered such scheme where Ag target is initially irradiated by the pre-pulse of smaller intensity, creating a preplasma. Then, it is irradiated by the main pulse of larger intensity, creating conditions that are optimal for the population inversion. Main pulse takes the form of the travelling wave irradiation. The angle of the travelling wave (TW), that is related to the velocity of TW irradiation, can be varied in the present version of the code; for the particular calculations we fixed it as 45° that corresponds to the velocity of the TW, which is equal to the speed of the light in the vacuum. As soon as the amplified spontaneous emission is generated, the HOH pulse is injected. It interacts with the laser-plasma amplifier, and produces some radiation output. To simulate Nilike Ag laser-produced plasma we used the code EHYBRID [8]. The following parameters were used as an input into EHYBRID. Intensity of the pre-pulse was taken to be 1012 W cm-2; intensity of the main pulse was 1015 W cm-2; the duration of the pre-pulse was 600 ps; the duration of the main pulse was 400 fs; the time interval between the pre- and main pulses was

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250 ps. The HOH pulse has Gaussian temporal and spatial shape of 15 fs temporal and of 30 µm spatial widths. The time of the injection of HOH pulse is a parameter in the code – it can be varied. For the particular calculations we fixed it as 2 ps with respect to the start of the travelling wave irradiation.

3 The code COLAX: present status and upgrade The code COLAX was originally written by Larroche et al. and has been used to model X-ray laser signal build-up [1]. The evolution of the electric field is described by Maxwell equation, which is transformed into paraxial envelope form,

∂E ± ∂E ± ic ∂ 2 E ± iω + = + (ε R E ± + 4πP± ) , c ⋅ ∂t ∂y 2ω ∂x 2 2c

(1)

where E+ and E- are the complex, slowly varying amplitudes of waves propagating in the positive and reverse directions. The Eq.(1) is selfconsistently bound with the equation describing the evolution of the polarisation,

∂P± = −γP± − iωDE ± + Γ± , ∂t

(2)

where γ has a meaning of the dipole de-phasing factor, and D is the reduced, non-dimensional population inversion between the upper and the lower X-ray lasing levels,

D=

d2 1 ( ρu − ρl ) = γGλ , hω 8π 2ω

(3)

where d is the absolute value of the non-diagonal matrix element of the dipole operator, ρ u ( ρ l ) are the dimensional populations of the upper, and lower levels, respectively, and the gain G takes into account the effect of the saturation,

G=

G0 1+

I

,

(4)

I sat

with G0 describing the small-signal gain, I is the electric field intensity, and Isat is the saturation intensity. Noise term, Γ+ , in the Eq.2 effectively describes spontaneous emission. To perform simulations we have upgraded COLAX. Travelling wave irradiation was taken into account in the following way. Local conditions of

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plasma were determined by the angle of the travelling wave and EHYBRID time-history of plasma. EHYBRID is 1.5 dimensional code. It provided us with the cell position, electron density, electron and ion temperatures, populations of the upper and lower X-ray lasing levels, smallsignal gain, dipole de-phasing factor, and the saturation intensity as functions of the Lagrangian cell positions and time. By fixing plasma conditions along transverse axis at fixed y-coordinate, conditions at other ycoordinates are calculated, using space and time interpolation procedure, taking into account time delay of the front irradiation of the travelling wave. Then, such interpolated quantities are used as an input parameters in the code COLAX. To account for the HOH pulse injection boundary conditions as functions of time were modified.

4 Results Typical output of COLAX is shown in Fig.1. It shows the snapshot of intensity distribution as a function of the longitudinal, y, and transverse, x, distances at t = 8 ps. Longitudinal axis is the one, along which the X-ray radiation propagates. It has dimension of 3mm. The dimension of the

Fig. 1. Intensity distribution as a function of y- and x-coordinates at t = 8 ps with respect to the start of the travelling wave irradiation.

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transverse axis is 140 µm, while the initial position of the target surface is located at x = -70 µm . Intensity is given in log-scale. The narrow feature at y = 1.85 mm corresponds to the HOH pulse. The HOH pulse has a Gaussian spatial profile along the x-axis. The peak of the HOH profile is at x = -33 µm. The Fig.1 refers to the case when the electric field wave propagates towards the plasma output in “+”-direction, that is

I + = c E+

a)

2

/(8π ) , where c = 3 ⋅ 1010 cm ⋅ s −1 .

b)

Fig. 2. Intensity snapshots at a) t = 4.5 ps and b) t = 11.5 ps

This figure allows making important conclusions. Firstly, the HOH pulse is weakly amplified. Secondly, high-order harmonic induces the wake, or the tail, that is apparent behind the pulse. Fig.2 shows the evolution of the intensity at two successive times, as the electric field propagates towards the plasma output. It is clear, that the amplification of the intensity takes place behind the HOH pulse in the area with 10-20 µm transverse range where the gain has the maximum values. Secondly, the length of the amplified area is not conserved – it becomes longer as the pulse propagates further. To understand the nature of such distribution we ran COLAX including only the HOH pulse, while arbitrarily setting spontaneous emission to zero. Results are shown in Fig. 3a. One can see that, indeed, the HOH pulse induces the tail. In Fig 3b no HOH was injected, i.e. only spontaneous emission is amplified. Comparison of Fig.1 and Figs.3 shows that the

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a)

b)

Fig. 3. Intensity distribution that includes a) only the HOH pulse, and b) only amplified spontaneous radiation; t = 8 ps.

Fig. 4. Intensity distribution assuming adiabatic model of COLAX calculations; t = 8 ps.

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total contribution of the HOH and the ASE leads to the little increase of the intensity in the area where the intensity has a maximum. Present version of the code COLAX allows making the electric field, and, respectively, intensity calculations in the adiabatic approximation, where the left hand side of the Eq.(2) equals to zero, that is

∂P+ = 0 . In ∂t

such approximation the polarisation is proportional to the electric field, and to the population inversion, according to the following equation,

P+ =

χ ω E + = −i DE + , 4π γ

(5)

where ω is the X-ray laser frequency. Such an approximation is widely used, and in particular it is implicit in the numerical codes based on radiative transfer description. Running COLAX in the adiabatic approximation mode we obtained significantly different results, both qualitatively and quantitatively. Fig. 4 shows the intensity snapshot calculated using this model, that is to be compared to Fig. 1. Firstly, the high-order-harmonic pulse is much more amplified in comparison to the time-dependent case. This can be seen in the centre of the pulse – the HOH pulse wings in the transverse direction have larger intensity values than in the case of the TD description. Secondly, the adiabatic approximation does not predict the existence of the electric field wake. Thirdly, the overall shape of ASE area differs from that of time-dependent calculations. Fourthly, the region of the maximum intensity is situated in the ASE feature. It is 20 times larger than that of the time-dependent case.

5 Conclusion In conclusion, we incorporated the travelling-wave model into the code COLAX. High-order harmonic seed was included as time- and spacedependence of the boundary conditions. Calculations demonstrate that, firstly, it is important to include time-dependent treatment of the polarisation, secondly, the high-order harmonic pulse leads to the wake that is amplified in time, and, thirdly, the wake lasts much longer than the HOH pulse. That can explain the experimental observations [4] in the spectral domain: namely, that, contrary to common belief, the HOH pulse is not amplified as a short, broadband pulse, but rather triggers a long-lasting (and thus possibly narrow-band) wake where most of the XRL energy goes. This fact is the principal difference between time-dependent and adiabatic models. Optimisation of the injection of the high-order harmonic

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pulse and the extension of the population inversion calculations using time-dependent rate equations will be the asset in other paper.

References 1. Larroche, O., Ros, D., Klisnick, A., Sureau, A., Möller, C., Guennou, H., “Maxwell-Bloch modelling of x-ray-laser-signal buildup in single- and doublepass configurations”, Phys. Rev. A 62, 043815 (13 pages), 2000. 2. MacGowan, B.J., Maxon, S., Hagelstein, P.L., Keane, C.J., London, R.A., Matthews, D.L., Rosen, M.D., Scofield, J.H., Whelan, D.A., “Demonstration of soft x-ray amplification in nickel-like ions”, Phys. Rev. Lett. 59, 2157-2160, 1987. 3. Ditmire, T., Hutchinson, M.H.R., Key, M.H., Lewis, C.L.S., MacPhee, A ., Mercer, I., Neely, D., Perry, M.D., Smith, R.A., Wark, J.S., Zepf, M., “Amplification of xuv harmonic radiation in a gallium amplifier”, Phys. Rev. A 51, R4337-R4340, 1995. 4. Zeitoun, Ph., Falvre, G., Sebban, S., Mocek, T., Hallou, A., Fajardo, M., Aubert, D., Balcou, Ph., Burgy, F., Douillet, D., Kazamias, S., de Lacheze-Murel, G., Lefrou, T., le Pape, S., Mercere, P., Merdji, H., Morlens, A.S., Rousseau, J.P., Valentin, C., “A high-intensity highly coherent soft X-ray femtosecond laser seeded by a high harmonic beam”, Nature 431, 426-429, 2004. 5. Kawachi, T., Nagashima, K., Kishimoto, M., Hasegawa, N., Tanaka, M., Ochi, Y., Nishikino, M., Kawazome, H., Tai, R.Z., Namikawa, K., Kato, Y., “Recent Progress in X-ray Laser Research in JAERI”, Proc. of SPIE 5919, 59190L (11 pages), 2005. 6. Hasegawa, N., Kilpio, A.V., Nagashima, K., Kawachi, T., Kado, M., Tanaka, M., Namba, S., Takahashi, K., Sukegawa, K., Peixiang, L., Huajing, T., Kishimoto, M., Renzhong, T., Daido, H., Kato, Y., “Higher harmonics generation for the high coherent x-ray laser”, Proc. of SPIE, 4505, 204-210, 2001. 7. Klisnick, A., Guilbaud, O., Ros, D., Cassou, K., Kazamias, S., Jamelot, G., Lagron, J.-C., Joyeux, D., Phalippou, D., Lechantre, Y., Edwards, M., Mistry, P., Tallents, G., “Experimental study of the temporal coherence and spectral profile of the 13.9 nm transient X-ray laser”, JQSRT 370-380, 2006. 8. Pert, G.J., “Model calculations of XUV gain in rapidly expanding cylindrical plasmas”, J. Phys. B 9, 3301-3315, 1976.

Feasibility of 3.4 nm Laser Pumped by Ultraintense RBS Laser S. Suckewer, Y. Avitzour*, W. Cheng, J. Ren and S. Li Princeton University, Princeton, NJ, 08544, USA

Summary. Our presentation consisted of two parts. In the first part we presented main theoretical results on the plasma and pumping conditions required to generate gain at 3.4 nm in H-like CVI ions in transition from the first excited state to ground state. Transient population inversion is generated during the recombination process. It was shown that high gain (up to G ~200 cm-1) can be achieved using currently available compact lasers. In the second part we presented a new type of compact laser generating ultra-short and ultra-intensive pulses via Raman Backscattering (RBS) amplification and compression in plasma. We achieved large (up to 1000) “seed” amplification and its compression from ~1 psec down to 150 fsec in only 2 mm long plasma pumped with ~ 1014 W/cm2 pulses. We also presented very recent experiments on amplification in 2 passes setup. Such RBS amplifier and compressor is expected to provide in not too far future intensities ~1020 W/cm2 at high repetition rate in compact (university type) system, which would be ideal pump not only for 3.4 nm laser but even for shorter wavelength lasers.

1. Introduction Remarkable progress has been made in the development of soft x-ray lasers (SXLs) since their first demonstration in 1984 in so called collisional scheme [1] and recombination scheme [2]. Each of these schemes evolved into sub-schemes like transient gain generation (see e.g. [3 – 5], and very recently grazing incidence pumping [6, 7] in the collisional scheme, and generation gain in recombination scheme in transitions to ground states of ions pumped by very high intensity fsec-type of lasers [8 – 10]. Advances in their performance (wavelength range, gain and beam energy) have been achieved together with simplifications of the technology required to generate gain. These achievements have, in part, been stimulated by the first applications of soft x-ray lasers to soft x-ray microscopy, microholography, very high plasma density measurements and their potential applications to semiconductor surface studies, nano-lithography, dynami-

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cal response of semiconductors and biological cells, and a number of other applications. A key element here is the cost and availability of these

Fig. 1. Generic recombination soft x-ray laser scheme with lasing to the ground state.

devices, and intensive efforts are being made to develop compact soft xray lasers that are suitable and convenient for applications in academic and industrial research laboratories. Excellent examples of the progress in this direction are demonstrated by the achievement of lasing actions in the region 40–50 nm in ArIX in a capillary discharge[11] and in Xe IX with femtosecond laser [12]. However, right now, the most urging issue, in our opinion, is the development of compact soft X-ray laser, operating at repetition rate >1Hz and at much shorter wavelengths than collisional schemes offer.

Fig. 2. Scaling of the wavelengths versus ion charge Z- 1, of H-like ions for 32 and 2-1 lasing transitions

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In Fig. 2 is shown the scaling of the wavelengths versus ion charge (Z1) of H-like ions for 3–2 and 2–1 transitions in recombination scheme. One may see fast convergence to region of shorter wavelengths even for quite moderate Z. Especially attractive is scaling for 2 – 1 transitions with Z reaching wavelength ~ 1 nm already for the H-like NeX. Because fast decreasing the wavelength and high quantum efficiency for 2 – 1 transition in H-like ions it is possible to achieve lasing within the “water window” (2.3 – 4.4 nm) at quite high repetition rate using relatively compact lasers as pumps as is shown in Table 1 for CVI ions at 3.4 nm. (Description of the computer codes and results of calculations are discussed in the next sections). Consideration of plasma and pumping laser parameters for gain creation in transition to ground state of H-like ions Ultrashort laser pump pulses are crucial to realize lasing to the ground state of ions in the soft X-ray spectral region in order to provide the population inversion between the excited and ground states (see Fig. 1 for generic recombination scheme for generation population inversion to ground states and Fig.3 for transitions to ground state in C VI ions). Fig.1 illustrates the idea of the process of recombination to ground state. First, the ions are fully stripped from their electrons by an intense ultrashort laser pulse. Then, the ions are recombined by three-body recombination, The rate of such recombination is proportional to Ne2 and n4 (Ne is electron density, and n is the principal quantum number) Therefore the transition from Fast collisional recombinations 18.2 nm

H-like CVI ion

3.4 nm

Fig. 3. Recombination scheme for C VI ion

Lasing to ground state (with fsec pumping)

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C6+ to H-like CVI occurs primarily to the states with high n (Fig. 3). Collisional and radiative transitions to level n = 2 occurs faster than to ground level n = 1, creating population inversion between n = 2 and n = 1 (inversion is also created between levels n = 3 and n = 2, which lasts much longer than between levels n = 2 and n = 1). The ionization process has to be very fast. Rapid ionization generates minimal heating of the plasma, which is crucial for a recombination laser (in order for the recombination process to be dominated by collisional relaxation processes). In addition, the ultrashort pumping pulses are necessary because of the very short radiative life time, τ , of the first excited levels of ions and the decrease of this time with Z as Z-4. For example, τ = 26 psec for Li III and τ = 1.6 psec for C VI [13]. In fact, this time is significantly shorter because at high electron density, which is required for high gain, collisional life time is much shorter than radiative time. In addition, as will be discussed in the next section, short pumping time is required because high gain exist before Maxwellization of electron energy distribution takes place. Hence, only the powerful femtosecond-type laser makes it possible to realize transient recombination systems with lasing to the ground state in ions. Ions are initially totally stripped of all their electrons by optical-field-ionization (OFI). This process was predicted theoretically and calculations were performed based on Keldysh theory [1416]. The required power densities (intensities) and energies of fsec-type of laser for effective ionization of H-like CVI ions are shown in Table 1. Table 1. Required energies and intensities to reach C6+

Important result towards generating lasing action in “water window” by transitions to ground state of H-like ions was demonstration of the gain at 13.5 nm in H-like Li III ions in transition to ground state [8]. This experiment followed by demonstration the lasing action in the same transitions at 2 Hz repetition rate [9]. In [9] the lasing was generated with only a 50 mJ in 250 fsec, 0.25 μm KrF laser beam. This relatively high efficiency was achieved by longitudinal pumping and high quantum efficiency due to lasing to the ground state. Importance of these experiments was that they in principle “opened the road” to compact SXLs at much shorter wave-

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lengths using H-like ions with higher atomic number Z . Later, using ~1 μm , 300 fsec Nd/Glass laser and longer plasma column (14 mm instead of 5 mm) gain-length product was slightly increased to GL ≈ 7.2 from GL ≈ 6.5 for a 5 mm long plasma in an experiment with 0.25 μm indicating a tendency of decreasing gain G with an increasing wavelength of pumping beam. This result, which was confirmed in a similar experiment using 0.8 μm Ti/Sapphire laser [17], seems to imply higher Optical Field Ionization (OFI) efficiency at shorter wavelength, in contradiction to the theory of tunneling ionization. Only recently, based on computer modeling of the ionization (including tunneling, multiphoton and collisional ionizations) and recombination processes combined with calculation of electron distribution function from Fokker-Planck equation and radial motion of particles in plasmas (from MHD code) we were able to understand this phenomena and show that there is no contradiction. The reason for seemingly contradiction with the theory is higher deposition of above threshold ionization (ATI) energy to electrons when OFI laser is operating at longer wavelength. Such electron heating is decreasing rate of 3-body recombination of Li3+ to Li III hence, of course, has very negative effect on gain generation [18]. Even more puzzling was very large fluctuations of 13.5 nm output radiation intensity in all these experiments. We have attributed such fluctuations to gain G fluctuations due to some non-uniformity of the plasma column. Therefore we have dedicated a lot of effort to improve the uniformity of the plasma. However, we did not see any improvement in 13.5 nm intensity reproducibility with improvement of plasma uniformity. Again, only recent computer calculations has shown that all these problems were related to plasma heating during optical field ionization (primarily tunneling ionization) leading to too high electron temperature at the time of threebody recombination.

3. Computer modeling results for gain at 3.4 nm in CVI Recently, we have developed an elaborate numerical model to characterize recombination gain in the 2 - 1 transition of LiIII at 13.5 nm [18]. The model describes the effects of different experimental parameters on the gain. We were able to explain the gain observed in the earlier mentioned experiments [9, 10] and showed that it is possible to achieve high gain on this transition, especially when mixing the plasma with hydrogen. These calculations were extended into C VI at 3.4 nm [19,20].

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Recombination gain relies on having fully stripped ions in a relatively cold plasma. The ionization mechanism that is used to achieve this plasma is tunneling ionization by ultra-short and ultra-intense laser pulses (with pulse-duration of ≤ 100 fsec and intensities in the range of 1017 - 1019 W/cm2 depending on the element being used). Due to the short pulseduration, minimal heating is produced during the ionization. However, when calculating the average energy that is absorbed during the ionization process we find that the absorbed energy still corresponds to an electron temperature that would not allow for population inversion in the transition to ground state to be generated during the recombination process. But taking into account the actual phase-space distribution function of the plasma, including effects from both the non-Maxwellian nature of the distribution function and the spatial expansion and cooling of the plasma after ionization, we have shown that high gain is indeed feasible in the LiIII 2 - 1 transition [18]. In addition, we have shown very recently that the gain can be enhanced and become less stringently-dependent on exactly matching the required values of the experimental parameters, if hydrogen is mixed into the plasma [19,20]. The process of gain generation can be divided into three stages: (a) Ionization and heating, (b) Expansion and cooling and (c) Recombination and gain. We shall repeat briefly here the principles of our model (described in detail in [18]), and discuss more deeply the adjustments and enhancements that were required in order to apply the model to the C VI ion. (a) Ionization and heating: Ionization is achieved by OFI using an intense laser pulse. The ionization rate is calculated by the tunneling rate of an electron under the influence of the laser electric field treated in semiclassical approximation [16].The classical motion of the ionized electrons in the laser field after ionization yields the so-called residual energy that is absorbed by the electrons during the ionization process. This energy is due to the phase mismatch between the ionized electrons and the oscillating laser electric field. It is proportional to the quiver energy of the electrons, εq, at the time of ionization. Though the residual energy is in fact much smaller than the quiver energy, it would be high enough to prevent recombination gain to occur if the plasma were Maxwellian. However, the ionization process yields a plasma with a highly non-Maxwellian electron distribution function (EDF) as was shown in [18,19].Qualitatively, one can understand the properties of the OFI-EDF by realizing that most of the electrons are ionized at the peak of the laser oscillating electric field and continue to move in phase with it. Therefore, the vast majority of the electrons in the plasma absorb very little residual energy, and only a small fraction of the electrons are ionized off the peak of the laser electric field and absorb high energy. These highly energetic electrons contribute much

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to the overall electron average energy, but have a relatively low probability of participating in collisional processes. This effect gives rise to enhanced three-body recombination and electron-impact de-excitation rates. In other words, the non- Maxwellian nature of the distribution function causes the “effective recombination temperature" of the plasma to be much lower then the temperature of the corresponding Maxwellian plasma, given by 2/3 of the average energy. The “effective recombination temperature" can be defined by comparing the actual three-body recombination rate to the same rate in a Maxwellian plasma. The effective recombination temperature is always much lower for OFI-plasma than for a Maxwellian plasma with the same average energy. The ionization was simulated by the iPIC (Ionization Particle in Cell) code. For a sufficiently high electron density (Ne≥ 5 1019 cm-3), and a fixed electron temperature, gain is higher for higher Z ions. Therefore, we can expect to get better results for CVI (Z = 6) than for LiIII (Z = 3). However, the required intensity for the ionization of CVI ions is almost two orders of magnitude higher than the intensity required to ionize LiIII ions, and with it, the average energy of the electrons. The effects of the residual energy on the recombination gain are reduced significantly when taking into account the non-Maxwellian nature of the distribution function and by adding hydrogen to the plasma Adding hydrogen supplies cold electrons to the plasma since the hydrogen atoms are ionized by the front of the pump pulse (or by the pre-pulse) and absorb very little residual energy. These electrons then participate in the recombination process and enhance the gain. In the CVI case however, higher densities are required to achieve gain (about an order of magnitude higher than that required for LiIII), and collisions during the ionization process become more significant since the collision frequency scales linearly with the density. Unlike the residual heating, collisional heating affects the electrons ionized from carbon (Celectrons) and the electrons ionized from hydrogen (H-electrons) in the same way. One way to counter this effect is to use a shorter pulse for the ionization. The overall collisional heating is roughly proportional to the product νcolτ , where νcol is an average collision frequency, and τ is the pulse-duration. Therefore, increasing the density (and with it the collision frequency) by a factor of 5-10 and reducing the pulse-duration by the same factor should have very little net effect on the collisional heating. Using shorter pump pulses requires the use of a slightly higher intensity, since the ionization has to be completed in a shorter time, and full ionization is crucial to achieve high gain. However, even with the higher intensity the shorter pulses contain lower energy, which means that using shorter pulses would be more energy-efficient.

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(b) Expansion and cooling: The expansion and cooling (along with Maxwellization) process is simulated by numerically solving the FokkerPlanck (FP) equation for the distribution function that is calculated by the iPIC code with an implementation of the SPARK code [18]. Since the OFI-EDF was generated by the iPIC code in planar geometry and since the charge separation and space-charge oscillations may not have cylindrical symmetry (recall that the pump beam is linearly polarized), the straightforward conversion between planar and cylindrical was not appropriate here and the planar geometry option of the FP solver code was used. Finally, we note that due to the higher density and the short time scales at which gain occurs (usually less than 1 ps after ionization), the expansion cooling plays a less important role here since very little expansion can happen in these time scales. (The main importance of solving the FP equation is for calculating the Maxwellization process, which has to be taken into account to get realistic results.) Therefore, in contrast to the LiIII case, there is no need for a tight focus of the pump pulse in order to achieve gain (other than for achieving the required intensity). This property of the gain may make it easier to achieve longer gain channels for gain saturation.

Pump diameter: 10µm

Pump diameter: 30µm

C VI 3.4 nm

C VI 3.4 nm

b)

a) Plasma radius

b) Plasma

radius

Fig. 4. Gain coefficient (in cm-1) for CVI 2→1 transition with initial conditions of nC=1019cm -3 and nH=1020cm-3 for 2 different pumping beam(OFI) diameters, both with intensity I ~ 10!9 W/cm2

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(c) Recombination and gain: The recombination process was simulated by solving the rate equations governing the process, taking into account three-body recombination, electron-impact ionization, electronimpact excitation and de-excitation, radiative recombination and radiative relaxation (spontaneous emission). The plasma was assumed to be optically thin, hence no photoexcitation processes were considered. The values of the rate coefficients in the rate equations were obtained by integrating the cross-sections of the different interactions over the actual nonMaxwellian, time-dependent, electron distribution function that was obtained from the iPIC and FP codes. The small-signal gain coefficient G was then calculated from broadening for the cold ions (the ions are assumed to be fixed during the whole process hence the ions temperature was taken to be the initial plasma temperature, i.e., Ti ≈1 eV) and the Stark broadening estimated for the Lyman-α line by the lesser of the widths given by the quasi-static linear Stark effect (Holtsmark theory) and electron impact broadening. In Figs 4a,b, are shown results for gain G (in cm-1) calculations for CVI 2–1 transition at 3.4 nm for 2 different diameters of pumping laser beam (50 fsec, 1019 W/cm2 ) versus plasma channel diameters and time of gain evolution. The maximum gain is reaching very high values in range G ≈ 150 - 200 cm -1, which is very encouraging result.

4. Raman Backscattering (RBS) Amplification and Compression The second part of our presentation was devoted to a new type of ultrashort and ultra-intensive compact laser system based on Raman Backscattering (RBS) amplification and compression in a few millimeter long plasma. In that presentation we briefly described the research and recent results with emphasis on multi-passes approach for maximizing system efficiency. The principle of RBS amplification in counterpropagating geometry is shown in Fig.5. Moderately intense, but long, laser pulses can be scattered into short very intense counterpropagating pulses in a plasma through stimulated Raman backscattering (RBS). Raman amplification of ultrashort pulses in a plasma is based on the three-wave interaction between the counterpropagating “seed” and “pump” pulses and the plasma waves[21] as is shown schematically in Fig.6. The plasma waves, with frequency ωpe (ωpe2= 4πe2ne/me), are ponderomotively driven by the periodic intensity pattern produced by the

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Raman amplifier

ω pump

ω pump ω ω ω + ω pe = ω seed

“Pump”

“Seed”

“Seed”

ω seed

ωpe

Plasma wave

Fig. 5. Principle of Raman backscattering amplification.

interference between the pump pulse and the seed (subpicosecond) pulse. If the frequency detuning between the two pulses matches the plasma frequency ωpe, i.e., ωpe = ωpump - ωseed, then the seed pulse can be amplified through the RBS instability of the pump.

ω

S eed

P um p

pum p

ω

se e d

P la s m a w a v e

ω p e 2 = 4 π n e e 2 /m R e s o n a n t C o n d itio n s: ω pum p = ω se e d k

pum p

=

k

se e d

+ +

ω k

e

pe pe

Fig.6. Schematic of three waves mixing

The RBS amplification can be divided into linear and nonlinear regimes. In the linear regime, the pump depletion is negligible and the gain is inde pendent of the seed intensity. The seed pulse is amplified and the pulse duration is increased due to the narrow bandwidth of the linear amplification (which is approximately twice the growth rate). The nonlinear regime is characterized by significant pump depletion and simultaneous temporal compression of the amplified pulse, as illustrated in Fig. 7. The front of the pulse is amplified while the tail part interacts with a depleted pump and is not amplified as much as the front. In this regime the efficiency of energy transfer from the pump to the seed can reach ~ 90% when ωpump ≥ 10

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ωpe according to theoretical predictions [22] through the following relation η = 1 - ωpe/ωpump. This could happen when the pump pulse duration is

Pump

P

Depleted pump

Seed

S Amplified Ampliseed

Plas ma

Fig. 7. Resonant Raman non-linear regime (pump depletion)

sufficiently long to match the length of the plasma and obtain nearly full pump depletion. Operating in this nonlinear regime of RBS amplification in the plasma is of highest interest. In Fig. 8 is shown schematically experimental setup on which nonlinear regime was reached [23]. The pump entered the plasma at point A, and the seed at point B. The spatial overlap of the pump and the seed were guaranteed by imaging the two beams above the nozzle with a CCD camera. The temporal overlap was achieved by scanning of the optical delay between the pump and seed with precision better than ps. The output seed passed through a long wavelength (> 850 nm) band pass filter so that any reflected pump beam light was filtered out. A small part of the amplified seed pulse was directed to a spectrometer for spectral analysis. The rest of the beam was split by a 50% beam splitter. One part was directed to a power meter and the second part was directed to an autocorrelator. When the amplification entered the nonlinear regime, the increased bandwidth made the growth of the seed pulse more robust than thermal Raman in the nonuniform plasma. Pulse compression in the nonlinear regime is accompanied by bandwidth broadening. The pump (for pumping of both the Barium Nitrate crystal and the plasma) and the input seed had a bandwidth of about 12 nm. The bandwidth of the amplified seed was ~ 19 nm FWHM, which is an independent indication of reaching the nonlinear regime. With the high amplification of the seed pulse, we were able to perform a pulse duration measurement of the amplified seed using a standard autocorrelator (Positive Light Model SSA) at various plasma length. The pulse

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Fig.8. Schematic of the RBS amplifier & compressor experimental setup

was observed to lengthen to a maximum of ~ 800 fs when the amplification was below 10. The pulse duration began to decrease when the ampli fication approached 30. he trend that the pulse became shorter as the amplification became higher is clearly shown in Fig. 9. The shortest pulse we have observed so far had a FWHM of ~ 150 fs when the amplification was ~ 60. At this point, the power of the seed pulse increased more than 200 times, and its intensity increased ~ 1000 times when spatial beam narrowing was taken into account. The intensity of the amplified seed pulse at point A in Fig. 8 was 1.7 x 1015 W/cm2. The pump pulse diameter was about 50 μm FWHM at point A and had an intensity of ~ 1 x 1014 W/cm2, hence the intensity of the amplified seed exceeded the pump intensity by more than order of magnitude. Simulation results are also shown in Fig.9. Simulations were performed using the average 1D particle-in-cell code (aPIC). The seed and pump pulses were assumed to be initially Gaussian with FWHM given by the experimental values of 500 fs and 10 ps, respectively. The initial seed intensity was 1.6 x 1012 W/cm2 and pump intensity was 1 x 1014 W/cm2. The plasma density was chosen so that the plasma wave (including a thermal shift) was resonant with the beat frequency of the lasers. The electrons were assumed to be initially homogeneous with a Maxwellian velocity distribution of Te=50eV and the ions were assumed to be motionless over the short timescale of the simulation. The seed energy amplification (the final seed energy divided by the initial seed energy) and the FWHM of the seed pulse duration are plotted as a function of the amplification of the seed (function of interaction length ). The simulation clearly shows pulse

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Fig. 9. Pulse duration vs. output energy (amplification); amplified pulses: modeling (solid lines) and experiments (circles)

stretching of the seed during the initial amplification (until roughly 1mm, corresponding to an energy amplification of ~20 ), followed by pulse shortening to ~240 fs at an energy amplification of ~180 at the end of the 2 mm plasma. While the pulse duration evolution agreed quite well with the experimental measurements, we did not observe an energy gain factor as high as 180. This may be because the amplified seed pulse experienced energy loss due to heating and ionization induced diffraction of the plasma. The simulation results shown here are one-dimensional and are, in detail, sensitive to the initial value chosen for the temperature (which is not yet well known experimentally). Nevertheless, the qualitative features of the experiment are well-reproduced including pulse expansion followed by noticeable compression and amplification of the seed pulse after its intensity becomes larger than that of the pump.

5. Two-passes RBS amplification In Fig. 10 are presented recent results for amplification in two-passes set up. The system employed additional mirrors, and interferometeric filters in order for pump pulse, after amplifying seed pulse in plasma in the 1st pass, to be directed back to approximately the same plasma region and interact again with reflected back into the plasma amplified seed. This way in the second pass the seed was increased farther amplified by factor ~2.

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Amplified Seed Energy

This was just demonstration of possibility to amplification in second pass due to quite significant “left over” pump energy from the 1st pass. Such 2passes or even multi-pass systems could significantly improve efficiency of RBS amplifier/compressor. Single pass

(a) Pump delay (psec)

Double

(b) Pump delay (psec)

Fig. 10. Amplified seed energy in single pass (a) and in double pass (b) for input seed of 5 μJ and pumping energy ~ 62 mJ in the 1st pass and ~ 40 mJ in second pass *) Present address: The University of Texas at Austin

References

1. Matthews, D, Hagelstein, P, Rosen, M., et al.: ‘Demonstration of soft X-Ray Amplifier’, Phys. Rev. Lett., 54, 110, 1985. 2. Suckewer, S., Skinner, C.H., Milchberg, H., Keane, C., and Voorhees, D.: ‘Amplification of stimulated soft-x-ray emission in a confined plasma column’, Phys. Rev. Lett., 55, 1753, 1985; also Suckewer, S., Skinner, C.H., Kim, D., Valeo, E., Voorhees, D., and Wouters, Al, ‘Divergence measurements of soft-x-ray laser beam’, Phys. Rev. Lett., 57, 1004, 1986. 3. Dunn, J., Osterheld, A.L., Shepherd, R., White, W., Shlyaptsev, V.N., and Stewart, R.E., ‘Demonstration of x-ray amplification in transient gain nickellike palladium’, Phys. Rev. Lett., 80, 2825-2828, 1998; also Dunn, J., Li, Y., Osterheld, A.L., Nilsen, J., Hunter, J.R., and Shlyaptwev, V.N. ‘Gain satura-

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tion regime for laser driven tabletop transient Ni-like ion x-ray lasers’, Phys. Rev. Lett., 84, 4834-4837, 2000. 4. Nickles, P.V., Shlyaptsev, V.N., Kalachnikov, M., Schnurer, M., Will, I. Sandner, W., ‘Short pulse x-ray laser 32.6 nm based on transient gain in Ne-like titanium’, Phys. Rev. Lett., 78, 2748-2751, 1997. 5. Nilsen, J., MacGowan, B., DaSilva, L.B., and Moreno, J.C., ‘Prepulse technique for producing low-Z Ne-like x-ray lasers’, Phys. Rev. A, 48, 4682-4685, 1993. 6. Keenan, R., Dunn, J., Patel, P.K., Price, D.F., Smith, R.F., and Shlyaptsev, V.N., ‘High- repetition-rate grazing-incidence pumped x-ray laser operating at 18.9 nm’, Phys. Rev. Lett., 94, 103901, 2005. 7. Luther, B.M., Wang, Y. M., Larotonda, A., Alessi, D., Marconi, M.C., Rocca, J.J., and Shlyaptsev, V.N., ‘Saturated high repetition-rate 18.9-nm tabletop laser in nickel-like molybdenum’, Optics Lett., 30, 165-167, 2005. 8. Nagata, Y., Midorikowa, K., Obara, M., Tashiro, H., and Toyoda, K., Phys. Rev. Lett., 71, 3774, 1993. 9. Korobkin, D., Nam, C.H., Goltsov, A., and Suckewer, S., ‘Demonstration of soft x- ray lasing to ground state in Li III’, Phys. Rev. Lett,. 77, 5206-5209, 1996. 10. Goltsov, A., Morozov, A., Suckewer, S., Elton, R., Feldman, U., Krushelnick, K., Jones, T., Moore, C., Seely, J., Sprangle, P., Ting, A., and Zigler. A., ‘Is efficiency of gain generation in LiIII 13.5-nm laser with 0.25μm subpicosecond pulses the same as with 1 μm?’, IEEE J. Sel. Top. Quantum Electron., 5(6):1453–1459, 1999. 11. Rocca, J.J., Shlyaptsev, V.N., Tomasel, F.G., Cortazar, O.D., Harshorn, D., and Chilla, J.L., Phys. Rev. Lett., 73, 2192, 1994 ; also Benware, B.R., Macchietto, C.D., Moreno, C.H., and Rocca, J.J., ‘Demonstration of a high average power tabletop soft x-ray laser’, Phys. Rev. Lett., 81, 5804-5806, 1998 ; also Macchietto, C.D., Benware, B.R., Rocca, J.J., ‘Generation of millijoulelevel soft-x-ray laser pulses at a 4-Hz repetition rate in a highly saturated tabletop capillary discharge amplifier’, Opt. Lett., 24, 1115-1117, 1999. 12. Lemoff, B.E., Yin, G.Y., Gordon III, C.L., Barty, C.P., and Harris, S.E., ‘Demonstration of a 10-Hz Femtosecond-Pulse-Driven XUV laser at 41.8 nm in Xe IX’, Phys. Rev. Lett ,74, 1574-1577, 1995. 13. Attwood, D.T., Soft X-rays and extreme ultraviolet radiation, Cambridge University Press, 1999. 14. Keldysh, L.V., ‘Ionization in the field of strong electromagnetic wave’, Soviet Physics JETP, 20, 1307, 1965. 15. Perelomov, A.M., Popov, V.S., and Terent’ev, M.V., Soviet Physics JETP, 23, 924, 1965. 16. Burnett N.H., and Corkum, P.B., ‘Cold-plasma production for recombination extreme-ultraviolet lasers by optical-field-induced ionization’, JOSA B, 6, 1995, 1989.

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17. Ping, Y. Ph.D. Thesis ‘Soft X-ray Lasers and Raman Amplification in Plasmas’, Princeton University, 2002. 18. Avitzour, Y., Suckewer, S., and Valeo, E., ‘Numerical investigation of recombination gain in the LiIII transition to ground state’. Phys. Rev. E., 69, 046409, 2004. 19. Y. Avitzour Ph.D. Thesis “Numerical Modeling of Recombination X-Ray Lasers in Transition to Ground State”, Princeton University (2006). 20. Avitzour, Y., Suckewer, S., ‘The feasibility of achieving gain in transition to ground state of CVI at 3.4nm’, submitted for publication (August.2006) 21. Shvets, G., Fisch, N.J., Pukhov A., and Meyer-ter-Vehn, J., ‘Superradiant Amplification of an Ultrashort Laser Pulse in a Plasma by a Counterpropagating Pump’, Phys. Rev. Lett., 81, 4879, 1998; also Fisch, N.J., and Malkin, V.M., ‘Generation of Ultra-high Intensity Laser Pulses’, Physics of Plasma, 10, 2056-2063, 2003. 22. Malkin V. M., Shvets G. and Fisch N. J., ‘Fast compression of laser beams to highly overcritical powers’, Phys. Rev. Lett., 82, 4448, 1999;also Malkin V. M., Shvets G. and Fisch N. J., ‘Detuned Raman amplification of short laser pulses in plasma’, Phys. Rev. Lett,. 84, 1208, 2000. 23. Cheng, W., Avitzour, Y., Ping, Y., Suckewer, S., Fisch, N.J., Hur, M.S., and Wurtele, J.S., ‘Reaching Nonlinear Regime in Large Raman Amplification of Ultrashort Laser Pulses’, Physical Review Letters, 94, 2005.

Status and Prospects on Soft X-Ray Lasers Seeded by a High Harmonic Beam at LOA

S. Sebban1 , Ph. Zeitoun1, G. Faivre1, S. Hallou1, A. S. Morlens1, J.P. Goddet1 B. Cros2, G. Vieux2 and G Maynard2,T. Mocek4 and M. Kozlová4, J.P. Causmes5 and H. Merdji5 1

Laboratoire d’Optique Appliquée, chemin de la hunière, 91128 Palaiseau LPGP, Université Paris-Sud, 91405 Orsay, France 3 Institute of Physics, Department of X-Ray Lasers, Prague, Czech Republic 4 Service des Photons, Atomes et Molecules, CEA, 91191 Gif-surYvette,France 2

Summary. Thanks to the most recent works on x-ray laser and on high order harmonics (HHG), it is now possible to produce an energetic beam having at the same time the required optical properties. The solution consists in seeding the XRL amplifier medium with another beam (HHG). This experiment was successfully realized in LOA. We studied seeding of two x-ray laser transitions, 4d-4p at 32.8 nm in Kr8+ and 5d-5p 41.8 nm in Xe8+. The amplifying medium is generated by focussing a high energy circularly polarized, 35 fs 10 Hz Ti: sapphire laser system in a few mm cell filled with gas (xenon or krypton). We succeeded to increase from a factor 10 to 200 the HHG energy, without deteriorating their optical qualities. The resulting beam was polarized, coherent and we estimate the output energy to be about 0.5 µJ.

1 Introduction For decades, synchrotrons have been the acme of XUV sources, providing X-rays for biology, chemistry, physics applications and industrial developments, resulting in major scientific progress. But tomorrow’s most attractive applications (e.g. structural Biology) require pulses with much shorter duration (fs) and much higher energy (mJ) than delivered by synchrotrons. X-ray Free Electron lasers should fulfil these requirements by providing ultra-intense beams, but their limited number will stir tremendous beamtime pressure, slowing down the spreading of applications. Laser-driven XUV sources are comparatively inexpensive and widely avail-

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able, but they have reached a bottleneck in the race for ultra-high intensities. In this pioneer work, we have set up and characterised the first true XUV laser chain, overcoming these bottlenecks for the first time. By combining the high optical quality of high harmonics as a seed [1] , with a highly energetic x-ray laser plasma amplifier [2-3], we produced the first highly saturated, energetic, femtosecond, fully coherent and fully polarised tabletop x-ray laser operating at 10 Hz [4]. This technique, easily applicable on all existing laser-driven XUV facilities, opens the way to ultra-high intensities studies worldwide. Since some years x-ray laser community try to promote this source for applications. In this aim, it is necessary to offer an optically good beam to the users. Nevertheless most of x-ray laser (XRL) are using amplified spontaneous emission, i. e. laser has no cavity to select a spatial mode. Consequently the beam can not be polarized or spatially coherent and the wave front is not regular. Thanks to the most recent works on x-ray laser and on high order harmonics (HHG), it is now possible to produce an energetic beam (from 0.1 to 1mJ) having at the same time the required optical properties. The solution consists in seeding the XRL amplifier medium with another beam (HHG). This experiment was successfully realized in LOA. We studied seeding of two x-ray laser transitions, 32.8 nm (Kr8+) and 41.8 nm (Xe8+). We succeeded to increase from a factor 15 to 600 the HHG energy, without damaging their optical qualities. This structure seems to be the beginning of a new generation of XRL, with considerable improvements compare to the actual XRL. Furthermore this technique can help for the measurement of many plasma parameters.

2 Experimental setup The XUV amplifying laser chain was made of three parts: a high harmonics generation (HHG) seed, a focusing system, and an optical field ionized x-ray laser (XRL) amplifier medium. The seed beam was obtained by focusing a 20 mJ, 30 fs, infrared laser in a gas cell filled with argon or xenon .This seed was image relayed onto the entrance of the x-ray laser (XRL) amplifier (Kr or Xe gas longitudinally pumped by a 1 J, 30 fs laser) by means of a toroidal XUV mirror. This X-ray laser operates at 32.8 nm and 42.8 nm using Kr and Xe respectively. After amplification, the output beam was either analyzed by an XUV spectrometer or XUV CCD camera. The experiment has been performed in LOA with the multiterawatt, 30 fs, 10 Hz, Ti:sapphire laser emitting at 815 nm. The laser delivers two chirped beams having separate pulse compressor enabling to optimise in-

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dependently the XRL or the HHG drivers. One beam, lately called “pump”, contains most of the energy (about 1 J on target) and is used for creating the amplifying XRL medium. The second beam, called “probe”, has energy around 20 mJ on target and generates the HHG (Figure 1) Harmonics were produced by focusing the probe beam into a gas cell of variable pressure and length, filled with argon. The linearly polarised beam was focused with a f=1.5 m, aspherical lens. The focal spot has been 15 -2 measured to be about 150 µm leading to an intensity of about 10 W.cm . The harmonic flux was optimised by changing the conditions of laser interaction with the active medium, such as moving the focal spot position, changing the gas pressure, and the cell length. The highest HHG flux was obtained for a pressure of 25 mbar, 10 mm long cell, and focal plane situated 4 cm behind the gas cell. The main optimisation was the fine adjustment of the wavelength of one harmonic (25th) so as to coincide with the 8+ wavelength of Kr XRL (32.8 nm). This was done on a day-to-day basisby adjusting the chirp of the laser generating the HHG [5-6].

Fig. 1. Schematic description of the experimental set-up

The amplifying plasma was created by focusing the pump beam into another gas cell of variable length (from 0 to 6 mm) and pressure. The cell was filled with krypton or xenon held at uniform pressure. Fundamental radiation from the Ti:Sapphire laser was circularly polarised by a quarterwave plate and focused with an f=0.85 m, spherical on-axis mirror into the gas cell. Circular polarisation ensures the creation of energetic free electrons that collisionally pump the 4d-4p or 5d-5p lasing lasing transitions. The measured focal spot was around 50 µm in diameter leading to a net in17 -2 tensity of about 5×10 Wcm . The output of the harmonic source was re-imaged on the entrance of the amplifier plasma, using a 1:1 grazing incidence (4°) gold coated toroidal

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mirror. The theoretical reflectivity is around 80%. The focal spot of HHG has been measured to be around 150 µm. Special attention has been paid to the temporal and spatial overlapping between the harmonic and the X-ray laser beams. As the OFI XRL is longitudinally pumped, the position of the gain region coincides with the position of the IR driving laser. Since also the HHG are collinear with the IR beam, the superposition of the HHG and the XRL gain region has been done in IR. Temporal synchronisation of the HHG with the period of XRL amplification could not be done in such a simple way since the plasma starts to amplify after the interaction of the driving laser with the gas. Based on previous experiment, we may assume that the gain will appear around 5 ps after laser interaction and will last about 8 ps [7]. Since HHG are emitted only during the interaction of the IR laser with the gas, the synchronisation of the seed and the XRL period of amplification was done by adjusting the delay between the IR pump and probe beams. The XUV beams generated in this experiment were analysed by an onaxis XUV spectrometer and by making monochromatic images of the beam cross-section. These images were obtained by placing a removable 45°, XUV mirror in the beam path, redirecting the beam towards a cooled, thin, back-illuminated charge-coupled device (CCD). A 300 nm thick aluminium filter has been used to remove the IR beams. The interferential multilayer mirror has been designed to achieve a high reflectivity (estimated at 50%) and a strong polarisation at 45°. The XUV mirror is made of a stack of 30 Mo/B4C/Si tri-layers.

3 Results and discussion The delay between XRL plasma creation and HHG injection was variable to reach optimum amplification conditions, synchronizing HHG seeding with maximum gain. Four emission spectra are displayed in figure 2, corresponding to (a) high harmonics alone, (b) x-ray laser alone, (c) XRL and HHG seeded long after gain extinction, and (d) HHG synchronised with maximum XRL gain. The amplification period starts 5 ps after the interaction of the IR laser with the gas and lasts about 8 ps. Figure 2 (d) clearly shows that a strong amplification of the seed has been achieved. The HHG were seeded at about twice the intensity of the ASE x-ray laser, leading to an enhancement of the output signal by a factor of 13. Since the level of seeding may influence many laser parameters (intensity, pulse duration, ratio of the energies in the seeded beam to this in the ASE beam), it is crucial to understand how is the seeding level related to the saturation intensity.

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Fig. 2. Experimental spectra under conditions : (a) HHG only, (b) ASE XRL only, (c) both HHG and XRL in a non-amplifying timing, and (d) the amplified seeded XRL.

The amplification law (output intensity versus amplifier length) of the amplified spontaneous emission (ASE) XRL has been measured to clarify the level of seeding. The gas cell length ranged from 0 to 4 mm and the intensities have been fitted taking into account saturation effects [3]. A -1 small-signal gain coefficient of 80 cm has been inferred, reaching saturation above 1.7 mm plasma length. Clearly, the spectrum in Fig. 2(d) was obtained for an HHG seeding above saturation intensity (about 4.5 times higher). In the second part of the experiment, the seeding intensity was reduced down to 1/50th of the saturation intensity. The output signal was 38 times higher than the saturation intensity; the amplification factor became as large as 200 i.e. 15 times higher than for the amplification achieved with above-saturation-intensity seeding. The delay line has also allowed to measure the gain duration for several pressure. This measurement was done for both gas, krypton end xenon. For the Xe8+ at 41,8 nm (fig3a), the maximum gain was obtained for a pressure of 15 Torr and the duration of the gain was about 8ps. For Kr8+ at 32.8 nm (fig3b) the best pressure was 15 Torr, and for this pressure the gain duration was 4 ps. Using this method the temporal profile of the gain of the collisionally excited Xe8+ laser at 41.8 nm has been measured for various gas densities and compared to simulations of the atomic processes

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a)

b)

c) Fig. 3. (a) Measured amplification, (b) extracted average gain and (c) calculated gain coefficient as a function of function of the injection delay for Xe, and for 5 gas pressures

performed with a time-dependent collisional radiative code as shown in figure 3 [8]. The seeded XRL beam was also characterised in terms of optical parameters such as divergence, spatial coherence and polarisation. These parameters were directly inferred from images of the beam cross-section (fig. 5 and 6). Theoretically, the ratio of the mirror reflectivity for the 25th harmonic (32.8 nm) to the 23rd (35.65 nm) or to the 27th (30.37 nm) is about 10. Therefore only the 25th harmonic and/or the XRL might be reflected towards the detector. The seed divergence is imposed by both the geometry of the toroidal mirror and the HHG intrinsic divergence. The divergence of the seeded XRL was slightly lower than those of the seed. The brightest part of the image in Fig. 4 corresponds to the seeded XRL while the weak surrounding, circular signal is the ASE x-ray laser. The diver-

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gence of the seeded XRL was slightly lower than those of the seed. The brightest part of the image in Fig. 4 corresponds to the seeded XRL while the weak surrounding, circular signal is the ASE x-ray laser. The divergence of the ASE x-ray laser was found to be much larger (>12 mrad) than that of the seeded beam (1 mrad).

Fig. 4. 3D images (false color) of the seeded XRL cross-section as recorded by the XUV CCD detector after reflection on the monochromatic XUV mirror. The central strong signal (gray) belongs to the seeded XRL while the ASE XRL illuminating essentially the whole filter generated a circular signal (purple). The insert shows the seeding HHG signal recorded with the same set-up and displayed on the same scale as the main image.

The multilayer mirror has been designed to be highly polarising. The extinction ratio (intensity peak/lowest intensity) has been investigated by measuring the reflected signal versus the angle of polarisation of the HHG. Figure 5 displays the variation of both the HHG and the seeded XRL intensity versus the angle of polarisation The extinction ratio of the mirror is as high as 20. From these curves, it appears that the seeded XRL is polarised and follows well the initial polarisation of HHG. No sign of depolarisation has been observed. Inserts in Fig. 6 show the beam cross-section when the HHG were s- polarised (peak reflectivity) and p- polarised (minimum reflectivity). As expected, the ASE XRL alone is unpolarized. Also we have observed that the coherence of the seeded XRL beam can be dramatically improved, with the respect to seed HHG beam. In this aim, we have characterized the spatial profile and conducted a series of Young’s two-slit experiments to measure and systematically compare the

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Fig. 5. Variation of the HHG (open diamond) and seeded XRL (black square) intensities versus the angle of polarization.

Fig. 6. Fringe visibility of the HHG beam, the ASE emission and the amplified 32.8 nm pulse as a function of the slit separation.

spatial coherence of the seed HHG beam, the ASE amplifier emission and the seeded amplifier emission at 32.8 nm. Figure 6 shows the normalized complex degree of coherence ⎟µ12⎟ plotted for a gaussian profile. The coherent radius of the ASE emission is about 98 µm which is about 150 times smaller that the measured beam diameter. As the OFI XRL emission can be considered as spatial incoherent but temporally coherent, the equivalent incoherent source size which is here about 76 µm should closely correspond to transverse dimension of the plasma amplifier. For the seed HHG beam we estimate a coherent radius of 102 µm which corresponds to about a quarter of full beam diameter. When amplified by the population inverted plasma, the coherent radius build upto 232 µm which corresponds to about 60% of the central disc of the beam profile, showing the benefic action of spatial filtering on the improvement of the transverse coherence of the generated pulse.

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4 Conclusion Future work will be in a near future to seed in an OFI capillary (ASE x30 compare to OFI in a gas cell). With this kind of amplifier, the expected output energy is about 30 µJ). Later we plan to seed an XRL plasma created from a solid target such as to increase the output energy by at least three order of magnitudes (~ 1 mJ) thanks to the much higher density of XRL amplifying medium [9]. This rise in density and temperature will also lead to a spectral width broadening and consequently to even shorter pulse duration. As this technique matures, future compact XUV laser chains should achieve beams performances close to those of VUV Free-electron lasers [10].

References [1] Kazamias, S. et al, Global optimization of High Harmonic generation. Phys. Rev. Lett., 90, 193901 (2003) [2] Sebban, S., Demonstration of a Ni-Like Kr Optical-Field-Ionization at 32.8 nm. Phys. Rev. Lett., 89, 253901 (2002). [3] Sebban, S. et al, Saturated Amplification of a Collisionally Pumped OpticalField-Ionization Soft X-Ray Laser at 41.8 nm. Phys. Rev. Lett. 86, 3004 (2001). [4] Ph. Zeitoun. et al. , A high-intensity highly coherent soft X-ray femtosecond laser seeded by a high harmonic beam, Nature vol 431, 426-429 (2004) [5] Lee, D. G., Kim, J. H., Hong, K. H., Nam, C. H., Coherent Control of HighOrder Harmonics with Chirped Femtosecond Laser Pulses. Phys. Rev. Lett, 87, 24, 243902 (2001) [6] Reitze, D. H., Enhancement of high-order harmonic generation at tuned wavelengths through adaptative control. Opt. Lett., 29 1, p. 86 (2004) [7] T. Mocek et al, Characterization of collisionally pumped optical-fieldionization soft x-ray lasers. Appl. Phys. B, in press [8] T. Mocek, S. Sebban, G. Maynard, Ph. Zeitoun, G. Faivre, A. Hallou, M. Fajardo, S. Kazamias, B. Cros, D. Aubert, G. de Lachèze-Murel, J. P. Rousseau, and J. Dubau “Absolute Time-Resolved X-Ray Laser Gain Measurement”, Phys. Rev. Lett. 95, 173902 (2005) [9] Y. Wang et al. Phys. Rev. Lett 97 (2006) 12901 [10] Ayvazyan, A. et al, A new powerful source for coherent VUV radiation : Demonstration of exponential growth and saturation at the TTF free-electron laser. Eur. Phys. J. D, 20, 149 (2002)

Generation of Efficient Optical-Field-Ionization X-Ray Lasers in Cluster Jets M.-C. Chou, T.-S. Hung and J.-Y. Lin* Department of Physics, National Chung Cheng University, Chia-Yi 621, Taiwan P.-H. Lin, S.-Y. Chen and J. Wang Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan

Summary: We experimentally demonstrate the amplification of optical-fieldionization soft x-ray lasers in krypton cluster jets at pump energy of only 200 mJ. With the employment of small f-number optics, nature diffraction and ionizationinduced refraction in plasmas can be suppressed to enable the pump pulse producing a longer column of gains provided the focal position is optimized. A simple wave propagation code is developed to study and optimize the laser propagation in optical-field driven plasmas. Good agreements between experimental observations and simulations are found. The further enhancement of Kr x-ray laser output at 32.8 nm is achieved by guiding the pump beam in the optically preformed plasma waveguide. More than 4 times of x-ray photons are generated from pure Kr plasma waveguide at the same pump energy. Significant reductions of the pump energy make these pumping configurations favorable for practical high-repetitionrate operations.

1 Introduction Optical-field-ionization (OFI) has been considered as an efficient way for pumping tabletop, high-repetition-rate soft x-ray lasers through collisional excitation or recombination processes, because the electron energy distribution and the ionization balance in plasmas can be precisely controlled by the pump laser intensity and polarization [1-5]. A linearly polarized laser pulse can minimize the mean electron temperature in plasmas and promote strong recombination, whereas the hot electrons produced by a circularly polarized pulse can be used for collisional-excitation pumping. Moreover,

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the appearance intensity for various ion species in the OFI plasma is discrete and highly selective. These properties can be applied to enhance ion utilization, thereby achieve efficient lasing. Saturated lasing of collisional excitation OFI x-ray lasers was first demonstrated in Xe8+ ions for the 5d-5p transition at 41.8 nm by focusing an intense, circularly polarized laser pulse into a gas cell filled with pure xenon [6]. A similar result was later obtained in a xenon cluster jet operated at high backing pressures [7]. Strong amplification at 32.8 nm for the 4d– 4p transition of Ni-like krypton has also been demonstrated with a 760-mJ, 30-fs laser pulse [8]. Recently, enhancement of OFI x-ray lasing in preformed plasma waveguides driven by discharge was reported. The gain media were a capillary tube filled with xenon and buffer gas [9] or a multimode capillary waveguide [10]. By seeding an OFI x-ray laser amplifier with a pulse produced from high harmonic generation, a 20-fold increase in the x-ray output was achieved and sub-picosecond x-ray pulse was produced [11]. In this paper, we demonstrate low-threshold lasing of the 32.8-nm Kr8+ 4d–4p line by using tight-focusing pumping configurations. In the meantime, we use gas jets as the gain media to avoid accumulated optical damage. The combination of low pumping threshold and gas-jet media facilitates long-time high-repetition-rate operation, which is an important aspect for practical applications. We show that low-threshold OFI x-ray lasing can be achieved by tight focusing the pump laser at an optimal focal position. Both computer simulation and experimental diagnosis show that the balance between the converging power of the focusing optics, diffraction, and ionization defocusing can increase the gain length significantly as the spatial profile of the pump beam is well controlled at the optimal size. Near saturated lasing was observed at a pump energy of only 200 mJ, and the lasing threshold is only 70 mJ. In order to further improve the efficiency and beam quality of OFI x-ray lasers, a preformed plasma waveguide is developed to guide the intense pump pulse in OFI plasmas. The guided laser pulse can delivered a high pump intensity in a smaller diameter at a considerably low pulse energy. The interaction length and thus the gain-length product of x-ray lasers can also be extended significantly. We show that the plasma waveguide can be efficiently produced in a Kr/H2 cluster jet operated at a high backing pressure with axicon ignitor-heater scheme [12]. More than 70% of the pump energy in the vacuum focal spot is observed to transmit through the all optically preformed waveguide. The waveguide with buffer gas H2 can be used to develop recombination OFI x-ray lasers as electrons generated from high-density hydrogen are relatively cool [13]. On the other hand, strong amplifications of collisional excitation OFI Kr x-ray laser at 32.8

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nm is observed in pure Kr waveguide. The spectral brightness of Kr lasers amplified in waveguides is enhanced by a factor of > 100 compared to that obtained with tight focusing configuration.

2 Experimental Setup The experimental setup was similar to that described in Ref. 7, 12. A 10TW, 45-fs, 810-nm, and 10-Hz Ti:sapphire laser system (upgraded from the laser system in Ref. 14) based on the chirped-pulse amplification technique was used in this experiment. The pump pulse was focused by an offaxis parabolic mirror of 30-cm focal length onto a cluster jet. The focal spot size of the pump pulse was 7.5-µm diameter in full width at half maximum (FWHM) with 80% energy enclosed in a Gaussian-fit profile. A quarter-wave plate was used to change the pump polarization. The cluster jet was produced from a slit nozzle with a 5-mm×500-µm outlet and a round throat of 1.2-mm diameter. In the major axis of the outlet, the inner opening angle of the nozzle is 5.4°, and in the minor axis the inner width shrunk from 1.2 mm at the throat to 0.5 mm at the outlet. To produce a gas target with sharp boundaries, a rectangular aperture was mounted on the output of the cluster jet. So, the gas density profile had a flat-top region of 3.5 mm in length and a sharp boundary of 450 µm at both edges along the major axis. The average atom density increased linearly with the backing pressure and was measured to be 2.8×1017–3.2×1019 cm-3 for a backing pressure of 0.041–4.8 MPa. The preformed plasma waveguide was produced in pure krypton gases or the mixture of krypton and hydrogen gases with the axicon ignitor-heater scheme. The ignitor was a compressed 45 fs pulse, and the heater was the uncompressed beam with a pulse duration of 80 ps. They were focused by an axicon of 30° base angle to a line focus of ~8-mm length. The longitudinal intensity distribution of the line focus can be approximately controlled by a beam expander installed before the axicon. A relay-imaging system was used to measure the injection beam profile at the end of the plasma waveguide to verify the guiding of the injection beam. The on-axis diagnostic was a flat-field spectrometer (FFS) made of an aperiodic grazing-incidence grating with an average groove density of 1200/mm and a back-illuminated 16-bit soft x-ray CCD camera. A 0.5 µm-thick Al filter is used to block the pump beam and to attenuate x-ray emission. A dipole magnet was put in front of the spectrometer to deflect the electrons emitted from the interaction region, guarding against false signals from electrons in the x-ray CCD camera. Mach-Zehnder interferometry with a probe pulse passing transversely through the cluster jet

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Fig. 1. X-ray laser output as a function of the focal position at atom density of 1×1018 cm-3. The pump energy was 200 mJ and the pump polarization ellipticity was 0.55. The effective f-number of the focusing optics is 7. Inset: Kr x-ray laser spectrum at 32.8 nm.

was used to measure plasma density distribution 5 ps after the pump pulse. The propagation of the pump pulse in the cluster jet can be analyzed from the interferograms. By calibrating the grating reflectivity, the filter transmittance, and the CCD response, the absolute emission yield was obtained.

3 Experimental results and discussions 3.1 Low-threshold OFI Kr lasers with tight focusing pumping To create a uniform and elongated plasma column for x-ray amplification, we scan the focal position of the pump laser in vacuum relative to the entrance of the gas target along the laser propagation direction. At each position, the diameter and the wave front curvature of the pump beam at the front boundary of the gas target is different, so is the nonlinear evolution of the beam profile in the plasma. Fig. 1 shows the strong dependence of the lasing signal on the focal position. The inset shows the on-axis time integrated Kr x-ray laser spectrum for a pump polarization ellipticity of 0.55 at an atom density of 1×1018 cm-3 and a focal position of 2.2 mm behind the front edge of the gas target. When the laser pulse is focused at the front edge, the intensity is about 5.5×1018 W/cm2, which is much higher than needed for producing the correct ionization balance. Over-ionization depletes Kr8+ ions and shortens the gain length. In addition, overproduction

Generation of Efficient Optical-Field-Ionization X-Ray Lasers in Cluster Jets 239

Fig. 2. Dependence of the calculated gain length on the focal position for different focusing optics. The parameters used in the simulation are the same as in Fig. 1, except that the focal length of the pump laser is varied.

of free electrons promotes ionization defocusing which makes the laser beam diverge quickly. As the laser intensity drops below OFI threshold of Kr8+ ions, the lasing gain is also terminated at the rear portion of the gas jet. On the contrary, if the focal spot is moved to the rear edge of the gas jet, the beam diameter at the front edge becomes relatively large. The pump intensity becomes too low to generate lasing ions at the front portion of the gas jet. Consequently there exists an optimal focal position to achieve a good balance among beam convergence, diffraction, and ionization defocusing for the laser beam to maintain its intensity over a long distance. To study and optimize the pump beam propagation in OFI plasmas, a source dependent expansion method [15] is used to numerically solve three-dimensional nonlinear wave equations for the pump pulse. The computation takes account of photoionization, ionization energy depletions, and laser propagations in a plasma with spatially and temporally varying density. Since the lasing plasma is predominately generated by the laser pulse via optical-field ionization, the ion density, electron density, and photonionization rate in specific stages of ionization can be calculated using the Ammosov-Delone-Krainov formulas for a given field [16]. In turn, the spatiotemporal electron and ion density profile determine the propagation of the pump pulse. These two processes are described by a system of nonlinearly coupled equations which can be numerically integrated. Fig. 2 shows that the dependence of the calculated effective length of the gain re

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Fig. 3. X-ray lasing signal and calculated gain length as a function of pump energy. Solid square: lasing signal at 32.8 nm produced by a pump pulse with a polarization ellipticity of 0.55 at an atom density of 1×1018 cm-3. The focal position is at 2.2 mm behind the front edge of the gas target. Solid line: calculated gain length under the same condition.

gion on the focal position for various focusing configuration. All the parameters used in the simulation are the same as in Fig. 1, except that the focal length of the pump laser is varied. The result shows that the x-ray amplification length is increasingly more sensitive to the focal position as the f-number decreases. The length of the gain region is clearly enhanced by tight focusing at an optimal position. The dependence of the lasing output on the pump energy was measured to explore how OFI lasers work under low-energy pumping. As shown in Fig. 3, it was observed that the x-ray laser output was enhanced dramatically (up to factor of 1000) from pump energy of 70 mJ to 200 mJ. In the small signal region, the laser output is expected to increase exponentially with the length of the gain region. Simulations reveal that the effective amplification length increases monotonically with the pump energy when the pump beam is focused at the optimal position. The departure of simulation results from experimental data at large pump energy indicates that the laser gain may have started to saturate, as the saturation effect is not included in the simulation model. A small signal gain coefficient of 61±9 cm-1 is derived from the experimental and simulation data at the pump energy up to 130 mJ in Fig.3. A gain-length product of 15.9±1.3 is expected when the pump energy is 200 mJ. The absolute yield under 200-mJ pumping is estimated to be ~1×109 photons/pulse. This value is close to that of

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saturated Kr x-ray lasers reported in Ref. 8 with a 760-mJ, 30-fs pump pulse. It is interesting to note that in our experiments the optimal polarization ellipticity for maximum x-ray lasing was found to be in the range of 0.5– 0.6 regardless of the atom density. The result can be explained by the preionization of the clusters at the ionization front. If collisional heating and ionization at the ionization front can ionize Kr atoms to Kr3+ or Kr4+, these pre-ionized electrons may lose their energy via radiative cooling during the nanoplasma expansion and through collision with other colder electrons or surrounding neutral atoms during the uniform plasma expansion. As a result, upon the arrival of the main peak of the pump pulse, the energies of these pre-ionized electrons may fall below the threshold of collisional excitation and thus they cannot contribute to collisional excitation. This will greatly reduce the gain. A reduction of the polarization ellipticity toward linear polarization can shift the electron energy spectrum toward the lowenergy end for subsequent ionization stages from Kr3+ or Kr4+, thereby increases the collisional excitation rate. The observation suggests that by using time-domain polarization shaping [17], it may be possible to further optimize the electron energy spectrum in accordance with the ionization stages. This will further increase the gain and efficiency. 3.2 Generation of OFI Kr lasers in preformed plasma waveguide Figure 4(a) shows the interferogram at an ignitor-heater separation of 200 ps and a probe delay of 2.5 ns with respect to the heater in the 5-mm Kr/H cluster jet operated at 630-psi backing pressure. The ratio of Kr to H2 in the gas reservoir of the cluster jet was 1:11. The pulse energy for ignitor and heater were 43 mJ and 290 mJ, respectively. It was found that plasma waveguide cannot be generated if only the ignitor or the heater was used. Instead, a uniform plasma waveguide extended to ~4.4 mm was observed when both ignitor and heater were deployed. These results show that the plasma waveguide can be produced much more efficiently when the axicon scheme is used in conjunction with the ignitor-heater scheme. When only a short laser pulse is used, even though it has sufficient energy to ionize the gas, the pulse duration is too short to heat the plasma via inverse bremsstrahlung absorption. When only a long pulse is used, the laser intensity is too low to produce seed electrons so that there is no inverse bremsstrahlung absorption to drive the formation of plasma waveguide. In the ignitor-heater scheme, the short low-energy pulse first ionizes the gas to provide seed electrons by multi-photon ionization, so that the following long high-energy pulse can be absorbed efficiently to drive the expansion

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Fig. 4. Interferogram (a) and beam profile of the injected pump beam at ~ 5 mm after its focus (b) for various cases in the mixture gas of 1:11 Kr/H at a backing pressure of 630 psi. The ignitor-heater separation is 200 ps.

and the subsequent collisional ionization which makes the plasma density higher in the outer region than in the center of the beam. Guiding of the pump beam was verified from the beam profile imaging at the end of the plasma waveguide for an injection delay of 2.5 ns. As shown in Fig. 4(b), the pump pulse can not be guided at a small beam diameter without the presence of the plasma waveguide. The guided beam size was measured to be ~ 14 µm (FWHM) with more than 60% of the energy in the vacuum focal spot transmitting through the preformed waveguide. It is also noted that the guiding efficiency of the Kr/H plasma waveguide was enhanced to ~75% when the energy of the pump pulse increased from 15 mJ to 210 mJ. The pedestal of the high-energy pump pulse may induce pre-ionization and heating of plasmas to enlarge the density dip for a better guiding. Although high quality plasma waveguide can be generated in the mixture of Kr and H2 gases, it is believed that cold electrons produced during the ionization of hydrogen atoms can promote strong recombination in Kr8+ ions and thus reduce the lasing gain significantly. In our experiments, the energy of the pump pulse was varied systematically to obtain the optimal pump intensity for producing the correct ionization balance in the plasma waveguide. No lasing signal of Ni-like Kr 4d-4p line was observed. The effective gain-length product in plasma waveguide may become too small to produce a strong lasing output as the small signal gain coefficient is reduced dramatically.

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Fig. 5. Interferogram and beam profile of the injected pump beam at ~ 5 mm after its focus for various cases in pure Kr at a backing pressure of 200 psi. The ignitor-heater separation is 200 ps.

Without doping hydrogen as the buffer gas, the high efficiency plasma waveguide can not be generated in the pure Kr as shown in Fig.5. Only ~10% of the energy in the vacuum focal spot is observed to transmit through the preformed waveguide. For pump energy of 210 mJ. The laser intensity at the exit of the waveguide was estimated to be 1.5 × 1017 W/cm2 which is high enough to ionize Kr atoms to Ni-like ion state. Strong lasing signals from Kr8+ 4d–4p transition at 32.8 nm was detected by the on-axis x-ray flat-field spectrometer. Compared to the optimal lasing output with tight focusing pumping, more than 4 times of x-ray photons were generated in the Kr plasma waveguide with a small divergence angle of ~ 6 mrad. This indicates the brightness of Kr lasers can be enhanced by a factor of > 100 when the preformed plasma waveguide is presented.

4 Summary In summary, a low-threshold configuration of OFI x-ray laser in krypton cluster jets was demonstrated. The reduction of the pump energy is achieved by carefully balancing the focusing, diffraction, and ionization defocusing to maintain a high-intensity pump profile over an extended length. In contrary, an efficient method for generating extended plasma waveguides is developed by using the axicon lens in conjunction with the ignitor-heater scheme. High efficiency plasma waveguides in Kr/H mixed gas jets are generated with more than 70% of pump energy observed to transmit through a ~5-mm long waveguide channel. This high efficiency plasma waveguide is particularly suitable for producing recombination OFI x-ray lasers as the electron generated from hydrogen can be very cool to promote recombination. The generation of collisonal excitation Ni-like Kr x-ray lasers at 32.8 nm in a 5-mm pure Kr waveguide at a pump energy

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of only 210 mJ is also demonstrated. The brightness of Kr lasers amplified in waveguides is enhanced by more than 2 orders of magnitude compared to that obtained with free propagation, tight focusing pumping. In order to further increase the x-ray laser efficiency, the ratio between Kr and H2 has to be optimized to obtain a reasonable gain coefficient and guiding efficiency in the preformed plasma waveguide. Such that the gain-length product of x-ray lasers can be maximized while the pump energy can be kept at low value. With time-domain polarization shaping, it is possible to further reduce the threshold and increase the efficiency. We believe this is a promising direction toward the development of low-cost, high-repetitionrate soft x-ray lasers for practical applications.

References 1. Nagata, Y. et al., Phys. Rev. Lett. 71, 3774 (1993). 2. Lemoff, B.E. et al., Opt. Lett. 19, 569 (1994). 3. B.E. Lemoff B. E et a., Phys. Rev. Lett. 74, 1574 (1995). 4. Korobkin D.V. et al.,Phys. Rev. Lett. 77, 5206 (1996). 5. Hooker S.M., Epp P.T., and Yin G.Y., J. Opt. Soc. Am. B 10, 2735 (1997). 6. Sebban, S. et al., Phys. Rev. Lett. 86, 3004 (2001). 7. Chu H.-H. et al., Phys. Rev. A 71, 061804(R) (2005). 8. Sebban S. et al., Phys. Rev. Lett. 89, 253901 (2002). 9. Butler A. et al., Phys. Rev. Lett. 91, 205001 (2003). 10. Mocek T. et al., Phys. Rev. A 71, 013804 (2005). 11. Zeitoun Ph. et al., Nature 431, 426 (2004). 12. Xiao Y.-F. et al., Phys. Plasmas 11, L21 (2004). 13. Grout M.J. et al., Opt. Commun. 141, 213 (1997). 14. Chu H.-H. et al., Appl. Phys. B 79, 193 (2004). 15. Sprangle P., Penano J.R., and Hafizi. B., Phys. Rev. E 66, 046418 (2002). 16. Ammosov, M.V., Delone N.B., and Krainov V.B., Soviet Phys. JETP 64, 1191 (1986). 17. Brixner T. and Gerber G., Opt. Lett. 26, 557-559 (2001).

Experimental Investigation of the Parameter Space of Optical-Field-Ionization Collisional-Excitation X-Ray Lasers in a Cluster Jet M.-C. Chou1,2, P.-H. Lin1,3, T.-S. Hung1,2, J.-Y. Lin2, J. Wang1,3,4 and S.-Y. Chen1,4 1

Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan

2

Department of Physics, National Chung Cheng University, Chia-Yi 621, Taiwan

3

Department of Physics, National Taiwan University, Taipei 106, Taiwan

4

Department of Physics, National Central University, Chun-Li 320, Taiwan

Summary. Optical-field-ionization collisional-excitation soft x-ray lasers in clustered gas jets were experimentally investigated in detail. A tomographic measurement based on laser machining technique was used to resolve the growth of x-ray lasing intensity as a function of position in a cluster jet, exploring the origins of the dependences of x-ray lasing intensity on atom density and laser polarization. The presence of optimal atom density was found to be a result of ionizationinduced refraction. An unexpected observation is that circular polarization appears to be not the optimal polarization ellipticity, which may be a manifestation of effects of pre-ionization at the laser-cluster ionization front.

1 Introduction The first saturated operation of collisional-excitation optical-fieldionization (OFI) x-ray laser was demonstrated with 5d-5p transition at 41.8 nm of Pd-like Xe in a xenon gas cell [1]. A similar result was later achieved in a Xe clustered gas jet [2]. Strong amplification at 32.8 nm for 4d-4p transition of Ni-like Kr has also been demonstrated with a 760 mJ, 30 fs laser pulse [3]. Recently, enhancement of OFI x-ray lasing in a preformed plasma waveguide driven by discharge in a capillary tube filled with xenon and buffer gas [4] and that in a multi-mode capillary waveguide [5] were reported. In addition, by seeding an OFI x-ray laser

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amplifier with a pulse produced from high harmonic generation, enhancement of the x-ray laser intensity and quality was achieved [6]. Here we report the investigation of the parameter space of OFI collisional-excitation x-ray lasers in a clustered gas jet for Pd-like Xe at 41.8 nm and Ni-like Kr at 32.8 nm. A tight focusing configuration was used to explore how the lasers work under low-energy pumping. A tomographic measurement technique based on laser machining was used to resolve the growth and decay of the x-ray lasing intensity as a function of position in the cluster jet. Maximum x-ray lasing was found to appear at a pump polarization ellipticity other than circular polarization. This may be ascribed to the effect of pre-ionization during the laser-cluster interaction at the ionization front.

2 Experimental setup A 10-TW, 45-fs, 810-nm, and 10-Hz Ti:sapphire laser system based on chirped-pulse amplification technique (upgraded from the laser system in Ref. 7) was used in this experiment. A 210-mJ, 45-fs pump pulse was used for preparation of the lasing ionization stages and above-thresholdionization (ATI) heating of electrons, and a 30-mJ, 45-fs pulse set to be 6 ns earlier than the pump pulse was used as the machining pulse for the tomographic measurement to be described below. The pump pulse was focused with an off-axis parabolic mirror of 30-cm focal length onto a cluster jet and the focal spot size was 10-μm in diameter. The cluster slit-jet has a 3.5 mm flat-top region with 750-μm slopes at both edges. Propagating perpendicularly to the pump pulse, the machining pulse was imaged from the location of a knife edge onto the interaction region by a spherical lens of 20-cm focal length with a demagnification factor of 3. In the meantime it was focused in the vertical direction to a width of 20 μm by this spherical lens in combination with a cylindrical concave lens of 75-cm focal length. Based on the laser machining technique as that in Ref. 8, by scanning the knife-edge position the end of the region in which the pump pulse interacts with clusters was varied and the growth of x-ray lasing intensity with pump-pulse propagation in the cluster jet was resolved tomographically. The primary diagnostics for x-ray was a flat-field grazingincidence x-ray spectrometer consisting of an aperiodically ruled grating and a 16-bit x-ray charge-coupled device (CCD) camera. The spectrometer was used to measure the x-ray lasing spectrum and the lasing divergence angle in the direction of pump laser propagation. Aluminum filters of 0.5 μm thickness were used to block transmitted pump laser pulses and attenu-

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ate x-ray emission. By calibrating the grating reflectivity, the filter transmittance, and the CCD response, the absolute emission yield was obtained.

3 Dependence on atom density The inset in Fig. 1(a) shows the Xe x-ray spectrum. The photon number of the 41.8 nm lasing line reached about 109 photons and the divergence angle was 13 mrad. The dependence of number of photons for Pd-like Xe on atom density is shown in Fig. 1(a). It was observed that an optimal atom density for maximum lasing is present at 7.4×1017 cm-3, which agrees with the number found in previous experiments using a gas cell [1]. It is expected that increase of atom density should result in a larger gain and thus a larger lasing photon number. However, if the atom density is increased beyond an optimal value, the lasing photon number is expected to drop as a result of ionization-induced refraction [1]. The ionization-induced refraction refers to the defocusing of a laser beam caused by the plasma with a higher on-axis density than that at the radially outer region produced by optical-field ionization. Similar results for 32.8 nm x-ray lasing were observed. The inset in Fig. 1(b) shows the Kr x-ray spectrum. The photon number of the 32.8-nm lasing line reached about 109 photons and the divergence angle was 14 mrad. The dependence of number of photons for Ni-like Kr lasing at 32.8-nm on atom density is shown in Fig. 1(b). The optimal atom density was 1.2×1018 cm-3.

Fig. 1. Number of photons of Pd-like Xe lasing at 41.8 nm, (a), and Ni-like Kr lasing at 32.8 nm, (b), as functions of atom density. Insets in (a) and (b) show the x-ray lasing spectrum at atom densities of 7.4×1017 cm-3 for Xe and 1.2×1018 cm-3 for Kr. The pump polarization ellipticity were 0.65 for Xe and 0.55 for Kr. The energy of the pump pulse was 210 mJ and the focal position of the pump pulse was 2500 μm after the entrance of the cluster jet both for Xe and Kr.

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To gain further insight on the decrease of lasing photon number at higher atom densities, we used the tomographic technique to measure the lasing photon number of Pd-like Xe at 41.8 nm as a function of position in the cluster jet at various atom densities, as shown in Fig.2. The results reveal that the decreased lasing photon number at an atom density higher than the optimal value comes not only from the decrease of gain length and increase of length of absorption as a result of ionization-induced refraction, but also from a reduction of gain. Aside from ionization-induced refraction, line-width broadening due to increased ion momentum obtained during dissociation of larger clusters and/or increased rate of collisional deexcitation of the upper level may also contribute to the reduction of gain.

Fig. 2. Number of photons of Pd-like Xe lasing at 41.8 nm as a function of position in the cluster jet for various atom densities. The energies of the pump pulse and the machining pulse were 210 mJ and 30 mJ, respectively. The pump polarization ellipticity was 0.65 and the focal position of the pump pulse was 2500 μm after the entrance of the cluster jet. The temporal separation between the machining pulse and the pump pulse was 6 ns.

4 Dependence on polarization ellipticity Figure 3 shows the number of photons of Pd-like Xe lasing at 41.8 nm and Ni-like Kr lasing at 32.8 nm as a function of pump polarization for various atom densities. The optimal polarization ellipticity for maximum x-ray lasing was found to be in the range of 0.6-0.7 for Xe and 0.55 for Kr regardless of the atom density. This shows that the effects of atom density

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and polarization ellipticity are decoupled. We observed unexpectedly that the optimal pump polarization ellipticity for maximum x-ray lasing is not the circular polarization.

Fig. 3. Number of photons of Pd-like Xe lasing at 41.8 nm, (a), and Ni-like Kr lasing at 32.8 nm, (b), as a function of pump polarization for various atom densities. The energy of the pump pulse was 210 mJ and its focal position was 2500 μm after the entrance of the cluster jet.

To further examine the x-ray amplification process under different polarization ellipticities of the pump pulse, the photon number of Pd-like Xe lasing at 41.8 nm as functions of position in the cluster jet were measured using the tomographic method, as shown in Fig. 4. This result indicates that a mechanism that changes the electron energy spectrum produced by ATI heating was present and resulted in a decreased collisional-excitation rate when the polarization ellipticity was larger than the optimal value. One possible explanation is the effects from pre-ionization of the clusters at the ionization front. If the collisional heating and ionization in the lasercluster interaction at the ionization front can ionize Xe atoms to Xe3+ or Xe4+, these pre-ionized electrons may lose their energy via radiative cooling during the nanoplasma expansion and through collision with other colder electrons or surrounding neutral atoms during the uniform plasma expansion. As a result, upon the arrival of the main peak of the pump pulse at roughly 2 ns later [2] the energies of these pre-ionized electrons may fall below the threshold of collisional excitation and thus they cannot contribute to collisional excitation. This will greatly reduce the lasing photon number. However, under this circumstance, if the ATI energies of the electrons produced from the subsequent ionization stages by the main peak of the pump pulse are lowered to fall in the region above and near the excitation threshold, in which the collisional-excitation cross section is larger, the gain can be raised. This can be achieved by shifting the polarization ellipticity of the pump pulse away from the circular polarization, resulting in

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Fig. 4. Number of photons of Pd-like Xe lasing at 41.8 nm as functions of position in the cluster jet for 7.4×1017 cm-3 atom density and various pump polarization ellipticities. The energies of the pump pulse and the machining pulse were 210 mJ and 30 mJ, respectively. The focal position of the pump pulse was 2500 μm after the entrance of the cluster jet. The temporal separation between the machining pulse and the pump pulse was 6 ns.

the observed optimal polarization ellipticity at less than 1. This also explains the decoupling of optimal atom density and optimal polarization ellipticity, because by the time the main peak of the pump pulse arrives to heat up the plasma again, the cluster structure has already disintegrated. Also note that in Fig. 4 the position of maximum lasing photon number does not shift with variation of laser polarization ellipticity. This is reasonable since the ionization fraction is not very different for varying polarization ellipticity when the laser intensity is well above the ionization intensity threshold.

References 1. 2. 3. 4. 5. 6. 7. 8.

S. Sebban et al., Phys. Rev. Lett. 86, 3004 (2001) H.-H. Chu et al., Phys. Rev. A 71, 061804(R) (2005) S. Sebban et al., Phys. Rev. Lett. 89, 253901 (2002) A. Bulter et al., Phys. Rev. Lett. 91, 205001 (2003) T. Mocek et al., Phys. Rev. A 71, 013804 (2005) Ph. Zeitoun et al., Nature 431, 426 (2004) H.-H. Chu et al., Appl. Phys. B 79, 193 (2004) C.-H. Pai et al., Phys. Plasmas 12, 070707 (2005)

Collisionally Pumped X-Ray Lasers for Shorter Wavelengths G.J. Pert Department of Physics, University of York, York, YO10
5DD, U.K.

Summary. The scaling of the pumping requirements for X-ray lasers in the range 50-100Å is investigated using analytic models for the interaction of the laser with solid targets. It is found that due to the rapid increase of the electron temperature required to establish Ni-like ionisation that the irradiance needed in the pre-pulse to generate the plasma increases rapidly with atomic number. In particular the mass of the heated plasma is dominated by upstream thermal conduction. In contrast due to the high temperatures achieved in the pre-pulse relatively little energy is required to further heat the plasma to generate strong gain. The large mass of upstream plasma at wavelengths ~50Å is comparable with that in freestanding foils, and suggests the use of the latter for targets at shorter wavelengths. The validity of these models is confirmed by simulation.

1 Introduction Soft X-ray lasers using grazing incidence pumping and nickel-like ions are now established as efficient sources of radiation in the super-100Å waveband [1]. Underlying this approach is the separation of the ionisation and excitation phases of the laser, and matching the operating density to the optimum for pumping the population inversion [2]. The first ionisation pulse (or pre-pulse) tends to be long and the second excitation (or main pulse) short. In this paper we examine whether these ideas can be applied to sub-100Å systems. We find two problems arise: firstly the optimum pumping density is at or above the critical density of the fundamental of the pumping laser, and secondly that the scaling of the electron temperature required to generate the Ni-like ionisation stage scales adversely with atomic number. The laser irradiation conditions required to achieve the necessary background plasma are identified by using appropriate analytic models of laser-plasma interaction developed many years ago. We find that, at the temperatures necessary for Ni-like ionisation, thermal conduction plays an important role, dominating the energy transfer upstream rather than

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G.J. Pert

downstream into the expanding plasma plume. This has the advantage that the plasma at densities in excess of that of the absorption layer will be hotter than predicted directly from the standard expansion models, and will allow more rapid ionisation and a higher pumping density. Using simulation applied to a variety of representative atomic systems suitable for generating laser action at these wavelengths, we identify a strategy which offers a possible route to achieving these aims reasonably efficiently. This is based on a pre-pulse comprising both fundamental and harmonic radiation generated from the pump laser, and a normally incident fundamental main pulse. However we find that the pump laser energy required scales very adversely with the atomic number and therefore wavelength to the extent that typically about 100J/cm for a target of width 100µm is required in the pre-pulse to ionise the shortest wavelength systems such as tantalum or ytterbium lasing at 45Å or 50Å respectively. In practice these values which neglect any transverse heat losses are probably an underestimate of those needed in an experiment. At these high pre-pulse energies a relatively small main pulse of only a few 10sJ/cm is needed to generate the gain. Energies typically of a few 10s of µJ are generated from these designs.

2 Analytic Models Simple one dimensional analytic models for the interaction of laser on solid targets were developed many years ago. These differ only in the nature of the absorption process and the role of thermal conduction. 2.1 Deflagration Model In this regime [3] the plasma flow is assumed steady state with localised absorption at the critical density,
c, by unspecified mechanisms. The upstream flow, and downstream isothermal rarefaction are both supported by thermal conduction from the absorption layer. The flow is therefore a classical Chapman-Jouget deflagration flow, with heat input given by the irradiance. The electron temperature is given by

Collisionally Pumped X-Ray Lasers for Shorter Wavelengths





253

Te
0.397

1 2 3  c 2 3 Z R g

where Z is the ionisation,

(1)

R g the gas constant per unit mass and


= 1 + Ti Z Te . The above equation neglects the energy required for ionisation and that held in the conduction zone, hence the effective irradiance
 is significantly less than that actually required. 2.2 Self-regulating Model In this case absorption is global by inverse bremsstrahlung absorption, and thermal conduction is neglected [4]. Since the plasma grows in time, the model is not steady state [5].

Te
0.423

1 b 1 4   1 2 1 4 Z R g

(2)

where
is the pulse length and b the appropriate inverse bremsstrahlung constant. The characteristic absorption density at the isothermal sonic point

 a
0.784 b  3 8   1 4  3 8

(3)

This model is closely related to that above when the time dependency and the different absorption density are taken into account 2.3 Thermal Conduction Zone Upstream of the absorption layer in either model, thermal conduction will be important if the temperature is high. This gives rise to layers of hot plasma, which over long times will pass through the absorption zone. However if the pulse is short (as is the case here) the upstream plasma will have a substantial heat content at the end of the pulse which must be included in the overall energy balance. The length, mass and energy of this zone may be expressed in terms of the characteristic length [6]

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G.J. Pert

2ac 4 L= a

c2 =


Z kTe M

(4)

determined by the values at the absorption layer. For a flux limiting factor of 0.1, the length, mass and energy of the layer take the values: Length 0.0629L : Mass 0.1767a L : Energy 0.1089ac2L

(5)

where a is the characteristic constant for electronic thermal conduction.

3 Ionisation We may estimate the minimum temperature needed to achieve the Ni-like ionisation stage in the plasma at the conclusion of the laser pulse from that needed for equilibrium at the appropriate ionisation stage. Using the screened hydrogenic model for the ionisation and excited state energy levels, we find that the ionisation temperature scales only weakly with electron density over the density range of interest, but strongly with atomic number Z:

Te
Aion Z 5.5

(6)

where the constant Aion varies with ionisation stage and density. For the Nilike ion and electron density 1021 cm-3 we find Aion
5.8710-8 eV. Using this temperature (6) we may use equations(1), (2) and (5) to calculate the minimum irradiance needed to achieve the Cu-like ionisation , since this has a sufficient population of Ni-like ions to generate gain. As a set of scaling relations we find for the irradiance

 Ade Z 8.25  Ace Z 13.4 
 e 10 +   Asr Z 

(7)

and for the mass ablation rate

 A m Z 3  A m Z 9 µ&
 dm 4.5  + c   Asr Z 

(8)

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255

where Ade , Asre and Ace , and Adm , Asrm and Acm refer to the empirical coefficients from the deflagration, self-regulating and thermal conduction models respectively. The self-regulating/deflagration transition is determined by the absorption density, namely if
a <
c the flow is selfregulating and vica versa. 3.1 Ionisation Time Thus far we have assumed that the ionisation takes place over times short compared to the pulse duration. To check this assumption is valid we show in fig. 1 the time taken to reach the Cu-like ionisation stage at the Ni-like equilibrium temperature. It can be seen that this time is nearly linearly proportional to the electron density. Furthermore we note that at an electron density of 1021 cm-3 the time is about 200ps. for Z=70 and increases rapidly thereafter. We therefore conclude that we require prepulse durations of at least 100ps. 1.5 20

-3

Ionization time (ns.)

5 × 10 cm 21 -3 1 × 10 cm 21 -3 4 × 10 cm 22 -3 1 × 10 cm 1

0.5

0 40

50

70 60 Atomic number

80

90

Fig. 1. Plot of the time required to achieve the Cu-like ionisation at the equilibrium temperature of the Ni-like ion as a function of the atomic number

4. Optimum Pumping Density It can be shown that there are electron densities at which the population inversion density and the gain are maximised. Fig.2 shows the variation of the fractional inversion density and a parameter measuring gain defined below in dysprosium over a range of electron densities and temperatures.

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G.J. Pert

  Population inversion fraction = 1  q 2
q1  q0  g 2 g1 

Gain parameter = Population inversion fraction
1020 ne

(9)

It is clear from Fig.1 and Fig.2 that typical conditions after the final heating require an electron density of about 1021 cm-3 to achieve both ionisation with a pulse length of about 100ps, and high gain. This is the critical density for the fundamental of Nd-glass laser radiation at 1.06µm. However since the absorption in these systems is dominated by inverse bremsstrahlung absorption, this suggests that we need to use the harmonic radiation at 0.53µm as the pre-pulse to generate the ionisation and create a suitable density profile. 10 500eV 1000eV 2000eV 3000eV

1

Gain

er

met

para

Population fraction

-1

10

-2

10

Inversion fraction -3

10

-4

10

-5

10

19

10

20

10

21

10 -3 Electron density (cm )

22

10

23

10

Fig. 2. Plots of the inversion density and gain parameter in dysprosium as functions of the electron density for different temperatures.

Unfortunately, harmonic generation is typically only about 50% efficient, the remaining 50% remaining in the fundamental. To obtain maximum efficiency therefore it is advantageous to focus both harmonic and fundamental on to the plasma, if a suitable focusing arrangement can be designed. We will assume this can be done. From equation (6) we see that for dysprosium, the temperature required for ionisation is about 500eV. From fig.2 it is clear that significant gain can be developed by the pre-pulse alone. Furthermore it can be seen that

Collisionally Pumped X-Ray Lasers for Shorter Wavelengths





257

an increase in temperature of a further 500eV, which is achieved without additional ionisation or hydrodynamic effects is all that is required from the main pulse. The energy needed by the main pulse is therefore substantially less than that in the pre-pulse.

4 Examples from Simulation The analytic modelling presented above has been entirely one dimensional, appropriate for a plasma width of 100µm. We will use the 1_d code EHYBRID to simulate such plasmas, where the hydrodynamics are essentially 1 dimensional. The pre-pulse will be assumed to have a constant irradiance over the full pulse length of 100 or 200ps and the main pulse a Gaussian temporal profile of 2ps half-width. The ionisation is calculated using screened hydrogenic energy levels for all ions except the lasing Ni-like stage. 4.1 Dysprosium (Z=66) Fig.3 shows the gain and electron density spatial profiles along the plasma axis at increasing times measured from the onset of the main pulse. It can be seen that the maximum gain increases with time until about 10ps and decreases slowly thereafter. However we note that increasing gain is associated with a shift to higher density. This is due to thermal conduction heating plasma at densities greater than the absorption density, with consequent higher gain as reflected in fig.2. However we also note that this move to higher density is accompanied by an increase in the gradient of the electron density, leading to progressive deterioration of the output due to refraction. We note that at the electron density of 1021 cm-3, the gain decreases slowly as the plasma cools. Fig.4 shows output from plasma similar to that shown in fig.3. It will be noted that although the magnitude of the outputs differ by a factor of 10, their temporal profiles are similar, indicating that the temporal profile is controlled by the spatial profile of the expansion resulting from the prepulse. The peak power occurring at 7.5ps is significantly earlier than gain maximum, reflecting the limitation imposed by the density gradient as the gain moves to higher density. The relatively large change in output from a small change in main pulse energy should be noted, cosequent to increased temperature and stronger pumping, consistent with fig.2.

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G.J. Pert

4.2 Ytterbium (Z=70) Ni-like ytterbium lases at 50Å. Fig.5 shows the gain and electron density profile in this case. It is immediately apparent that the pre-pulse energy is greatly increased over that needed for dysprosium (by a factor 4) despite the relatively small increase in the atomic number. This is larger than our

1e+23

80 70

−1

Gain (cm )

50

1e+22 −3

1e+21

40

Electron density (cm )

2 ps 6 ps 10ps 14ps 18ps

60

30 1e+20

20 10 0 −0.001

0

0.001 0.002 Distance (cm)

0.003

1e+19 0.004

Fig. 3. Plots of the gain at 59 Å and electron density for dysprosium pumped by a pre-pulse of mixed harmonic and fundamental of 23.75 J/cm in 200 ps and a fundamental main pulse of 8.8 J/cm in 2 ps all at normal incidence.

model predictions (factor 2), even when account is taken of the reduction in inverse bremsstrahlung absorption due to the higher temperature. The additional energy is required to meet the increasing demands of radiation escaping from the hot plasma. It can be seen that reasonable gain is generated over quite a large plasma body with a small density gradient lasting quite long times ~25ps. We therefore expect to obtain a relatively long output pulse at quite low power, but with significant total energy. Fig.6 confirms this expectation.

5 Foils at Shorter Wavelengths Referring to equation (8) we see that the mass scales rapidly with atomic number. Fig.7 illustrates this behaviour and shows that for Z > 67 the mass ablated exceeds 100µg. This suggests that we may limit the mass of ionised plasma by using thin foils, which are uniformly heated by thermal

Collisionally Pumped X-Ray Lasers for Shorter Wavelengths





259

conduction – exploding foils. The analysis of this system can be carried out reasonably easily and shows that the ratio of kinetic to thermal energies is about unity for a foil expansion. This is significantly larger than for slabs, where much of the mass is in the slowly moving conduction zone. Consequently the energy balance is in favour of slabs up to atomic numbers of about 73. 250 Power

Power (MW)

8.8J/cm 5.4J/cm (×10)

10

200

150

100

Energy

Energy (µJ)

Energy

20

Power 50

0

0

5

10 Time (ps)

0 20

15

Fig. 4. Plots of the output power and energy at 59 Å generated from a 1 cm. length of dysprosium plasma by pre-pulse irradiation with a pure harmonic beam of 23.75 J/cm in 200ps and a main pulse irradiation by normally incident fundamental beams of 5.4 J/cm and 8.8J/cm Note that in the 5.4 J/cm case the power and energy are both multiplied by a factor of 10.

23

60

Gain(cm

-1)

40

22

10

30

21

20

10

-3

2.5ps 5.0ps 7.5ps 10.0ps 12.5ps 15.0ps 17.5ps

50

Electron density (cm )

10

10

0

20

0

0.001

0.002 Distance (cm)

0.003

10 0.004

Fig. 5. Plots of the gain and electron density from ytterbium at 50 Å pumped by a combination harmonic/fundamental pre-pulse of energy 97 J/cm in 200 ps and a fundamental main pulse of 23 J/cm

260





G.J. Pert

10

80 70

8

50

Power Energy

6

40 4

Energy (µJ)

Power (MW)

60

30 20

2 10 0

0

10

5

15 Time (ps)

20

0 30

25

Fig. 6. Plot of the output power and energy at 50 Å from a 1cm plasma length of ytterbium heated by a pre-pulse of 97 J/cm in 200ps and main pulse 23 J/cm in 2 ps. 20000

Foil Slab

-2

-2

Mass (µg/cm )

Energy

10000 200 Mass

0 60

65

70 Atomic number

Total energy (J/cm )

400

75

0 80

Fig. 7. Comparison of the mass and energy required to achieve Cu-like ionisation in slabs and 100 µ g foils with a laser pulse of 100 ps duration at 0.5 µ m wavelength.

However foils have two further advantages. Firstly the density gradient at peak density is zero due to their symmetry. Secondly it is possible to use

Collisionally Pumped X-Ray Lasers for Shorter Wavelengths





261

them at high density by adjusting the pulse length so that the main pulse is applied before much expansion has occurred. This requires a short pulse and one must take care to ensure that thermal conduction has burnt through the plasma and that the ionisation is completed. With care operation at electron densities ~1022 cm-3 can be achieved.

6. Conclusions Simple analytic models have been used to identify the conditions necessary to pump Ni-like ions to generate laser action in the range 5070Å. It is found that ionisation is a limiting factor, both in respect of the pre-pulse input energy and the time required. Since the densities required both for ionisation and inversion are high > 1021 cm-3, harmonic radiation at 0.53 µm is needed, and grazing incidence pumping does not offer any advantage. At the high temperatures needed thermal conduction, even when flux limited, plays a key role. Although greatly increasing the energy demands, it does allow a mixture of the fundamental and harmonic wavelengths to be used, provided that the practical difficulties can be overcome. Since the temperature is high at the conclusion of the main pulse, a relatively small additional energy is required from the main pulse, which being short is not affected by hydrodynamic or conduction losses. The main pulse energy required is therefore only about _ of that in the prepulse. For shorter wavelengths it is suggested that foils with limited mass may allow a reduction in the pump energy, and improve the density and gradients in the plasma.

References 1. Y.Wang et.al. Phys. Rev. A 72, 053807, 2005 2. G.J.Pert Phys. Rev. A, 73, 033809, 2005 3 C.Fauquignon and F.Floux Phys. Fluids 13, 386, 1970 4 I.V.Afanas’ev et.al. Appl. Maths. Mech. 30, 1218, 1966 5 G.J.Pert J Plasma Phys. 36, 415, 1986 6 G.J.Pert J Plasma Phys. 29, 415, 1983

Inner Shell Lasing In Titanium via Electron Collisional Ionization E. F. Spracklen and G. J. Pert Department of Physics, University of York, York, YO10 5DD, UK

Summary. The possibility of generating gain in the x-ray region of the spectrum through the technique of electron collisional ionization is studied in titanium . As in previous work transient inversions of moderate size are seen to be produced on the L2 – M1 and L3 – M1 transitions provided that the collisional effects of the secondary and Auger electrons are ignored. Inclusion of these effects is seen to significantly decrease both the magnitude and duration of the gain obtained.

1 Introduction Inner-shell x-ray laser schemes present the possibility of generating gain at wavelengths of several angstroms in small scale devices. Conventionally such techniques have involved using x-ray photo-pumping to generate the inner-shell transitions as originally discussed by Duguay [1]. Widespread implementation of such devices has however been curtailed due to the difficulty of generating x-ray pulses with durations of the order of the inversion lifetimes. An alternative approach, outlined by Barty et al [2], is to use fs electron pulses to generate the inversion. However, although such pulses can be relatively easily produced via laser-plasma interactions, atomic electron impact cross-sections favor outer shell over inner shell ionization. Such techniques therefore cannot produce gain directly and instead rely upon Auger transitions to generate transient inversions. Initial studies into the possibility of generating gain in such a manner identified Ti as the most favorable candidate for lasing and predicted gains of up to 30 cm-1 [3]. The work in question however assumed mono-energetic electron pulses and ignored the collisional effects of the secondary and Auger electrons produced. Further simulations carried out using more realistic electron

264

E. F. Spracklen and G. J. Pert

fluxes predicted gains of only around 10-3 cm-1 [4]. Yet again however this work ignored the secondary electron effects. This paper investigates the possibility of generating gain on the L2 - M1 and L3 - M1 transitions in Ti using physically realistic electron pulses and taking full account of the collisional effects of secondary and Auger electrons.

2 Method The production of a hot electron flux via a laser-plasma interaction is simulated using a 2-D PIC code. The superthermal electrons produced are followed using Monte-Carlo methods with the titanium level populations obtained by numerical solutions of the relevant rate equations. Within this atomic code the secondary electron energies are calculated using the symmetrized binary encounter theory of Burgess and Percival [5]. In all the simulations performed the titanium lasing media is assumed to be initially un-ionised and at solid density.

3 Results Simulations performed using a variety of laser and plasma parameters predict larger gains upon the L3 – M1 transition in contradiction of the work of Barty et al [3] – figure 1. However, in Barty’s work the L2 and L3 levels are treated as having identical transition rates and electron impact cross-sections. The larger degeneracy of the L3 level therefore leads to smaller gains being generated upon the L3 – M1 transition. Treating the L2 and L3 levels separately it can be shown that L2 states possess faster filling rates and smaller impact cross-sections [6,7] explaining the larger L3 – M1 gains observed. Asides from this discrepancy it can be seen that the gains obtained are in the region of those predicted by Barty et al rather than those forecast by Upcraft [4]. Examining the spectra in more detail it is seen that the gain in the initial titanium regions is not consistent with that obtained at larger depths. This feature arises as the initial gain is produced by thermal electrons obtained in the PIC simulation before the hot electrons are generated. The gain in the deeper regions meanwhile is produced by the hot electron flux with the gain fall-off obtained with increasing depth a consequence of the small number of hot electrons produced in typical laser plasma interactions.

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The thermal electron effects can be negated by allowing the plasma electron flux to pass through a thin atomic filter – figure 2. It can be seen that, provided the filters are thick enough, the anomalous behaviour of the gain at small penetration depths disappears. However as the filter thickness is increased the gain produced is seen to decrease as a result of the increasing numbers of electrons being removed from the flux. 12

8

Gain (cm**-1)

6

9

4

6

2

3

0

0

0.2

0.4

0.8 1 0.6 Penetration Distance (microns)

1.2

0

0.2

0.4

0.8 1 0.6 Penetration Distance (microns)

1.2

Gain Duration (fs)

L3-M1 L2-M1

L3-M1 L2-M1

0

Fig. 1. Titanium gain characteristics obtained from electron fluxes produced in the interaction of a 10 fs, I
2 = 1018 W cm-2 µm2 laser with a 1 keV plasma. 12

8

9

4

6

2

3

0

0

0.2

0.4

0.8 1 0.6 Penetration Distance (microns)

1.2

0

0.2

0.4

0.8 1 0.6 Penetration Distance (microns)

1.2

Gain Duration (fs)

6

Gain (cm**-1)

X=0 X = 0.1 X = 0.3 X = 0.5

X=0 X = 0.1 X = 0.3 X = 0.5

0

Fig. 2. L3-M1 gain characteristics for electron fluxes produced in the interaction of a 10 fs, I
2 = 1018 W cm-2 µm2 laser with a 1 keV plasma filtered by aluminum filters of thickness X µm.

Allowing for different irradiance beams it is seen that all the gain spectra exhibit the same behaviour at shallow penetration depths due to the thermal plasma electrons – figure 3. For deeper regions however larger but

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E. F. Spracklen and G. J. Pert

shorter lived gains are obtained for the more intense beams. This feature can be attributed to the increasing number of hot electrons generated by the higher intensity pulses. These electrons are capable of penetrating further into the titanium and thus produce a more significant inversion in the deeper segments. The increasing electron number however causes more rapid over-ionisation leading to the afore-mentioned decrease in gain duration. 30

X = 16 X = 17 X = 18 X = 19

6 Gain (cm**-1)

X = 16 X = 17 X = 18 X = 19

25

20

15

4

Gain Duration (fs)

8

10

2 5

0

0

0.2

0.4

0.8 1 0.6 Penetration Distance (microns)

1.2

0

0.2

0.4

0.8 1 0.6 Penetration Distance (microns)

0

1.2

Fig. 3. L3-M1 gain characteristics for electron fluxes produced by the interaction of 10 fs, I
2 = 10X W cm-2 µm2 lasers with 1 keV plasmas.

Allowing for the collisional effects of the secondary and Auger electrons generated during the interaction is seen to significantly decrease both the gain magnitude and duration – figure 4. This decrease arises as a result of the fact that the secondary electrons are overwhelmingly produced at low energies [5] and thus act to destroy any inversion. 4

2

1.5

2

1

1

0.5

-1

Gain (cm )

3

0 0.2

0.4

0.6

0.8 1 Penetration Distance (µm)

1.2

0.2

0.4

0.6

0.8 1 Penetration Distance (µm)

1.2

Gain Duration (fs)

X = 16 X = 17 X = 18 X = 19

X = 19 X = 18 X = 17 X = 16

0

Fig. 4. L3-M1 gain characteristics for electron fluxes produced by the interaction of 10 fs, I
2 = 10X W cm-2 µm2 lasers with 1 keV plasmas allowing for secondary and Auger electrons.

Inner Shell Lasing In Titanium via Electron Collisional Ionization

267

Similar effects are also seen in simulations of photo-ionised inner-shell devices. In such schemes it is possible to somewhat alleviate the effects of the secondary electrons by doping the lasing material with hydrogen [8]. Such an approach cannot however be adopted in electron collisional devices due to the similar electron impact cross-sections of hydrogen and titanium at intermediate to high energies.

4 Conclusions The gain and population dynamics of the L23 – M1 transitions in titanium have been investigated in the case of electron collisional ionization. Moderate gains of fs duration are predicted when the collisional effects of the Auger and secondary electrons are ignored. Inclusion of these effects is seen to significantly decrease both the magnitude and duration of the gains obtained.

References 1. Duguay, M. A. and Rentzepis, P. M., Appl. Phys. Lett., 10, 350 (1967) 2. Barty, C. P. J., Guo, T., Le Blanc, C., Raksi, F., Rose-Petruck, C., Squier, J., Walker, B. C., Wilson, K. R., Yakovlev, V. V. and Yamakawa, K., X-ray Lasers IOP Conference Series, 151, 282 (1996) 3. Kim, D., Toth, C. and Barty, C. P. J., Phys. Rev. A., 59, 4129 (1999) 4. Upcraft, L. M., X-ray Lasers 2002: 8th International Conference on X-Ray Lasers, 349 (2002) 5 Burgess, A. and Percival, I. C., Adv. At. Mol. Phys., 34, 109 (1968) 6. Deutsch, H., Margreiter, D. and Mark, T. D., Z. Phys. D., 29, 31 (1994) 7 Chen, M. H. and Crasemann, B., At. Data Nucl. Data Tables, 24, 13 (1979) 8. Kapteyn, H. C., Appl. Opt., 31 4931 (1992)

Gain Generation in the Critical Density Region of a TCE XRL D. Ursescu1, D. Zimmer1,2, T. Kühl1,2, B. Zielbauer1,2,3 and G.J. Pert4 1

Gesellschaft für Schwerionenforschung mbH, Darmstadt, Germany; Johannes Gutenberg Universität, Mainz, Germany; 3 Max Born Institute, Berlin, Germany; 4 University of York, United Kingdom

2

Summary. Significant reduction of the total pumping energy for a transient collisionally excited (TCE) x-ray laser (XRL) was made possible by using nonnormal main pulse pumping. In the attempt to scale to shorter XRL wavelengths, it is described here a theoretical investigation of the influence of the pumping pulse parameters on the gain generation in a Ni-like Ag x-ray laser (XRL). The possibility of gain generation closer to the critical density is shown by the EHYBRID code for a set of optimized parameters, corresponding to a possible setup at the PHELIX laser facility.

1 Introduction The advance of the TCE XRL in the last few years was marked by the introduction of a non-normal incidence focusing system (see e.g. [1]) and of the grazing incidence angle pumping (GRIP) technique for the main pumping pulse (MP) [2]. At the introduction of GRIP technique it was largely believed that the optimal angle is determined by the density where the gain appears, in the range of 1020 cm-3. A number of experiments were then investigating the effect of the MP non-normal incidence angle on the XRL output [3,4,5], with the results that slightly smaller incidence angles on target are beneficial to the output of the XRL. Also on the theoretical side, a study concerning Ag and Sm [6] has shown that the incidence angle for Sm of 45° at 1054 nm would reduce the pumping needs of the XRL a factor of three. In the present paper the same modeling program is used as in [6] and the influence of the incidence angle is investigated for Ni-like Ag XRL. It is found that the incidence angle of the main pulse has

270

D. Ursescu et al.

different effects depending on the pumping conditions. With parameters typical for the PHELIX preamplifier [7], the optimal MP incidence angle is found to be 45° (see section 2). Moreover a simple plasma shaping technique is implemented to control the density profile of the pre-plasma, by a variation of the incidence angle of the pre-pulse (PP). It is found that for large PP incidence angles on target, the XRL output improves, due to a better interplay of the electron temperature and the electron density in the gain region.

2 Influence of the MP incidence angle The parameters used for the modelling of the Ag Ni-like XRL were selected to fit a possible experiment with the PHELIX preamplifier. Two pulses are used, a long one to create the pre-plasma, and the short pulse which produces the strong excitation needed for lasing. The PP duration is 800 ps with a total energy of 4 J in a line focus of 10 mm length and 50 μm width and it is followed at it's conclusion by a MP with 2 ps duration and 2 J energy, with the same line focus length. In this evaluation the PP incidence angle on target is 0° while the MP incidence angle is varied from 0° to 75°. The EHYBRID code was used employing detailed level information of the Ni-like Ag ions, in order to obtain good description of the main lasing line, at 13.9 nm wavelength. The local XRL signal is defined as the product of the density normalized to critical density with the exponential of the gain g multiplied with the length of the target l, for a small target length (l=0.1 mm).

sl =

ne ⋅ (e gl − 1) nc

The results for the local XRL signal are shown in fig.1 for MP incidence angles from 0° to 75° on a logarithmic scale at the moment when the highest local signal is obtained, relative to the arrival of the main pulse. For the 75° incidence angle the MP energy is deposited in a quite diluted plasma region (0.5 1020 cm-3) and the local signal is less than unity. The highest local signal obtained is for 45° incidence angle, and corresponds to a density close to critical density which is 1.1 1021 cm-3 in this case. The gain appears after the MP is gone, when the heated plasma region reaches the Ni-like state. However, due to ionization and plasma expansion, the electron density at that given distance from the target increases so that the local signal is enhanced.

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When the MP incidence angle is 0°, the energy is deposited close to the critical density so the heated mass is much larger and the heat conductivity is large, so the temperature reached at the end of the MP is about 500 eV.

Fig. 1. Local signal as a function of the position relative to the target for several main pulse incidence angles

Increasing the angle, the maximum temperature increases to a value of 2150 eV in the case of 45° and the cooling of the plasma takes longer time. This time is needed to build up the Ni-like charge state which, as a consequence, will see higher temperatures of the electrons. For larger MP angles, the maximum electron temperature further increases but the ionization process is becoming slower and the Ni-like charge state appears at a much later time when the plasma cooled again; in this case also the electron density does not increase any more in a significant way. In conclusion, the balance of the ionization dynamics and temperature dynamics determines the optimal angle for MP. In the optimal case, the local gain is enhanced by the increase of the electron density in the gain region.

3 Influence of the PP incidence angle Further optimization was performed by variation of the PP incidence angle. This is a simple plasma shaping technique which allows controlling the density profile together with the temperature and the charge state of the plasma generated by the PP. With this technique, the plasma is heated at a given density region determined by the chosen incidence angle in the same way as in the MP case.

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The highest local signal is obtained in the case of a large incidence angle of 75° for a 30° MP incidence angle as shown in fig. 2. For comparison the maximum local signal for PP incidence angles from 0° to 75° are also represented.

Fig. 2. Local signal as a function of the position relative to the target for several prepulse incidence angles

The local XRL signal builds up in a region close to the target surface and in the simulation is a factor of 6 higher than the one obtained in the best case of the 0° PP angle (shown in fig. 1). In the cases presented in fig. 2, the electron density region has densities above the critical density of the pumping laser, being placed at 1.5 to 1.9 1021 cm-3 electron density. In conclusion, here we presented a systematic modelling study of the influence of the incidence angles for the PP and MP for a Ag XRL. It is found that strong local signal appears for MP angles around 45° in the case of normal PP incidence. When varying the PP angle, the optimal angle is found 75° for PP using an MP incidence angle of 30°. In this last case a factor of 6 in the local XRL signal is expected. The results correspond to a possible setup at the PHELIX laser facility. Furthermore they open new perspective for scaling TCE XRL towards sub-10 nm wavelengths [7].

References 1. Neumayer, P.; Alvarez, J.; Mos, B.B.; Borneis, S.; Brück, K.; Gaul, E.W.; Häfner, C.; Janulewicz, K.A.; Kuehl, T.; Marx, D.; Reinhard, I.; Tomaselli, M.; Nickles, P.V.; Sandner, W.; Seelig, W.: 'X-ray laser spectroscopy on

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lithium-like ions', Soft X-Ray Lasers and Applications IV, SPIE, 4505, 236242, 2001 2. Keenan, R.; Dunn, J.; Patel, P.K.; Price, D.F.; Smith, R.F. & Shlyaptsev, V.N.: 'High-Repetition-Rate Grazing-Incidence Pumped X-Ray Laser Operating at 18.9 nm', Phys. Rev. Lett., 94, 103901, 2005 3. Neumayer, P.; Seelig, W.; Cassou, K.; Klisnick, A.; Ros, D.; Ursescu, D.; Kuehl, T.; Borneis, S.; Gaul, E.; Geithner, W.; Haefner, C. & Wiewior, P. 'Transient collisionally excited X-ray laser in nickel-like zirconium pumped with the PHELIX laser facility', Appl. Phys. B, 78, 957-959, 2004 4. Kazamias, S.; Cassou, K.; Ros, D.; Plé, F.; Jamelot, G.; Klisnick, A.; Lundh, O.; Lindau, F.; Persson, A.; Wahlström, C. G.; de Rossi, S.; Joyeux, D.; Zielbauer, B.; Ursescu, D.; Kühl, Th.: 'A 10 Hz, 3 µJ transient X-ray laser pumped in grazing incidence geometry', these proceedings 5. Luther, B.M.; Wang, Y.; Larotonda, M.A.; Aless, D.; Berrill, M.; Marconi, M.C.; Rocca, J.J. & Shlyaptsev, V.N.: 'Saturated high-repetition-rate 18.9-nm tabletop laser in nickellike molybdenum', Opt. Lett., 30, 165, 2005 6. Pert, G.J.: 'Optimizing the performance of nickel-like collisionally pumped xray lasers', Phys. Rev. A, 73, 033809, 2006 7. Kühl, Th.; Ursescu, D.; Bagnoud, V.; Javorkova, D.; Rosmej, O.; Zimmer, D.; Ros, D.; Cassou, K.; Kazamias, S.; Klisnick, A.; Zielbauer, B.; Janulewicz, K.; Nickles, P.; Pert, G.; Neumayer, P.; Dunn, J.: 'A Non-Normal Incidence Pumped Ni-like Zr XRL for Spectroscopy of Li-like Heavy Ions at GSI/FAIR', these proceedings

2-D Hydrodynamic Simulation of Laser Plasma Generation For Transiently Pumped Soft X-Ray Amplifier K. Cassou, S. Kazamias, A. Klisnick and D.Ros LIXAM– Université Paris XI 91400 Orsay – France

Ph. Zeitoun Laboratoire d’optique Appliquée – ENSTA, Ecole Polytechnique - 91620 Palaiseau France

E. Oliva, P. Velarde, C. Garcia and F. Ogando Institute de Fusion Nuclear (DENIM), Universidad Politecnica de Madrid Madrid Spain

Summary. A soft x-ray laser amplifier based on solid target plasma is numerically investigated using a 2-D hydrodynamic code ARWEN with radiative transport solved by multigroup method based on adaptive mesh refinement. The code has been used to describe the spatial and temporal plasma evolution and, ultimately, to understand how to generate an ideal preformed plasma in the transient collisional pumping scheme. Firstly, we examine the influence of the laser driver spatial profile on the characteristics of the preformed plasma. We show that using a super Gaussian, instead of gaussian, spatial transverse profile leads to a substantial reduction of the transverse refraction by two orders of magnitude and to an enlargement of the gain zone surface by about a factor of 2. Secondly, we perform a study on the pre-pulse significance in the transient collisional scheme, as it was done several years ago for the J=0-1 Ne-like line in the quasi-steady-state pumping. All above studies were carried out for an iron target with gain on the J = 0- 1 neon like transition at λ= 25.5nm

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1 Introduction These In recent years, worldwide soft-x-ray laser research has progressed to the point where many laboratories have routinely been able to produce stimulated emission over a wide range of wavelengths. Demonstration of multi-millijoule soft-x-ray laser has been achieved in the quasisteady-state (QSS) collisional pumping scheme [1]. Significant progress has also been made in the past few years to push the soft-x-ray lasers toward higher intensity, shorter pulse duration, shorter wavelength, and particularly much higher repetition rate with much less pumping laser energy. These accomplishments were made by the use of high-repetition-rate laser system, and the implementation of the transient-collisional-excitation (TCE) x-ray laser scheme [2,3] TheTCE scheme is often poorly homogeneous exhibiting many large- and small-scale structures. Since the beam homogeneity is a key parameter for focusing applications or imaging experiments, the problem has to be overcome. These structures originate from two separate phenomena. First, speckle-like pattern is generated from the interferences of several incoherent sub-pupils [4]. This effect may be easily alleviated by seeding the amplifier with a nearly fully coherent source such as high harmonic generation [5]. This has been achieved recently [6] and opens the route to a new generation of soft-x-ray lasers [7]. The second phenomenon is the beam degradation because of its propagation along the plasma amplifier that is non-homogeneous. Control and improvement of the plasma homogeneity remains one of the key studies for the increase of soft-x-ray laser performance. More precisely, the non-uniformity of the plasma density induces a spatial fluctuation of the index of refraction that in turn refracts the soft-x-ray laser beam. Although soft-x-ray laser beam degradation was observed on other pumping schemes, it was not as crucial as now with the transient scheme. Deleterious effects of refraction associated to the transient scheme consist in beam degradation but also in the reduction of the output soft-x-ray laser energy by refracting the beam out of the gain region before reaching the end of the amplifier [8]. All the previous works related to the refraction underwent by soft-x-ray laser has shown that the refraction impacts the beam propagation in not only horizontal but also in vertical directions (Fig. 1). It has been demonstrated that the use of bent target and pre- or double-pulse pumping compensate for horizontal refraction of the soft-x-ray beams in the plasma [9, 10]. The hydrodynamic of soft-x-ray plasma amplifier is a bidimensional problem. Up to now, vertical refraction has been treated only with phenomenological modeling using 1.5D hydrocode post-

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processed by ray-tracing code but assuming ab initio plasma vertical profiles [11]. This approach prevents one from a realistic description of plasma structure along the vertical direction. As it will be pointed out in this paper, the two dimensional (2D) effects are strongly impacting the plasma shape, requiring a full 2D hydrocode for approaching a realistic description. Furthermore, the bidimensional modeling pointed out a large overestimation of the vertical size of the gain zone calculated with 1.5D hydrocode. In this conference, we report numerical modeling of the impact of the spatial shaping of the driving laser beam in order to improve the soft-x-ray laser amplifier quality by reducing the vertical refraction combined with a broadening of the amplification surface, in the transient collisional schme. We demonstrate by numerical modeling that refraction might be dramatically reduced by using (n=10) super-Gaussian laser (SGL) spatial profile instead of the classical Gaussian laser (GL) spatial profile [12]. We also observed that for (n=10) super-Gaussian, the gain region size might be increased by a factor of 2 as compared to the Gaussian spatial profile case, doubling the soft-x-ray laser (SXRL) output energy. This additional unexpected result enhances the interest of SGL spatial profile. We show that even with low prepulse energy before the long pulse, the effect reminds for optimal pre-plasma formation.

2 ARWEN code and modelling To model the laser deposition influence and the following hydrodynamic plasma evolution we used the bidimensional (2D) hydrocode ARWEN. The ARWEN [13] code is based on adaptive mesh refinement (AMR) fluid dynamic and radiation transport calculations. The radiation intensity is calculated with a discrete energy multigroup scheme [14] coupled to the adaptive algorithm. To our knowledge this is the first time that an AMR code is used to model SXRL plasmas. As compared to older 2D hydrocodes, AMR technique is much faster enabling to run a full, highly resolved hydrodynamic case in a reasonable CPU time (8h) as required to achieve a complete case. Simulations are realized with a base cell grid of 128×64 cells and two refinement levels. The radiation transport is initialized with 16 angles. The simulation window is defined by a 240 µm×120µm square side with a slab target of 10 µm. The vacuum in front of the target is set at a baking pressure of 10−3 mbar. The goal of hydrodynamic modeling of the

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Fig. 1. Schematic view of modeling geometry

laser-produced plasma is to find optimum laser drive spatial conditions for the long laser pulse to obtain the largest possible gain region associated with negligible vertical density gradients (Fig. 1).For the sake of clarity we define the axis along which the soft-x-ray laser propagates as z, the vertical direction y as the axis perpendicular to the driving laser incidence, x direction. For all the simulations of interest, the target is illuminated by a λ=800 nm laser having a Gaussian pulse duration of 400ps full width at half maximum (FWHM) and 1 J energy corresponding to the typically

Fig. 2. Transverse vertical spatial laser profiles for different n-value

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uncompressed chirped pulse of Ti:Sa laser system. 100ps after the peak of the long pulse, a second short 5ps (FWHM) duration pulse of 2 J heats preformed plasma with temporal and spatial shape identical to the long laser pulse. The spatial deposition profile of the laser pulse energy on the target, modeled by: 2n

⎛ y ⎞ ⎟ −⎜ ⎜ 2σ y ⎟ ⎝ ⎠

I ( y) = I0e

is Gaussian for n=1 or super-Gaussian for n greater than 1. Our study has been performed considering the cases of n=2, 5, and n=10. For all Gaussian or super-Gaussian lasers, the widths at half maximum are set at 100 µm (Fig. 2). The target length is set at 5 mm. We assume a homogeneous deposition along the z direction. The SGL spatial profile can be realized experimentally by using diffractive optics or by coupling a standard combination of a cylindrical and spherical lens to an adaptive mirror [15]. With this scheme the line focus is achieved thanks to the use of the lenses while the adaptive optic [16] serves to shape the transverse (vertical) profile of the line focus. The longitudinal line shape is normally sufficiently homogeneous to prevent any correction. We consider that both the long and short pulses are focused with the same optics meaning that the gain region properties of interest (ions density, electron density gradient, sizes) are given by the energy deposition of the long pulse while electronic temperature profile is given by the short laser pulse.

3 Vertical shaping of the pre-plasma It is fairly justified to expect that the preforming process (i. e. long laser pulse or combination of prepulse and long pulse) is very important for SXRL operating in transient collisional scheme and more especially for SXRL pumped in the GRIP geometry [17,18]. As not only the state of the plasma column but also the pump pulse propagation are affected by the plasma preforming process. We concentrated our interest on the plasma density shape and temperature. The ionization is not illustrated because in the LTE assumption it follows the electron temperature. On the other hand the parameters of the heating pulse decide about the final plasma temperature.

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3.1 Influence of transverse spatial profile (n) Figures Fig. 3 and Fig. 4 displayed respectively 2D maps of the electron densities and temperatures for n=1 (left side) and n=10 (right side) for a delay of 100ps after the peak of the long laser pulse. During the early times of the laser-target interaction, the laser pulse shapes strongly imprint Gaussian or super-Gaussian density profiles. However, later during the plasma evolution, at delay Δt=100ps, when we choose to fire the short pulse to heat up the plasma, the density and temperature profiles do not reproduce so precisely the laser shapes (Figs. 3a,b). On both plasmas created by Gaussian and super-Gaussian lasers the edges looks perturbed. For n =10 SGL, at 100 ps after the peak of the long pulse, plasma jets appear clearly around y=40 µm and 190 µm while the central part of the plasma is homogeneous in terms of electron density and temperature. For both GL and SGL generated plasmas cases, the plasma centers are expanding with the highest velocities because most of the laser energy is laid down there, while the sides are cooler and less dense leading to lower lateral velocities.

a)

b)

Fig. 3. Electron density map,

These results in the plasma inhomogeneities observed on the edges. For plasma created by SGL profile (Fig. 3b) there is no cold dense plasma on each side formed by the feet of the Gaussian laser pulse that increase the cooling of the plasma by thermal conduction, as compared with plasmas created by GL profile pulse. This is even reinforced by the lateral expansion for the case of plasmas created by super-Gaussian beam which creates jets containing the expansion in the x-axis. Besides, the density profiles follow somehow the laser deposition profile, creating a kind of

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plateau on the electron density with sizes increasing with n. For n=1, the plateau is about 25% of the laser full width while it rises 40% for n=5 to 60 % for n=10 SGL profile. On other and, we can notice in Fig. 4a,b the electron temperature is more homogeneous in the dense part of the plasma for the SGL spatial profile. The homogeneous region, in terms of temperature follows the size of the density plateau. During the plasma expansion, the edge of the plasma in the case of SGL profile, the temperature decrease rapidly but the center part remind homogeneous. We can observe cold plasma region on each side of the main plasma in the case of SGL spatial profile, where there is no laser energy lay down. These plasmas are created by the x-ray coming from the main plasma which produced dense and cold plasma. The direct consequence of this enlargement of the hottest and densest parts of the plasmas, is that neonlike ions, i.e., lasing ions, are found in regions with boundaries at ±25 µm from the plasma centre for GL pulse, increasing to ±40 µm for n=5 SGL pulse up to ±50 µm for n=10. Note that for all GL or SGL cases, lasing ions are found from x=20→40 µm. This means that the potentially amplifying surface, and then the maximum output energy of the SXRL, is multiplied by a factor of 2 for n=10 SGL vertical profile as compared to GL.

Fig. 4. Electron temperature distribution for a) GL profile, n=1 b) SGL profile, n10 for a delay Δt=100ps after the peak of the long pulse.

As previously discussed, the electron density gradients, particularly along the y direction, may dramatically reduce the net SXRL amplification and destroy the beam homogeneity. Comparison of figures (Fig. 3a) and

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(Fig. 3b) shows an impressive reduction by three orders of magnitude of the vertical density gradient in the region of peak gain localization for n=10 SGL ∇yNe~1.1×1021 cm−4 as compared to n=1 case ∇yNe~6.0×1024 cm−4. Following the calculation in the paraxial approximation propagation of soft-x-ray beam, this shows that the refraction is negligible for n=10 SGL profile [19]. Note that electron density gradients along the x direction are equivalent for any GL- or SGL-produced plasmas (n=2, 5 and 10). 3.2 Prepulse influence on the vertical plasma shape As we show, the electron density and temperature mainly follow the laser energy deposition. We investigate now the effect on the imprint of the laser energy deposition when the long pulse irradiated the plasma formed by low energy prepulse.

Fig. 5. Pre-plasma formed by combination of prepulse and long pulse for a delay of 100 ps after the peak of the long pulse: a) GL laser spatial profile b) SGL spatial profile

We add a prepulse 2.3 ns before the peak of the long pulse containing 0.1% of its energy. This leads to laser intensity on the target of 2 1010 W.cm-2 and 5 1011 W.cm-2. The prepulse spatial profile width and shape are the same as the long pulse, considering they are often focused by the same optical system. To decrease the computation time we cut the simulation window in half in the y direction using the x-axial symmetry. We Show in Fig. 5 that the density distribution (logarithm scale) is still more homogeneous in the case of SGL spatial profile in the vicinity of the critical surface. If we compare with the Fig.3 where there is no pre-pulse,

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the electron density gradient fall by 2 orders of magnitude on the x-axis [20, 21]. In the case of SGL profile, the density is higher for a same x coordinate compared to GL profile case. This could be explained by the difference in the velocity distribution and particularly, the difference of the ratio of (vx/vy) which is closer to one in the case of SGL profile. Finally, we can notice, the beginning of a jet formation in y=60µm generated by the long pulse and the second one expanding to the top of the figure from y=75µm to y=120µm. These structures are not generate in the case of a perfect GL spatial profile.

4 Plasma heating and gain estimation Thus at high electron density Ne~1020–1021 cm−3, where the second pulse is absorbed, the GL generated plasma has a temperature of about Te~470 eV at its center y=120 µm dropping to Te~ 200 eV at y=75 µm and y=175 µm. For SGL profile pulse, the peak temperature is nearly the same, however on the edges y=75 µm and y=175 µm a much higher temperature of Te ~320 eV is achieved. Besides, the density profiles follow somehow the laser deposition profile, creating a kind of plateau on the electron density with sizes increasing with n. For n=1, the plateau is about 25% of the laser full width while it rises 40% for n=5 to 60 % for n =10 SGL profile. This means that the potentially amplifying surface, and then the maximum output energy of the SXRL, is multiplied by a factor of 2 for n=10 SGL vertical profile as compared to GL.

Fig. 6. Gain map a) Super Gaussian profile, n=10 b) Gaussian profile, n=1.

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To achieve 2D gain maps, we postprocessed the outputs of ARWEN with a simplified three-level atomic model. Such a calculation is known to slightly overestimate the gain [20]. We assumed that the fundamental level 1s22s22p6 is much more populated than the other levels. The upper lasing level (1s22s22p53p,J=0) is linked to the fundamental level by a forbidden transition and following the conclusions of Goldstein et al. [22], we assume that is mainly populated by direct collisional excitations. The lower lasing level (1s22s22p53s,J=1) is populated and depopulated through both collisional and radiative transitions. Collisional and radiative rates have been obtained from previous works on neon-like iron [23]. Spectral width is calculated assuming both homogeneous and inhomogeneous broadening based on ARWEN output. The electron density is given by ARWEN at the instant of firing the second pulse. From Figs.6a and 6b we can observe in the 2D gain maps that the shapes of the gain regions follow the energy deposition profiles. Close maximum gain, around 136 cm−1, is found for all profiles. Yet, it is interesting to note that the peak gain zone is two times larger over the y direction for the n=10 SGL 80 µm as compared to GL case 40 µm.

5 Conclusion This study underlines the need of complete bidimensional hydrodynamic code to achieve realistic soft-x-ray plasma amplifier description. Indeed, we show that lateral thermal conduction reduces the gain zone to a third of laser width when Gaussian laser shape is considered. By using a 2D hydrocode, we have numerically demonstrated that n=10 SGL spatial profile reduces the vertical refraction to an insignificant level. Consequently, an amplified soft-x-ray beam of high homogeneity would be achievable. Another beneficial phenomenon observed is an enlargement of the gain region surface by a factor of 2 while using super- Gaussian spatial profile as compared to classical Gaussian laser profile. Broadening of effective amplification surface would lead to doubling of the output energy while keeping driving laser energy constant. These two points allow a better output soft-x-ray laser energy extraction ensuring to double the output energy without increasing the driving laser energy.

2-D Hydrodynamic Simulation of Laser Plasma Generation

References 1. B. Rus et al., Phys. Rev. A 66, 063806 (2002). 2. P. V. Nickles et al., Phys. Rev. Lett. 78, 2748 (1997). 3. J. Dunn et al., Phys. Rev. Lett. 84, 4834 (2000). 4. O. Guilbaud et al., Europhys. Lett. 74, 823, (2006). 5. R. Bartels, Nature 406, 164 (2000). 6. Ph. Zeitoun et al., Nature 431, 427 (2004). 7. Y. Wang et al. Phys. Rev. Lett. 97, 123901 (2006) 8. S. Le Pape and Ph. Zeitoun, Opt. Commun. 219, 323 (2003). 9. J. G. Lunney, Appl. Phys. Lett. 48, 891 (1986). 10. R. Kodama et al., Phys. Rev. Lett. 73, 3215 (1994). 11. J. A. Plowes, Opt. Commun. 116, 260 (1995). 12. K. Cassou et al. Phys. Rev. A, 76, 1 (2006) 13. F. Ogando and P. Velarde, J. Quant. Spectrosc. Radiat. Transf. 71, 541 (2001). 14. L. H. Howell et al., Numer. Heat Transfer, Part B 35, 47 (1999). 15. G.-Y. Yoon et al., Appl. Opt. 36, 847 (1997). 16. T. A. Planchon et al., Opt. Commun. 216, 25 (2003). 17. K. Cassou et al. Optics Letters, to be published. 18. S. Kazamias et al, in this proceedings 19. E. Fill, J. Opt. Soc. Am. B 14, 1505 (1997). 20. J. Nilsen et al., Phys. Rev. A, 48, 4682 (1993) 21. Y. Li, G. P. Preztler et al., Phys. Plasmas 4, 164 (1997). 22. W. H. Goldstein et al., Phys. Rev. A 36, 3607 (1987). 23. M. Cornille et al., At. Data Nucl. Data Tables 58, 1 (1994).

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2D Hydrodynamic Simulation of Focus-Line Plasma in Ni-Like Ag X-Ray Laser Research W. Zheng and G. Zhang (Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing 100088,China)

Summary. In the research of X-ray laser (XRL) driven by line focused laser, because focus-line had very large aspect ratio with narrow width (100μm), the jet of plasma showed clear 2D structure, and all sorts of peculiar 2D distributions of near-field and far-field XRL intensity were already observed in experiments, such as “bow-like” field image of XRL on ShengGuang-II facility. In order to understand and simulate this phenomenon, we developed a 2D non-equilibrium radiation hydrodynamics code named XRL2D, which was introduced in this paper briefly. The hydrodynamics behavior of Ni-like Ag XRL had been simulated by XRL2D code, simulation results were also presented in this paper. Similar to the QSS XRL experiments on ShengGuang-II, a slab Ag target was irradiated by a 1ω laser beam (85J) with 100μm×1.8cm focus-line, drive laser included a pre-pulse (2.55J) and a main pulse(82.45J), both with width of 100ps, and the interval of two pulses was 3ns. The abundance distribution of Ni-like ion appeared bow-like structure. The 2D gain calculation was our future work.

1. Introduction In the study of X-ray laser (XRL) driven by laser, line-focus beam were used popularly. Because focus line had a long length and a narrow width (100μm), the plasma expanded two dimensionally, in addition to the nonuniform of drive beam, hydrodynamic behavior of plasma and gain distribution of XRL can’t been described by 1D code. For this 2D characteristic of plasma expansion, many peculiar distributions of near and far field XRL intensity have been observed in many experiments [1-4]. In the experiments conducted on ShengGuang-II facility, the near- and farfield intensity distribution of Quasi-Steady-State (QSS) Ni-like Ag 13.9nm XRL presented a bow-like shape, which were showed in fig.1. This XRL were produced by irradiating Ag slab target (1.6cm long) with 100μm×1.8cm line focused beam (1ω/100ps/100J) at an intensity of 4~6×1013W/cm2, drive laser beam included two pulses, energy rate of pre-

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pulse and main-pulse was 3~5%, main-pulse delayed by ~3ns. There were two reasons to explain this bow-like shape. First, the gradient of electron density of plasma made XRL refracted out of the center area. Second, the gain of XRL maybe have this bow-like profile. In order to understand physical processes in it exactly and to study 2D effects of interaction between laser and plasma, we developed a non-equilibrium radiation hydrodynamics 2D code (XRL2D). The brief introduction of this code was presented in this paper, as well as the hydrodynamic simulation result of QSS Ni-like Ag XRL.

Fig. 1. The intensity distribution of Ni-like Ag 13.9nm XRL (experiments on ShengGuang-II facility). (a) Near-field image of two opposite coupling targets, and (b) far-field image of single target. x was the normal direction of target surface, y was the tangent direction of target surface. θ was the refraction angle

2. Introduction of XRL2D code Inverse bremsstrahlung absorption and resonant absorption of drive laser were considered, and geometric optic approximation was used. Flux-limit heat-conduct approximation and flux-limit multi-group diffusion approximation (~100 groups) were adopted. Average atomic model only considering principal quantum number was used in code. Considered micro-processes included bremsstrahlung and its inverse process, electron collisional ionization and three-body recombination, photo ionization and photo recombination, electron collisional excitation and de-excitation, line emission and line absorption, di-electron recombination and self ionization. In the view of Lagrange, equations of irradiation hydrodynamics employed by code were listed below, v du 1 ≈ − ∇( pe + pi + pr + q ) dt ρ

(1)

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v d (CveTe + V ) 1 d ⎛1⎞ ≈ − ∇ ⋅ Fe − pe ⎜⎜ ⎟⎟ + Wie + Wl − Wr ρ dt dt ⎝ ρ ⎠

(2)

v d (CviTi ) 1 d ⎛1⎞ ≈ − ∇ ⋅ Fi − pi ⎜⎜ ⎟⎟ − Wie ρ dt dt ⎝ ρ ⎠

(3)

v ρν ∂fν ∂ ⎛ 1 ⎞ ∂fν = −∇ ⋅ Fr + ⎜ ⎟ + Dν − Cν fν ∂t 3 ∂ν ∂t ⎜⎝ ρ ⎟⎠

(4)

v

In which, u was the hydrodynamic velocity, ρ was the matter density, pe, pi and pr were the pressures of electron respectively, ion and irradiation, q was the Von-Neumann viscosity, CveTe and CviTi were the electron and ion internal energy per unit mass, fv was the photo number of unit quantum state, v was the frequency of photo. V was combine energy of ion, Wie was the term of energy exchange between electron and ion, Wl was the term of laser energy deposit, Wr was the term of energy exchange between matter and irradiation. Dv, Cv were the emission and absorption coefficients of photo. Fe, Fi and Fr were flux of electron, ion and irradiation respectively. r Fe = FDe ⋅ f e FLe

and

F

( Fr

De

were

Le v FLe = N e kTe kTe / me

+ f e FLe

), where, f

diffusion

e

flux

v

was electron flux-limitv factor, FDe

and

direct

flux,

FDe = − K e ∇Te

,

, so as well as flux of ion and irradiation. ALE method adopted by code included three steps. First was Lagrange step. Differential scheme of momentum equation was IGA scheme. In order to decrease calculation amount, split scheme was used, diffusion processes of electron, ion and irradiation were separated from local processes such as atomic processes, energy exchange between electron and ion, temperature increase induced by energy deposit of laser, and local photo-absorption and irradiation et al. using implicit scheme, local processes were all coupled. Second step was rezone, mesh were rezoned every time-step. Last step was remap, 2-order precision remap scheme were adopted.

3. Hydrodynamic simulation of QSS XRL The calculation model was according to the experiments of Ni-like Ag XRL on ShengGuang-II described above. Drive laser (1ω) irradiated Ag slab target with 100 μm×1.8 cm line focused at a intensity of 4.7×1013 W/cm2, laser beam included pre-pulse (2.55 J) and a main-pulse (82.45 J)

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delayed 3ns. Both were Gaussian pulse in time with a width of 100ps, and flat-top pulse in space. Electronic flux-limit factor (fe) of 0.03 was applied. The incidence direction of drive beam was reverse to x axis,

Fig. 2. Electron temperature and density distribution before the main-pulse. Meshes were also plotted.

Fig. 3. Electron temperature and density distribution 20ps after main-pulse peak time.

initial target surface was located at x=0, the target thickness was 30μm. The tota l mesh number was 150×100. At the beginning, area out of target surface was filled with rareness gas (Ag) with a density of 10-6g/cm3. In calculation, meshes were kept perpendicularly always by rezoning, see in fig.2-3. For the symmetric of problem, only half physical area was calculated. Fig.2 showed the simulation results before main-pulse. Pre-pulse only prepared a pre-plasma. After expanding for 3ns, Pre-plasma cooled down

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no more than 20 eV, and while approaching target surface, electron temperature decreased more and more. Simulation results 20 ps after main pulse peak time showed in fig.3, when gain of XRL would appear (the result from 1D simulation of JB19 code). According to our simulation, in the

Fig. 4. At center of focus line, electron temperature Te, radiation temperature Tr, electron density Ne, abundance of Ni-like ion PNi_like and laser energy deposit WL distribution along normal direction of target surface, 20ps after main-pulse peak time.

period of incidence of main pulse, plasma moved a little because the width of main pulse was short enough. With the arrival of main-pulse, plasma at laser energy deposit area was heated and ionized dramatically. At this area, for rapid electron collisional ionization, Ni-like ion dominated at lower electron temperature (<300 eV), with the increasing of temperature, plasma was over ionized quickly, so there was no gain of Ni-like Ag 4dÆ4p 13.9 nm line for this area at all. For electron collision and irradiation transfer, energy was transported out, then plasma at lower density (electron density Ne=1~4×1019 cm-3) was warned up. At this low density area, process of ionization was slow relatively, when Ni-like ion was dominant, a higher electron temperature (Te=400-650 eV) were maintained, that can be seen in fig.4, according to experience of inversion kinetic calculation, gain would appear at this area which was about 150μm far away from target surface. “Bow-like” distribution of Ni-like ion abundance appeared in our simulation results! It can be seen in fig.3 and fig.5, and this bow-like structure moved slowly away from the target surface. We could predict that gain distribution would be bow-like, though we have not done the calculation of inversion kinetics.

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The gradient of electron density (|∇Ne|) was another important factor for intensity distribution of XRL. It can be seen from fig.3 that bow-like shape of Ni-like ion abundance had two narrow limbs, and gradient of electron

Fig. 5. The evolution of abundance distribution of Ni-like Ag ion. The times in picture were relative to main-pulse peak time.

density of limbs (|∇Ne|~4.4×1022 cm-4) were much large than that of central part of bow (|∇Ne|~6.2×1021 cm-4). According to refraction rule of XRL, for long target, the ray emitted from limbs could not been amplified efficiently, then there would be no thin and long limbs in near- or far-field intensity distribution of XRL. In addition, refraction was not very serious for Ni-like Ag 13.9nm XRL because of low electron density at gain area (<1020 cm-3) actually.

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3. Conclusion To get enough abundance of Ni-like ion was the necessary condition of obtaining gain of Ni-like XRL, and gain-area must be located near the area with high abundance of Ni-like ion. The bow-like distribution of Ni-like ion abundance given by our 2D simulation only supplied the indirect evidences that gain and intensity of QSS Ni-like Ag 13.9nm XRL distributed spatially like a bow, which were agree with experimental results on ShengGuang-II facility qualitatively. We can not give out gain and field image right now, because we have not developed the codes of 2D inversion kinetics and 3D propagation and amplification of XRL, that were going to become our future work.

Reference 1 2 3 4

J. Zhang, P. J. Warwick E. Wolfrum et al. Saturated output of a Ge XXIII xray laser at 19.6 nm Phys.Rev.A 54(6) : R4653~4656. 1996 Joseph Nilsen Juan C. Moreno Luiz B. Da Silva Two-dimensional spatial imaging of the multiple-pulse- driven 196-Å neonlike germanium x-ray laser Phy. Rev. A 55, 827-830 1996 J. Nilsen J. Zhang A. G. MacPhee et al. Near-field spatial imaging of a Nilike Ag 140-Å x-ray laser Phy. Rev. A 56, 3161-3165 1997 Ch. Siegel M. Braud J.E. Balmer et al,. Near-field spatial imaging of the Nilike palladium soft-X-ray laser Optics Communications, 210 305–312 2002

Theoretical Research on Ni-like Ag 13.9nm X-Ray Laser Driven by 3μm and 6μm Wavelength laser G. Zhang, T. Zhang, W. Zheng and X. Qiao Institute of Applied Physics and Computational Mathematics P.O.Box 8009 Beijing 100088 China

Summary. In experiments such as Ni-like Ag Ni-like Pd driven by 1ω laser very little energy of driving laser is deposited in gain region the heating of gain area depends on electron heat conduction and most of energy is wasted. In order to reveal the shortcoming of 1ω laser with normal incidence and the good qualities of 1ω laser with grazing incidence in this paper the schemes of Ni-like Ag driven by normal incidence lasers with longer wavelengths of 6μm and 3μm are studied.

1. Introduction In experiments such as Ni-like Ag X-ray laser (XRL) driven by 100ps Nd:glass laser at 1.053μm wavelength gain region was located ~ 100μm from the target surface with electron density of about 1019cm-3[1] and as the driving laser energy was mainly deposited near critical surface with higher density only very small amount was deposited in the gain region and the electron temperature in the gain region was mainly increased by electron thermal conduction. In this sense most of laser energy was wasted so that J. Dunn et. al. had proposed [2] a conception of grazing incidence technique in the transient collisional scheme. We think that this kind of technique may be adapted to quasi-steady state (QSS) collisional scheme [3,4]. If the wavelength of driving laser increased to 6μm or 3μm the corresponding critical density would be 3.19×1019 cm-3 or 1.28×1020 cm-3 with normal incidence driving laser energy could be deposited in gain region or nearby. Not only the conversion efficiency of the driving energy to X-ray laser energy would increase but the driving energy would greatly decrease. In this paper Ni-like Ag 13.9nm X-ray laser driven by two 100ps lasers at 6μm and 3μm wavelength were studied by our series code[5]. In order to consider plasma aging in simulating XRL transport and

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amplification the XRL photon meets different plasma status after traveling 1ps.

2. Ni-like Ag X-ray laser driven by two 100ps pulses at 6μm wavelength The main pulse transversely irradiated the 20mm long slab target following a 10 % or a 1 % low intensity prepulse and the energy and intensity of the main pulse at the target surface was 5 J and 2.27×1012 Wcm-2 respectively. The line focus produced was 22mm long and 100μm wide. Optimization to the interval between the prepulse and main pulse t12 was done and the effective gain Gef and the absorption of driving laser energy ηa vs. t12 were put in fig.1a and fig.1b respectively. For the two driving conditions with different prepulse Gef varied very similarly and small difference could be seen. And it firstly quickly increased to the maximum of about 20.7 cm-1 at t12=11ns and t12=11.5 ns for 10 % and 1 % intensity ratio respectively and then it varied very smoothly. The energy absorption ratio ηa increased approximately linearly with the increase of t12. ηa for η=10 % was a bit larger than that for η=1 %. Where Gef peaked ηa were 21.5 and 17.5 % respectively while for the Nd:glass laser at 1.053 μm wavelength the ratio ηa was close to 100 %. 20

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Next let’s look at the model Asiw its η was 1 % and t12 was 11.5 ns. According to simulation for 20 mm long slab target the refracted angle θph the divergence angle ϕph the position of peak intensity xph and the full width at half maximum (FWHM) dxph in the near field were 1.32 mrad 0.57 mrad 72.9 μm and 4.9 μm respectively and the peak time and time width in FWHM of output intensity were 29 ps (the peak time of main pulse as 0ps) and 10.9 ps respectively. When tp was 29 ps XRL photon

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contributing to output peak intensity arrived at the middle of target and plasma status of the gain region at this time and time evolution of gain was shown in fig2.a and fig2.b. From fig.2a in the gain region the electron temperature Te had a flat top and the electron density Ne varied very

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smoothly and it had a mild pit in the middle of the gain region which was in favor of XRL propagation in the plasma waveguide. At 29 ps the peak of gain Gp its position xp and the width dx in FWHM of gain region were 25.3 cm-1 63.8 μm and 19.4 μm respectively where Te ion temperature Ti Ne and the abundance of Ni-like ions ηNi were 814 eV 21.1 eV 2.78×1019 cm-3 and 43.6 % respectively. The average gradient of electron density

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dNe/dx was -1.14×1022 cm-4 in gain region. For 13.9 nm XRL line the ratio of refracted angle dθ/dz was 0.98 mrad/cm here z is the target length in cm. For half target length the refracted angle θ1 was 0.98 mrad and the deflected distance x1 was 4.9 μm approaching to ~25 % of dx. From fig.2b the gain region incessantly moved outside. It lasted 85 ps when Gp was bigger than 15 cm-1. From 19 ps to 59 ps the position of Gp moved 10.1 μm the average moving angle θ2 was 0.84 mrad the total refracted angle θ=θ1+θ2 was 1.83 mrad and the corresponding θph calculated by series codes was 1.32 mrad. For half target length the distance x2 that the position of Gp moved was 8.4 μm.The position of peak output XRL intensity in near field x =x1+x2+xp was 77.1 μm and the corresponding xph calculated by series codes was 72.9 μm. Duo to plasma waveguide θ and x calculated from dNe/dx was bigger than the corresponding values calculated by series codes. Comparing the results with that in model Asn7 in which the Nd: glass laser at 1.053 μm wavelength was used as driving laser[6] the Gef increased from 12.9 cm-1 to 20.7 cm-1 increasing by 60%. At tp and xp Te Ti Ne and ηNi increased by about 70% -7% -55% and 20% respectively resulting in 38% increase of Gp and another 22% increase of Gef came from suppressed refraction effect duo to plasma waveguide.

3. Ni-like Ag collisional scheme driven by two 100ps lasers at 3μm wavelength The driving laser energy and the intensity at target surface of the main pulse was 15 J and 6.82×1012 Wcm-2 respectively. The line focus was 22 mm long and 100 μm wide. Other conditions were the same as models with 6μm wavelength driving laser. And the ratio of prepulse intensity to main pulse η was 10 % and 1 % respectively. Optimization to t12 was done and Gef and ηa vs. t12 were put in fig.3a and fig.3b respectively. From fig.3a Gef for η=10 % first decreased from 13.0 cm-1 at t12=2 ns to the minimum of 12.1 cm-1 at t12=2.25 ns and then it sharply rose to a maximum of about 18.0 cm-1 at t12=3.25 ns. And after a small steep fall of 1.26 cm-1 it once more began to increase smoothly to 18.8 cm-1 at t12=6 ns and the peak value of 20.7 cm-1 was achieved at t12=7 ns. And after a steep decrease it varied little from t12=9 ns to t12=13 ns. For η=1 % on the curve for Gef a large fall of 3.8 cm-1 first appeared at t12=2 ns with Gef of 16.0 cm-1 which was followed by a zigzag rise until t12=5 ns with Gef of 14.6 cm-1 then it fast rise until t12=10 ns when t12≥10 ns it

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gentle rise and the peak value of Gef was 21.2 cm-1 at t12=12.5 ns and this model could be called model Asky. From fig.3b the two curves for ηa varied almost linearly. And for η=1% ηa was obviously smaller than that for η=10 %. Where Gef reached the maximum ηa was 42.6 and 54.1 % for η=1 and η=10 % respectively. Comparing with that for 6μm wavelength driving laser ηa increased by 1 to 2 times. 22

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Next let’s look at in model Asky. According to simulation for 20 mm slab target θph ϕph xph and dxph were 3.08 mrad 0.86 mrad 113 μm and 9.4 μm respectively. The peak time and time width in FWHM of output intensity were 16 ps and 27.7 ps respectively. When tp was 16ps the plasma status of gain region at this time and time evolution of gain was shown in fig4.a and fig4.b respectively. From fig.4a the electron temperature Te had a flat top of 1232 eV but gain region was located on the descending slope with Te of only about 50 % of the peak value. And in gain region the maximum of Te and Ne was about two times of the minimum for each. At tp=16 ps Gp dx and xp were 28.6 cm-1 13.7 μm and 91.6 μm respectively where Te Ti Ne and ηNi were 669 eV 21.2 eV 4.76×1019 cm-3 and 38.6 % respectively. Comparing with model Asn7 [6] Gef was raised from 12.9 cm-1 to 21.2 cm-1 increasing by 64 %. At tp and xp Te Ti Ne and ηNi increased by 40 % -6 % 10 % and 6.6 % respectively resulting in 56 % increase of Gp and another 8 % increase for Gef was from better propagation of XRL in plasma. dNe/dx was -2.53×1022 cm-4 and dθ/dz was 2.19 mrad/cm for half target length x1 was 11 μm approaching to about 80% of dx suggesting still large influence of refraction effect on XRL’s propagation and amplification. From fig.4b the Gp reached its peak of 36.4 cm-1 at -40 ps and the narrow gain region and steeply varying electron density limited the output XRL intensity so that tp was 16ps. And gain region incessantly moved

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outside and it lasted 120 ps when Gp was bigger than 20 cm-1. And at the beginning of this process the gain region extended for a short time. From 50 to 70 ps the position of Gp moved 53.6 μm θ2 was 1.49 mrad x2 was 14.9 μm. θ=θ1+θ2 =3.68 mrad it was about 16 % bigger than θph=3.09 mrad. Ni-like Ag Asky

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x=xp+x1+x2=117.5 μm it was about 4% bigger than xph=113 μm so that average refracted angle calculated by series codes was about 1.60 mrad the refracted distance was 8μm it was about 58% of dx

4. Conclusion Ni-like Ag 13.9 nm X-ray laser driven by two 100 ps lasers respectively at 6μm and 3 μm wavelength were simulated. And different intensity ratios of 10 % and 1% between prepulse and main pulse were considered. And optimization to interval time t12 was made. It was found that with 6μm wavelength laser with only 5 J energy less than 1 J energy was absorbed and the effective gain was 20.7 cm-1 which suggests that deeply saturated operation with gain length product GL of 41.4 could be obtained. Comparing the results with model Asn7 in reference [6] in which the main pulse was Nd: glass laser at 1.053 μm wavelength with only 19 % driving energy the effective gain increased by 60% and the width of gain region in FWHM increased from 13.2 μm to 19.4 μm. With 3 μm wavelength laser with only 15 J driving energy about 8 J driving energy was absorbed directly in the gain region and effective gain of 21.2 cm-1 was achieved and deeply saturated operation with GL of 42.4 could be obtained. Comparing with model Asn7 in reference [6] with only 57 % driving energy the effective gain increased by 64 %. In one word as driving laser for Ni-like

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Ag 13.9 nm XRL the lasers at 6μm and 3μm wavelength work better than the Nd:glass laser at 1.053 μm does. Such driving lasers are not available now but by this paper it can well understand the advantages of grazing incidence. As the Nd: glass laser deposit its energy near critical surface because of fast ionization the plasma near critical surface was quickly over-ionized before the electron temperature rises high enough to produce gain. And though the energy absorption ratio is very high more energy is conversed into radiation energy and kinetic energy greatly reducing the electron temperature in gain region. If the driving laser irradiates the target with a grazing incidence angle and it can directly deposit its energy in the gain region or nearby the electron temperature in the gain region is greatly increased so does the gain of XRL.

Acknowledgements This work was supported by Chinese national 863 high technology plan ICF field (grant No. AA847010). This work was directed by Prof. Yu. Min. We would also like to thank prof. Li Yuemin Yan Jun Qiu Yubo and Fang Quanyu for provided atomic data.

References [1] Zhang G P Zhang T X Zheng W D.High Power Laser and Particale Beams 16(11) 1375(2004) [2] Keanan R Dunn J Patel P K. Phys. Rev. Lett. 94(10):103901(2005) [3] Zhang G P Zhang T X Zheng W D. High Power Laser and Particale Beams 17(12) 1817(2005) [4] Zhang G P Zhang T X Zheng W D High Power Laser and Particale Beams 18(2) 210(2006) [5] Zhang G P Zhang T X Wu J Z. High Power Laser and Particale Beams 10(3) 352(1998) [6] Zhang G P et al. in these proceedings

Theoretical Research on Ni-like Ag X-ray Laser by Grazing Incidence Pumping G. Zhang, T. Zhang, W. Zheng and X. Qiao Institute of Applied Physics and Computational Mathematics P.O.Box 8009 Beijing 100088 P.R.China

Summary. LLNL proposed a conception of grazing incidence technique using short pulse and realized saturated output of Ni-like Pd x-ray laser using only 450 mJ driving energy. We think that this kind of technique may be adapted to quasisteady state (QSS) collisional scheme with 100ps driving laser. In this paper using our series code Ni-like Ag 13.9 nm XRL driven by laser two 100 ps pulses with grazing incidence was studied. Two different main pulses with intensity of respectively 1.2×1013 Wcm-2 and 4.3×1013 Wcm-2 were considered and optimization to grazing incidence angle φ and time interval t12 was made. And comparisons were made with models with the same pumping conditions except that the main pulse came normally with varying t12.

1. Introduction In experiments such as Ni-like Ag and Pd X-ray Laser (XRL) driven by 1ω laser the electron density in the gain region was about 1019 cm-3 [1] little driving energy was deposited in gain region. The heating of gain region mainly depended on electron heat conduction and the electron temperature in gain region was only about 30 % of that near the critical surface so most of energy was wasted. To avoid this trouble LLNL proposed a conception of grazing incidence technique using short pulse and realized saturated output of Ni-like Pd XRL using only 450 mJ driving energy [2]. In one dimension with grazing angle φ of 13.6 degree the driving laser was deflected at the electron density Ne* where Ne*=(sin2φ)Nc. there Nc=1.1493×1021λ-2 cm-3 was critical density λ was driving laser wavelength in μm. In LLNL’s experiments Ne*=5.73×1019 cm-3. With grazing incidence technique as the pumping laser had longer path length near the deflecting point the absorption ratio ηa of driving laser would greatly increase and so did the electron temperature in the gain region. In some aspect grazing incidence pumping could operate as quasi-traveling

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pumping did for example with φ of 13.6 degree the velocity of driving laser on the axial direction was about 97 % of light velocity and plasma aging could been overcome widely increasing the effective gain of XRL. We think that this kind of technique may be adapted to quasi-steady state (QSS) collisional scheme with 100ps duration driving laser. In this paper using our series code [3] Ni-like Ag 13.9 nm XRL driven by 100 ps laser with grazing incidence was studied. Due to low intensity and short duration the pre pulse irradiated the target with normal incidence and resonance absorption ratio of 3 % was included but for the main pulse no resonance absorption was considered to exclude the effect of uncertainty of resonance absorption because of low absorption of inversebremsstrahlung. The driving lasers were both 100ps Gaussian pulse at 1.053 μm wavelength.

2. 1.2×1013 Wcm-2 grazing incidence in main pulse [4] The intensity of pre pulse was 1.2×1011 Wcm-2. The flux limit factors of electron thermal conduction fe were 0.6 for pre pulse and 0.3 for main pulse respectively. The line focus was 11 mm long and 100 μm wide with target length of 9.9 mm. The optimization to interval t12 between pre pulse and main pulse had been done by our series code with φ=15° the effective gain Gef and ηa vs. t12 were put in Fig.1(a). The model Asmu with t12=10.5 ns was best its Gef was 22.1 cm-1. Because Ne* was much smaller than Nc although the light path widely increased near the deflecting point Ne* the ηa was still small and when t12 varied between 2 ns and 8 ns ηa fluctuated between 16 % and 18 % after t12 bigger than 8 ns ηa increased as t12 rising linearly when t12 was 12.5 ns ηa reached the 27 % after that ηa gently increased [1]. 25

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With t12 of 10.5 ns the optimization to φ had been done Gef vs. φ been put in Fig.1(b). The model Asq6 was best with φ=16°. Its Ne* was 7.88×1019 cm-3 and Gef was 23.8 cm-1. At tp=26 ps (the peak time of main pulse as zero ps) XRL photon contributing to output peak intensity arrived at the middle of target at this time the plasma status of gain region was put in Fig. 2(a). Here the peak gain Gp was 29.9 cm-1 its peak position xp was 146 μm (initial target surface as zero μm) here the electron temperature Te ion temperature Ti electron density Ne and the fractional abundance of Nilike ions ηNi were 697 eV 14.8 eV 3.65×1019 cm-3 and 39.4 % respectively. xp was about 36 μm outside farther than the deflecting point so Ne was only 46 % of Ne*. The full width at half maximum (FWHM) of gain region dx was found to be ~12 μm.

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Simulation was also done at the same pumping conditions as model Asq6 except that the main pulse came with normal incidence with varying t12 and simulation indicated that the model Asn7 with t12=3.5 ns worked best and the Gef achieved was 12.9 cm-1. Plasma status of gain region at tp=40 ps was put in Fig.2 (b). It showed that the peak gain Gp was 18.3 cm1 its xp was 68.7 μm here Te Ti Ne and ηNi were 479 eV 22.7 eV 4.31×1019 cm-3 and 36.2 % respectively and the gain region was ~13.2 μm wide. Comparing the above model Asq6 with model Asn7 it was found that for model Asq6 the 46% increase of Te together with 35% decrease of Ti resulted in about 64% increase of Gp in the gain region but the Gef increased by 84% relative to the corresponding values in model Asn7. It suggests that about 75% of increase in Gef comes from the increase of Gp while about 25% of increase from contribution of quasi-traveling wave from grazing incidence pumping.

3. 4.3×1013 Wcm-2 grazing incidence in main pulse [5] The intensity of pre pulse was 4.3×1011 Wcm-2. The flux limit factors of electron thermal conduct fe were 0.03 both for pre pulse and main pulse. The line focus was 100 μm wide. The optimization to t12 had been done by our series code for φ of 15° the effective gain Gef and ηa vs. t12 were put in Fig. 3. Gef first quickly went up until t12 increased to 4ns after that inflected between 47 cm-1 and 33 cm-1.

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There were three peaks of 47.2 cm-1 45.2 cm-1 and 43.3cm-1 at about 4.75 ns 8.0 ns and 10.5 ns these corresponded to three models called Asgc Asgp and Asgu respectively. And ηa was observed to rise from about 5 % to 12 % as t12 varied from 2 ns to 13 ns after experienced a small fluctuation it

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was much smaller than the values in the above models with 1.2×1013 Wcm2 grazing incidence pumping. 1000

Ni-like Ag Asgc, 100ps,1ω, 1%prepulse 4.3× 1013Wcm-2 -1 G/0.1cm t12=4.75ns, φ=15o

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At first let’s look at model Asgc at its tp time the Gp was in the 525th mesh and the plasma status in this mesh was shown in Fig. 4. It displayed that when time t went earlier that -62 ps Ne is smaller than Ne* and laser energy was deposited here Te sharply increased until it reached about 650 eV when time went forward but earlier than -57 ps the electron density Ne is larger than Ne* no laser energy was deposited here and the increase of Te slowed and when time went after -57 ps the electron density Ne was once again smaller than Ne* driving laser again came back and in the following 1 ps Te once more rose from 674.6 eV to 953.3 eV and at the same time the abundance of Ni-like ions ηNi happened to reach its peak causing Gain jumping from 40.6 cm-1 to 55.1 cm-1. But this coincidence happened with little probability that it could not be counted on! From Fig. 3 when t12 was

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close to 4.75 ns a sharp peak appeared on the curve for Gef. Because our simulation was yet not so precise and the experimental conditions also had fluctuations the Gef of 47.2 cm-1 in Model Asgc was inaccessible. For models Asgp and Asgu which had higher Gef when the Gain reached its peak the electron density near deflecting point varied very smoothly and electron density in several meshes was close to Ne* resulting in large absorption of laser energy and also it was not possible for the same theoretical and experimental reasons mentioned above. But From Fig. 3 when t12 varied between 6.75 ns and 10.5 ns Gef was bigger than 40 cm-1 so it was possible to obtain gain of about 40 cm-1 instead of gain higher than 45 cm-1.With t12= 8.5 ns Gef vs. the ratio of intensity for pre pulse to main pulse η was put in Fig.5. When η varied between 0.2 % and 1.5 % Gef was also bigger than 40 cm-1. Ni-like Ag Asgr φ=15

-1

G/0.1cm

ο

a)

t=-44ps

Te/10eV

100

Te/10eV

ηNi/%

10 19

-3

Ne/10 cm

Ti/10eV

1

25

-1

-3

Srr/10 kev.s .cm 90

100

110

120

130

140

150

the distance from target surface/μm

1000

b) Te/10eV

G/0.1cm

-1

Ni-like Ag Agn3 t12=2.5ns t=6ps

Te/10eV

100

19

-3

Ne/10 cm

ηNi/%

10

Ti/10eV

25

-1

-3

Srr/10 kev.s .cm

1 40

50

60

70

80

90

100

the distance from target surface/μm

Fig. 6. Status of gain region in model (a) Asgr and (b) Agn3.

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For model Asgr with t12 of 9 ns and η of 1 % plasma status of gain region at tp=-44 ps was presented in Fig.6(a) and Gp indicated here was 49.0 cm-1 locating at 125 μm from target surface here Te Ti Ne and ηNi were 956 eV 18.5 eV 6.90×1019 cm-3 and 29.5 % respectively. And the gain region spanned the deflecting point with width dx of about 7.8 μm. The Gef was 41.4 cm-1. Simulation was also done at the same pumping conditions as model Asgr except that the main pulse came with normal incidence with varying t12 and optimization to t12 indicated that the model Agn3 worked best with t12=2.5ns and the Gef achieved was 12.8 cm-1. Plasma status of gain region at tp=6 ps was presented in Fig. 6(b). It showed that the peak gain Gp was 16.6 cm-1 xp was 66.7 μm here Te Ti Ne and ηNi were 504 eV 27.8 eV 4.17×1019 cm-3 and 37.0 % respectively and the gain region was ~11.3 μm wide. Comparing the above model Asgr with model Agn3 it was found that for model Asgr though ηNi decreased by about 20 % the 90 % increase of Te and 65 % increase of Ne together with 33 % decrease of Ti resulted in about 195 % increase of Gp in the gain region and the Gef increased by 233 %. It suggests that about 87 % of increase in Gef came from the increase of Gp while about 13 % of increase from contribution of quasi-traveling wave from grazing incidence pumping.

4. Conclusion Ni-like Ag 13.9nm XRL was theoretically studied driven by two 100 ps pulses in which the main pulse came with a grazing incidence angle. Driven by different main pulse with peak intensity of respectively 1.2×1013 Wcm-2 and 4.3×1013 Wcm-2 was simulated and optimization to grazing incidence angle φ and time interval t12 was made. And in order to see the effect of grazing incidence technique for each case simulation was done by keeping the pumping conditions the same except that the main pulse came normally with optimum t12. And it was found that in models with higher pumping intensity by grazing incidence pumping laser energy was mainly deposited in the gain region and electron temperature there dramatically rose resulting in great increase of gain and if the grazing incidence angle φ takes about 15 degree and t12 varies from 7 ns to 10.5 ns the Gef could reach 40 cm-1 about 3.4 times that in models by normal incidence pumping. If such a pumping pulse with about 50 J energy irradiates a single target deep saturated output XRL with gain-length product (GL) of about 40 could be obtained. For the models with low pumping intensity by

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grazing incidence pumping and if the grazing incidence angle φ takes about 16 degree and t12 takes 10.5 ns the optimized Gef obtained was 23.8 cm-1 about 84 % larger than that in models by normal incidence pumping and if such a pulse with about 13 J energy irradiates a single target deep saturation output XRL with GL of about 23.8 could be achieved.

Acknowledgement This work was supported by Chinese national 863 high technology plan ICF field (grant No. AA847010). This work was directed by Prof. Yu. Min.

References 1 2 3 4 5

Zhang G P Zhang T X Zheng Wn D.High Power Laser and Particale Beams 16(11) 1375 2004 Keanan R Dunn J Patel P K. Phys. Rev. Lett. 94(10):103901(2005) Zhang G P Zhang T X Wu J Z. High Power Laser and Particale Beams 10(3) 352 1998 Zhang G P Zhang T X Wu J Z. High Power Laser and Particale Beams 17(12) 1817 2005 Zhang G P Zhang T X Wu J Z. High Power Laser and Particale Beams 18(2) 210 2006

Theoretical Research on Enhancement of Gain for NiLike Ag 13.9nm X-Ray Laser Using a New Two-Layer Target G. Zhang, T. Zhang, W. Zheng and X. Qiao Institute of Applied Physics and Computational Mathematics P.O.Box 8009 Beijing 100088 P.R.China

Summary. In experiments such as Ni-like Ag X-Ray laser driven by 1ω laser the gain region is only several nm depth near the target surface so we propose a new two-layer target in which a thin layer (several nm depth) of silver is plated on the surface of some other materials. And in this paper the Ni-like Ag 13.9nm X-Ray laser produced by three new kind of two-layer target with CH Al and Ge as foundation was theoretically studied with our series code.

1. Introduction In experiments such as Ni-like Ag X-ray laser (XRL) driven by 1ω laser with 100 ps duration gain region was located ~ 100 μm from the target surface with electron density of about 1019cm-3 [1]. In this sense most of laser energy was wasted so that J. Dunn et. al. proposed [2] a conception of grazing incidence technique in the transient collisional scheme. We think that this kind of technique may be adapted to quasi-steady state (QSS) collisional scheme with 100ps laser duration [3]. Since the gain region is only several nm depths near the target surface and we wonder that if a thin layer of silver (~ several nm depth) was plated on some other materials can we get higher gain? We call this kind of target as two-layer target. In this paper Ni-like Ag X-ray laser produced by using this two-layer target was studied. And three different kinds of targets with CH Al and Ge as foundation were respectively considered.

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2. Optimization to silver thickness on Ni-like Ag 13.9nm laser line The driving laser was a 100ps Gaussian pulse with 95J energy at 1.053μm wavelength and it was preceded by a 1% prepulse and both pulses are in normal incidence. The interval between the prepulse and main pulse t12 was 2.5ns. The line focus was 22mm long and 100μm wide the target was a)

Te

pure Ag

16

Ge 1.5

1.5

Al CH

1.0 0.5

ηa

pure Ag Ge

1.0

b)

CH

2.0

ηa

Gef /cm-1

Temax/keV

2.0

Ge

14 Pure Ag

Al

Ni-like Ag 100ps ω 1%prepulse t 2.5ns

12

12

Al

0.5 CH 5

10

15

dAg/nm

20

-2

10

43TWcm 20mm slab target 5

10

dAg /nm

15

20

Fig. 1. (a)Temax and ηa vs. dAg and (b) Optimization to dAg for 13.9nm line

20 mm flat target. In order to consider plasma aging in simulating XRL transport and amplification the XRL photon meets different plasma status after traveling 1ps. The optimization to silver thickness dAg was done. The absorption ratio of driving laser ηa the maximum of electron temperature in the plasma Temax and the effective gain Gef for 13.9 nm line vs. dAg were shown in fig.1 a and fig.1 b respectively. For pure silver target ηa Temax and Gef were 67.5 % 1919 eV and 12.8 cm-1 respectively. For two-layer target ηa and Temax decreased. When dAg was 2.4 nm ηa and Temax were 29.0 % and 1208 eV with CH foundation 42.1 % and 1552 eV with Al foundation and 66.0 % and 1823 eV with Ge foundation respectively. For target with Ge foundation these were close to those for pure silver target. When dAg was 4.8 nm for the three different targets they increased to 30.6 % and 1262 eV 44.8 % and 1587 eV and 66.5 % and 1816 eV respectively. For each target when dAg increased to 11.4 nm 9.0 nm and 4.8 nm respectively ηa was close to that for pure silver target. When dAg further increased ηa could be sometimes a little bigger than that for pure silver target. It was due to a weak shock wave at the interface of two different layers when the main pulse came. It also resulted in the fluctuation of Temax and Gef . As dAg increased Gef first quickly increased to a maximum and then slowly decreased. For two-layer target with CH and Al foundation Gef varies very similarly and they both reached the maximum 16.9 cm-1 at

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dAg=4.8 nm about 30 % bigger than that for pure silver target. For twolayer target with Ge foundation when dAg was 4.2 nm its Gef reached maximum of 16.9 cm-1 which is 20 % larger than that for pure silver target.

3. Analysis and discuses to results of two-layer target Firstly we study Ni-like Ag 13.9 nm laser line. For pure silver target the model was Agn3. At tp=6 ps (the peak time of main pulse as zero ps) XRL photon contributing to output peak intensity arrived at the middle of 1000

a)

T /10eV

T e /10eV 100

19

N e /10 cm

G /0.1cm

Ni-like Ag A gn3 t=6ps -1

-3

η N i/%

10

T i/10eV 25

1

-1

Srr/10 kev.s .cm 40

50

60

-3

70

80

90

100

The distance from target surface / μ m

20

Ni-like Ag Agn3 -4ps 6ps 16ps 26ps -14ps

15

-24ps

66ps

-34ps

-1

G/cm

b)

46ps

76ps

10 -44ps

86ps

5

0 30

40

50

60

70

80

90

100

The distance from target surface/μm Fig. 2. (a) Plasma status of gain region and (b) Time evolution of gain for model Agn3.

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target the plasma status of the gain region at this time and time evolution of gain were shown in fig2.a and fig2.b., respectively. It showed that near the critical surface electron temperature Te had a quite flat top with ~1820 eV. But plasma here was over ionized and the abundance of Ni-like ions ηNi was very small. The gain region was ~60-70 μm (initial target surface as zero μm) . In gain region Te was from 670 eV down to 420 eV it was only 28 % of that near the critical surface. The maximum of gain Gp was 16.6 cm-1 and its position xp was 66.7 μm. There Te ion temperature TiηNi and electronic density Ne were 504 eV 27.8 eV 37.0 % and 4.17×1019cm-3 respectively. Table 1. The status of gain region Model

tp

xp

dx

Gp

Te

Ti

ηNi

Ne

ps

μm

μm

cm-1

eV

eV

% 37.0

1019 cm-3 4.17

Agn3

6

66.7

11.3

16.6

504

27.8

B5n3

11

75.0

14.2

21.7

604

33.9

46.4

3.66

L8n3

17

82.2

12.4

22.9

588

31.2

46.2

3.81

G9n3

21

74.6

15.7

20.1

526

29.8

46.9

3.59

Table 2. For 20mm target the estimated refraction angle and peak position in near field Model

Agn3 B5n3 L8n3 G9n3

dNe/dx 1022 cm-4 -1.99 -2.20 -2.00 -1.88

dθ/dz Mrad cm-1 1.72 1.90 1.73 1.62

θ1 mrad

θ2 mrad

θ mrad

θph mrad

x1 μm

x2 μm

xp μm

x μm

xph μm

1.72 1.90 1.73 1.62

0.96 0.95 0.96 0.85

2.68 2.85 2.69 2.47

2.61 2.37 2.53 2.20

8.60 9.50 8.65 8.10

9.60 9.50 9.60 8.50

66.7 75.0 82.2 74.6

84.9 94.0 100.5 91.2

85.4 93.0 98.0 87.9

For model Agn3 the full width at half maximum (FWHM) of gain region dx was 11.3μm. The average gradient of electron density dNe/dx was -1.99×1022 cm-4 in gain region. For 13.9 nm XRL line the gradient of refracted angle dθ/dz was 1.72 mrad/cm here z is the distance in axial direction. For half target length the refracted angle θ1 was 1.72mrad and the deflected distance x1 was 8.6 μm approach to ~76 % of dx. From fig.2(b) the gain region incessantly moved outside. It lasted100ps when Gp was bigger than 12 cm-1. From 6 to 66 ps the gain region moved 17.2 μm the average moving angle θ2 was 0.96 mrad the total refracted angle θ=θ1+θ2 was 2.68 mrad and the corresponding θph calculated by series

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codes was 2.61 mrad. For half target length the distance x2 that the peak gain moved was 9.6 μm. The position of peak output XRL gain for 1000

a)

-1

Gain/0.1cm

19

10

-3

Gain/cm

Te/10eV

100

ηNi/%

Ne/10 cm

50

-29ps

60

25

-1

70

80

31ps 51ps 71ps 91ps

111ps

10

90

100

121ps

5

Ti/10eV

-3

B5n3

-9ps 11ps

-49ps

15

0

Srr/10 keVS cm

1 40

b)

20 -1

Te/10eV

25

Ni-like Ag B5n3 t=11ps

110

The distance from target surface/μm

40

60

80

100

120

The distance from target surface/μm

Fig. 3. (a) Plasma status of gain region and (b) Temporal evolution of the gain in the model B5n3.

intensity in near field x =x1+x2+xp was 84.9 μm and the corresponding xph calculated by series codes was 85.4 μm. For two-layer target with CH foundation the model B5n3 with dAg=4.8 nm was best. And tp was 11ps and the plasma status of gain region at this time and the time evolution of gain was shown in fig. 3a and fig.3b. It revealed that two smoothly varying regions appeared on the curve for electron temperature one was near critical surface with ~1200 eV and another was in the silver plasma with ~ 880 eV. Here plasma was over ionized and ηNi was low. The gain region was ~65-80 μm. In gain region Te was from 870 eV down to 500 eV it was ~50 % of that near the critical surface. The gain region incessantly moved outside. It lasted 110ps when Gp was bigger than 18 cm-1. The characteristics of the gain region and that of the refraction for XRL line were put in Table 1 and 2 respectively. Compared with model Agn3 Te and ηNi increased by 20 % and 25 % -1

Ni-like Ag L8n3 t=17ps

Gain/0.1cm

Te/10eV 19

-3

ηNi/%

Ne/10 cm 10

Ti/10eV

-13ps

b)

25

7ps

-33ps

Gain/cm

Te/10eV

100

-1

a)

L8n3 47ps 67ps 87ps 107ps

20 -53ps

15

27ps

10 5

1 50

25

-1

-3

Srr/10 keVS cm 60

70

80

0 90

100

110

The distance from target surface/μm

40

60

80

100

120

The distance from target surface/μm

Fig. 4. (a) Plasma status of gain region and (b) Time evolution of gain for model L8n3.

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although Ti increased by 20 % and Ne decreased 25 % however Gp increased 30 % dx increased 25 %. xp moved outside by ~10 μm dNe/dx and θ2 were bigger than those in model Agn3 by about 10 %. For two-layer target with Al foundation the model L8n3 with dAg=4.8 nm was best. The plasma status of gain region at tp=17 ps and time evolution of gain was shown in fig.4a and fig.4b. It showed that near the critical surface and in the silver plasma there both appeared a quite similar flat top each with ~ 1550eV and 930eV on the curve for Te. Here plasma was over ionized and ηNi was low. The gain region was ~70 – 85 μm. In gain region Te was from 846 eV down to 530 eV it was ~38 % of that near the critical surface. The gain region incessantly moved outside. It lasted 110ps when Gp was bigger than 18cm-1. The characteristics of the gain region and that of the refraction for XRL line were also put in Table 1 and 2 respectively. Compared to model Agn3 Te and ηNi increased 17% and 25 % although Ti increased 12% and Ne decreased 9 % Gp increased 38 % dx increased 10 %. xp moved outside ~15 μm dNe/dx and θ2 were almost the same as those in model Agn3. a)

-1

Ni-like Ag G9n3 t=21ps

Gain/0.1cm

20

b)

-1

100

Gain/cm

Te/10eV

Te/10eV ηNi/% 19

10

-3

Ne/10 cm

Ti/10eV 25

-1

-3

Srr/10 keVS cm 60

70

80

-9ps 11ps 31ps G9n3 51ps 71ps 91ps 111ps

10 5

-49ps

0

1 50

15

-29ps

90

100

The distance from target surface/μm

40

60

80

100

120

The distance from target surface/μm

Fig. 5. (a) Plasma status of gain region and (b) Time evolution of gain for 13.9nm line.

For two-layer target with Ge foundation the model G9n3 with dAg=4.2 nm was best. The plasma status of gain region at tp=21 ps and time evolution of gain was shown in fig. 5a and fig.5b. Different from the above two models the curve for Te displayed one flat top near critical surface with ~ 1810 eV while in silver plasma it showed a quite smooth slope. The plasma here was over-ionized and ηNi was low. The gain region was ~60 – 80 μm. In gain region Te was from 780 eV down to 480 eV it was approach to ~29 % of that near the critical surface. The gain region incessantly moved outside. It lasted 100 ps when Gp was bigger than 18 cm-1. The characteristics of the gain region and that of the refraction for XRL line were also put in Table 1 and 2 respectively. Compared with

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model Agn3 Te and ηNi increased 4 % and 27 % although Ti increased 7 % and Ne decreased 14 % Gp increased 20 % dx increased 39 %. xp moved outside ~8 μm dNe/dx and θ2 were smaller than those in model Agn3 by about 10 %. For two-layer target with CH and Al foundation the main reason for enhancing Gef was the increase of Te and ηNi but for two-layer target with Ge foundation the main reason was the increase of ηNi. And one must note that for the three kinds of two layer target the peak intensity of spontaneous radiation intensity for the 13.9nm laser line was larger than that for pure silver target by about 32.6 % 37.7 % and 28.9 % respectively. -1

Gain/0.1cm

a)

19

100

Ne-like Ge G9n3 t=-23ps

-3

T /10eV e

Ne/10 cm

Te/10eV

ηNi/%

10 25

-1

-3

Srr/10 keVS cm

Ti/10eV 1 0

10

20

30

40

50

60

The distance from target surface/μm 25 20

Ne-like Ge G9n3 -43ps

-23ps -13ps -3ps -33ps

b)

7ps

Gain/cm

-1

17ps

15

27ps 37ps 47ps 57ps

-53ps

10 5 0 0

10

20

30

40

50

60

The distance from target surface/μm

Fig. 6. (a) Plasma status of gain region and (b)Time evolution of gain for 19.6 nm

In the last we studied the Ne-like Ge 19.6 nm laser line. In model G9n3 tp was -23 ps at this time the status of gain region and time evolution of gain was shown in fig.6a and fig.6b. The gain region was near the critical surface and from 5 μm to 35 μm. In gain region Te varied little with difference less than 10 %. Gp was 22.0 cm-1 xp was 29.0 μm. At xp Te Ti ηNi and Ne were 1319 eV 107 eV 61.4 % and 3.74×1020 cm-3 respectively. dx was 17.7 μm. dNe/dx dθ/dz θ1 and x1 was -1.38×1023 cm-4 23.8 mrad/cm 23.8 mrad and 119 μm. For 20 mm propagating length most of

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laser lines were refracted outside of gain region. From 11μm to 19 μm the gain ranged from 12cm-1 to 14cm-1 Ne varied smoothly the dNe/dx was 0.235×1023 cm-4 so that dθ/dz was 4.0 mrad/cm for half target length the refracted distance was 20μm and most of laser lines were also refracted outside of gain region. But from 12 μm to 17 μm there was a concave distribution of electron density which was favorable to XRL line propagation and amplification. The gain region incessantly moved outside too. It lasted 70 ps when Gp was bigger than 16 cm-1. θ2 was 1.4 mrad. Because of refraction for the 19.6 nm line although the Gp was 10 % bigger than that mentioned above for the 13.9 nm line its Gef was 60 % less than the latter one. For the two laser lines there was a 10 mrad difference in the refracted angle so it was easy to disjoin them. By two-layer target with Ge foundation two laser lines with different wavelength could be produced at one shot. By the way for the Ne-like Ge 19.6 nm line the best choice was 3 % prepulse and t12= 7.5 ns and in this case Gef was 13.3 cm-1 [5]. In order to get the two laser lines with large intensity further optimization was needed.

4. Conclusion First the absorption of laser energy for two-layer target dramatically decreased and as a result the peak electron temperature in plasma also dramatically decreased. But on the other hand as more laser energy was reflected near critical surface a large amount of energy could be deposited in the gain region. Secondly because such materials as CH Al and Ge radiates less X-ray emission compared with silver the electron thermal conduction was relatively intensified making the electron temperature varying very smoothly so compared with pure silver target the electron temperature in the gain region slightly increased and in addition the reduced x-ray emission resulted in increase of abundance of Ni-like ions due to less photo-ionization of M shell electron of silver. To see the effect of photo-ionization clearly the width of the focus line was increased and the Gef for pure silver target was found to decrease but not for the two layer target. Finally compared with pure silver target for 4.8 nm thickness silver the Gef increased by 30 % for two-layer target with CH and Al foundation respectively and for 4.2 nm thickness silver Gef increased by 20 % for two-layer target with Ge foundation. In conclusion the two-layer target was a good X-ray laser amplifier. For the two-layer target with Ge foundation two saturated output laser lines at 19.6 nm and 13.9 nm could be obtained at one shot and this would have special application in future.

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Acknowledgements This work was supported by Chinese national 863 high technology plan ICF field (grant No. AA847010). This work was directed by Prof. Yu. Min.

References 1 2 3 4 5

Zhang G P Zhang T X Zheng Wn D. High Power Laser and Particle Beams 16(11) 1375(2004) Keenan R Dunn J Patel P K. Phys. Rev. Lett. 94(10):103901(2005) Zhang G P et al. in these proceedings Zhang G P Zhang T X Wu J Z. High Power Laser and Particle Beams 10(3) 352(1998) Zhang G P Zhang T X Zhang W D. X-Ray Lasers 2004:9th International Conference on X-Ray Lasers C186381(2004)

Modelling of an Inner-Shell Photo-Ionization X-Ray Laser Using a Recently Demonstrated Betatron Source S. Jacquemot, K. Ta Phuoc*, A. Rousse* and S. Sebban* Laboratoire pour l’Utilisation des Lasers Intenses (LULI) Ecole Polytechnique 91128 Palaiseau France * Laboratoire d’Optique Appliquée (LOA) chemin de la Hunière 91761 Palaiseau France

Summary. Recent advances in the production of ultra-short intense and collimated x-ray pulses by using fs laser-produced plasmas now allow investigating the old – but not yet demonstrated - inner-shell photo-ionization (ISPI) x-ray laser scheme. This paper will present simulations for lasing near 1.5 nm from NeI pumped by the so-called betatron source which has been developed at LOA and currently delivers in the keV range up to 109 photons per pulse in less than 50 fs.

1 Introduction Photons in the proper energy range impinging upon an atom can preferentially remove inner-shell electrons and thus induce population inversions with respect to outer-shell electrons [1]. Such a scheme (labeled ISPI) could potentially lead to transient (a few ten’s of fs) lasing at very short (< 15 Å) wavelengths along Kα lines. But despite numerous extensive studies [2] it has never been demonstrated facing out the technological difficulty to produce an x-ray blackbody emitter with a rapid (less than 1 ps) rise time and an effective radiation temperature near 1 keV [3]. Due to the broad range of applications opened in ultra-fast x-ray science through techniques such as x-ray diffraction [4] and limitations of the current fully divergent Kα x-ray sources [5] interest in this design has been renewed and its feasibility seriously envisaged thanks to the advent of the CPA technique and of the new opportunities offered by relativistic laser-plasma interaction.

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Fig. 1. Energy diagram of the neon ISPI x-ray laser.

2 Laser-based betatron radiation When an intense (~100 TW) laser pulse (called hereafter pump) interacts with a low-Z plasma the ponderomotive force associated with the laser field gradient pushes electrons away from the high-intensity central regions and creates an ion cavity backwards. Because of the presence of strong electrostatic fields electrons trapped in this cavity are longitudinally accelerated to relativistic energies and if off axis undergo oscillations; the plasma acting as both an accelerator and a conventional wiggler then emits x-ray betatron radiation.

Fig. 2. Principle of a keV betatron source as recently developed at LOA.

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323

Such a beam has been recently produced at LOA [6] using a 50TW / 30 fs pump laser focused into an helium gas jet; its characteristics (collimation: θ ~10 mrad brightness: ~109 photons per pulse keV energy spectrum and sub-30 fs duration) apparently fit the requirements as previously determined for photo-pumping Kα transitions.

3 Inner-shell photo-ionization x-ray laser Based on a numerical tool developed at the University of York [3] and kindly provided par Prof. G. Pert the computer code that has been used allows calculating the local gain coefficient (α) along the Lorentzian (“naturally” broadened) lasing line. The atomic population kinetics is solved assuming (i) a 3.5µm-thick Be filter to remove undesirable lowenergy (below 800 eV) photons [7] and (ii) a time-dependent synchrotronlike flash lamp defined by: B(hν) = Φtot S(x) / (1.6Δt) with x = hν / Ec(t) S(x) = 1.71857 x0.281526 exp(-0.968375x) Ec(t) = Emax sin4(½π t/Δt) / 0.29 the betatron source being in fact described with the help of 3 parameters: Φtot (total photon number per cm2) Emax (peak energy) and Δt (rise time). Only 11 populations are computed (all the ground states from NeI to NeV plus the 1s22s2pm and 1s2s22pm - m=4-6 - “hollow” configurations) but the major populating and depopulating processes (photo-ionisation [8] collisional ionisation [9] assuming a Maxwellian free electron distribution Auger and radiative decay) are included. The lasant material is pure neon initially at ambient temperature dilution in a matrix of frozen molecular hydrogen [23] being not considered here because experimentally hard to implement. Ionic abundances electron density and electron temperature are self-consistently calculated.

4 Results and discussion As shown on Fig. 3 a population inversion clearly occurs in the rising edge of the ionizing pulse and exhibits shorter lifetime which is full of promise for ultra-fast x-ray science applications. A flash lamp duration as brief as 30 fs is required for significant (> 20 cm-1) lasing a peak local gain

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coefficient as high as 90 cm-1 being even reached below 10 fs. Δt is thus one of the key parameters for demonstrating the ISPI scheme; it can reasonably be estimated to a fraction of the pump duration but has not yet been measured. It also strongly influences the total number of photons per surface unit required to lase. For Δt=25 fs (Fig. 4) more than 1018 photons/cm2 (5 1010 photons focused to a 2 µm diameter spot) have to interact with the neon gas to produce noticeable amplification. Such a value is far from the current performances of the betatron source; improvements (mainly aiming at increasing the pump/helium interaction length) have then to be done. The peak energy Emax has also been varied: the local gain coefficient appears to be not really sensitive to that parameter above some threshold (~500 eV). Electron acceleration to GeV energies is then not required and demonstration of the scheme on 100TWclass pump lasers could be foreseen.

Fig. 3. Time evolution of the peak local gain coefficient versus the rise time of the betatron source (Φtot=1.6 1018 photons/cm2).

Fig. 4. Influence of the total photon number per cm2 (Φtot) on the peak local gain coefficient.

Modelling of an Inner Shell Photo-Ionization X-Ray Laser

325

As stated out in the 70’s [10] collisional ionization of the outer-shell (2p) electrons is the primary process limiting in time the population inversion. All the simulations above have been performed for an ion density equal to 1020 cm-3: a slight increase of this value could help (at 8 1020 cm-3 α is multiplied by 3.5). Looking in more detail to one particular case (as defined on Fig. 3 for 25 fs) it can be shown (Fig. 5) that at the time of maximum gain coefficient (just before the peak of the pump x-ray pulse) the plasma temperature is ~360 eV and the neon is ~5% ionised. The pumping radiation intensity is ~2.2 1016 W/cm2 ~9% within the 870-1350 eV range directly useful for producing the population inversion. The Be foil has absorbed ~9 eV/atom and still functions as a filter.

Fig. 5. Time evolution of the local gain coefficient electron temperature (Te) and average ionization degree (Z*).

5 Conclusion The COCKER project aiming at demonstrating the ISPI x-ray laser scheme has been recently financed for 4 years. First steps will be (i) experimental determination of the betatron source duration (ii) refinements of the computations (improve atomic physics introducing LSJ levels free from Mawellian electron hypthesis coupling the current numerical tool to a 0D Fokker-Planck code …) (iii) design of the x-ray focusing optics. If successful extrapolation to shorter lasing wavelengths could be envisaged in the framework of the Extreme Light Infrastructure (~500 TW in ~10 fs) project.

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References 1. Duguay M.A. and Rentzepis P.M.: 'Some approaches to vacuum UV and x-ray lasers' Appl. Phys. Lett. 10 350 1967. 2. Kapteyn H.C.: 'Photoionization-pumped x-ray lasers using ultrashort-pulse excitation' Appl. Optics 31 4931 1992. 3. Healy S.B. and Pert G.J.: 'Simulations of inner-shell photoionization x-ray lasers' Inst. Phys. Conf. Ser. 151 169 1996. 4. Rousse A. et al.: 'Femtosecond x-ray cristallography' Rev. Mod. Phys. 73 17 2001. 5. Rousse A. et al.: 'Efficient Kα x-ray source from femtosecond laser-produced plasmas' Phys. Rev. E 50 2200 1994. 6. Rousse A. et al.: ’Production of a keV x-ray beam from synchrotron radiation in relativistic laser-plasma interaction’ Phys. Rev. Lett. 93 135005 2004 - Ta Phuoc K. et al.: 'Laser based synchrotron radiation' Phys. Plasmas 12 023101 2005. 7. Henke B.L. et al.: 'X-ray interactions: photoabsrption scattering transmission and reflection at E=50-30000eV Z=1-92' Atomic data & Nuclear Data Tables 54 181 1993. 8. Verner D.A. et al.: 'Analytic fits for partial photoionization cross sections' A. & A. 109 125 1995. 9. Moores D.L. et al.: 'Ionization of highly charged ions' J. Phys. B. 13 385 1980. 10. Axelrod T.S. 'Inner-shell photoionization-pumped x-ray lasers. Sulfur' Phys. Rev. A 13 376 1976.

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Similarity Model of Longitudinally Pumped X-Ray Laser Y. J. Li12, X. Zhang12, X. Lu2 and J. Zhang2 1)

Physics department China University of mining & Tech. (Beijing) Laboratory of Optical Physics Institute of Physics Chinese Academy of Science

2)

Summary. A similarity model of the hydrodynamics of longitudinally pumping xray lasers was set up. The calculations show that (1) The pedestal of the longitudinal pumping pulse play an important role in the Ni-like ionization state (2) The absorption of longitudinally pumping laser in the plasma result in the asymmetry of the temperature and the density so that the gain length of x-ray laser is limited. (3) It is an effective method to choose the proper element of which the required density is low in the gain region.

1 Introduction Since high gain transient collisional excitation (TCE) scheme was first demonstrated in 1997 with only a few Joule pump energy [1] great attention was attracted. However the gain length of TCE plasma is limited by the life of TCE population inversion which the maximum length is only 5mm. In order to overcome the problem R.Li proposed the longitudinally pumping scheme in 1998 [2]. In 2002 the scheme is experimentally demonstrated in Ni-like Mo by T.Ozaki et al. [3]. Nevertheless only 2mm length is still too short to obtain the saturated x-ray laser output while the divergence of the beam of the scheme is obviously improved. And the shorter gain length is due to the influence of the plasma absorption and the refraction of the plasma density gradient to the longitudinally pumping laser [4]. In order to help understand the longitudinally pumping x-ray lasers the similarity model is set up for investigating the hydrodynamics of the x-ray laser.

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2 The model of the longitudinally pumping x-ray laser The transient similarity model in Ref. 5 is modified to be fit for the hydrodynamics of the longitudinally pumping x-ray lasers. The convenient units in Ref. 4 is employed which scale the variable with underline to simplify the calculation. The processes of laser pulses interacting with plasmas are divided into six distinct periods. They are t ≤ t1L t1L≤ t ≤ tm tm≤ t ≤ t2trans t2trans≤ t ≤ t2L t2L≤ t ≤ t3L and t3L≤ t respectively where t1L=Δt1L is the long pulse duration Δtm is the delay time tm=Δt1L+Δtm is the time when the pedestal pulse arrives Δt2L is the pedestal pulse duration t2L= tm+Δt2L is the turning off time of the pedestal pulse Δt3L is the short pulse duration t3L= t2L+Δt3L is the turning off time of the short pulse. Otherwise the laser intensity reductive formula with the longitudinal length z and the incidence angle ϕ1 in the plasma in Ref. 4 is adopted. According to above longitudinally pump processes the similarity model is set up. The solutions of the transverse pre-pulse are same as Ref. 5 below.

T = 8.54 keV I

5/9

−2

2/9

A λ

L = 4.83 × 10 cm I

10 / 27

−3

n0 = 10.84 × 10 cm I 20

2/3

A

Λ

2/9

−2 / 27

11 / 54

A

λ

t

2/9

4/9

4 / 27

λ

Λ

4 / 27

−5 / 9

t

Λ

31/ 27

−2 / 54

(t ≤ t1L)

t

(1)

−14 / 27

here I is laser intensity A is atomic mass λ is laser wavelength Λ is coulomb logarithm; T L and n0 are temperature scale length and maximum electron densityrespectively. 2 / 3 −2 / 3

T = T1L t 1L t

−5 / 9

L = L1L t 1L t

5/9

n0 = n1 L t1 L t

(t1L≤ t ≤ tm)

7/9

−7 / 9

(2)

The main pulse model is set up in the four distinct periods. a) During the time of tm≤ t ≤ t2trans The pedestal laser pulse is used to create the optimized plasma. The tm=z/c (c light speed) from the geometry. The m = m0 t1L2 / 3 and the heating rate H=I/m are assumed a constant after the time t1L with τib >1 because the preplasma is not transparent for the pedestal pulse. The solutions are

Similarity Model of Longitudinally Pumped X-Ray Laser

329

4/3 8/9

T = a1 t 3/ 4

3/ 4

(1 − t m t 17 / 9

−17 / 9

Tm t m

+

t

L = b1 t

3/2

)

3/ 4

, here a

1

a1

(1 − t m t 17 / 9

−17 / 9

Lm t

+

−1

= 28.45 I m 1 L A

2/3

−17 / 9

2

1/ 2

−17 / 9

10 / 9

)

1/ 2

, here b

1

b1 t m

= 17.81 × 10

−1

−4

I m1 L

(3) 1/ 4

c1 t

n0 = (1 − t m t 17 / 9

−17 / 9

−5 / 4

, here c

1

c1

+

28 / 9

4

t

−17 / 9

)

20

= (5.69 × 10 )

4

−1

I

−2

5

m1 L A

1/ 4

nm t m

b) During the time of t2trans ≤ t ≤ t2L

The plasma changes to be transparent for the pedestal pulse again with the laser heating. Considering the physics meaning of the t2trans we get

t 2 trans = 0.51 I

−7 /15

23 / 15

m1 L A

−2 / 3

Λ

8 /15

λ

16 /15

(4)

Also 5/ 2

T = a2 (1 − t 2 trans t 2/5

5/3

−5 / 3

L = b2 t [1 − t 2 trans t 4 / 15

5/3

+

−5 / 3

5/3

T2 trans t 2 trans t +

−5 / 3

a2 15 / 4 −5 / 3 L2 trans t 25 / 12

2/5

]

b2 t 2 trans

4 / 15

t[1 − t 2 trans t 5/3

−5 / 3

+

(8.08 × 10 )

20 15 / 2

c2

c2 t 15 / 2

, here c2 =

−5 / 3 35 / 6

]

2 / 15

2

, here b2 = (1.29 × 10 −2 )15 / 4 a2 A

2 / 15

n0 =

−1

) , here a2 = 19.46 I m1 L λ Λ

a2 A

−5 / 4

15 / 2

m1 L

5/2

n2 trans t 2 trans (5)

c) During the time of t2L≤ t ≤ t3L

The main pulse is so short that the plasma is not transparent for the laser and there is not enough time to change the state of ion charge. At time t2L

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Y. J. Li et al.

the solutions can be obtained by considering the initial conditions before t2L: 2/3

5 / 3 −5 / 3

T = a 3 t (1 − t 2 L t

+

T2 L t 2 L

t

−5 / 3

−1

), here a 3 = 23.12 keV I 2 m AZ

−1

a3 2

1/ 2 3 / 2

L = b3 t

n0 = c3 t 1/ 2

5 / 3 −5 / 3

(1 − t 2 L t

−3 / 2

L2 L

+

t

4/3

−5 / 3 1 / 2

)

b3 t 2 L −5 / 3 −5 / 3

(1 − t 2 L t

2

−1

3

c3

+

, here b3 = (5.16 × 10 −2 ) 2 I 2 m

4/3

t

−5 / 3

n2 L t 2 L

)

−1 / 2

, here c3 = (3.16 × 10 ) 20

2

m Z 1

2 2

I2 A (6)

d) During the time of t3L≤ t

After the time t3L the main pulse is turned off and the plasma continues to expand adiabatically. The solutions can be obtained using the condition before t3L: 2/3

T = T3 L t 3 L t

−2 / 3

−5 / 9

L = L3 L t3 L t

5/9

7/9

n0 = n3 L t 3 L t

−7 / 9

(7)

here T3L L3L and n3L are the temperature scale length and density at the t3L respectively.

3 Results and Discussion We firstly calculate the experiment results of T.Ozaki et al. under the same condition to demonstrate the credibility of the model. Then we investigate the hydrodynamic of longitudinally pumped x-ray laser plasma using the model. 3.1 Credibility of the model

We calculate the longitudinally pumped nickel-like molybdenum slab xray lasers under the same experimental conditions of T.Ozaki’s. The calculation results indicate that the average ionization state only reach to 10 not 14 required by nickel-like molybdenum at the pre-pulse laser intensity of 1.5×1011 W/cm2 and the duration of 300ps which is a bit bigger than 9 from T.Ozaki et al. But the pedestal of main pulse with the intensity

Similarity Model of Longitudinally Pumped X-Ray Laser

331

3.0×1011 W/cm2 and the duration 300ps heat the electron to 88.1 eV which is quite similar to Ozaki’s results. The ionization is 14.04 and the electron density reach to 1.01×1020 cm-3 according with Ozaki’s results. The comparison shows successfully that the results from this simplified model well match the calculation by Ozaki. 3.2 Affection of the pedestal of main pulse on the ionization

In order to realize the affection of the pedestal to x-ray laser we calculate the affection on the ionization of pulse pedestal with different duration and intensity respectively as shown in Fig 1. 14.15

Z (Average ionization)

(a) 14.10 14.05 14.00 13.95 13.90

0.1

0.2

0.3

0.4

0.5

0.6

7

8

t2L (ns)

(b)

Z (Average ionization)

16.0 15.5 15.0 14.5 14.0 3

4

5

6 11

2

Intensity (10 W/cm )

Fig. 1. The average ionization vs the duration (a) and the intensity (b) of the pedestal of the main pulse.

332

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Fig.1 shows that the ionization just decreases from 14.12 to 13.93 (stay Ni-like) with the increase of the duration of main pulse pedestal from 100 ps to 600 ps under the condition that the intensity is invariable (3.0×1011 W/cm2). While the ionization increases rapidly from 14.03 to 15.96 (over Ni-like state) with the increase of intensity of pulse pedestal from 3.0×1011 W/cm2 to 8.0×1011 W/cm2 when the duration of main pulse pedestal (300 ps) is invariable. It is clear that the variety of the ionization is sensitive to the intensity of pulse pedestal. 3.3 The hydrodynamic of the longitudinally pumped x-ray laser

We know that people always pay more attention to the variety of temperature scale and density of plasma with different value of z along propagation of pumped laser (z axis) in longitudinally pumped scheme due to its direct affection if the plasma can form the uniform population inversion and if x-ray laser can be amplified effectively instead of being absorbed. In order to investigate the above problems particularly we calculate the electron temperature the ionization state and the variety of density respectively with the different value of z under the same experimental conditions of T.Ozaki’s as shown in Fig.2. We firstly calculate different value of z dependent electron temperature before the ending of the main pulse pedestal as shown in Fig.2 (a). It should be noted that the temperature rapidly decreases from 90 eV to 5.9 eV before 600 μm and then approaches to 5.6 eV after 600 μm which is the same to the electron

temperature without main pulse pedestal indicating that the pumped laser intensity has approached to 0 after 600 μm. The different value of z dependent electron temperature in Fig.2 (b) has also demonstrated the above conclusion: the ionization decreases from 14.03 to 5.69 with the variety of z from 0 to 600 μm and then approaches to 5.6. At last we calculate the variety of the electron density with the different value of z (shown in Fig.2 (c)). The electron density varies from 1.01×1020 cm-3 to 1.84×1020 cm-3 and then approaches to 1.95×1020 cm-3 after 600 μm. Therefore we can conclude that the intensity of pumping laser decreases rapidly along propagation in the plasma due to the absorption and refraction. When the value of z exceeds a definite value the proportion of Ni-like ion is much little because of the low temperature. Here the x-ray laser will be absorbed instead of being enhanced by plasma. So it is important to choose the appropriate slab length. We also calculate the different value of z dependent electron temperature at the end of pulse pedestal with different electron density as shown in Fig.2(d) due to the condition that we can vary different incident

Similarity Model of Longitudinally Pumped X-Ray Laser

333

100

14

Z (Average ionization)

(a)

80

T (eV)

60 40 20 0 0.00

0.05

0.10

0.15

(b)

12 10 8 6 4

0.20

0.00

0.05

0.10

0.15

0.20

z (cm)

z(cm)

100

2.0

(c) 80

(d)

1.4

T (eV)

-3

1.6

20

n0 (10 cm )

1.8 60 40 20

1.2

0

1.0 0.00

0.05

0.10

z (cm)

0.15

0.20

0

500

1000

1500

2000

-3

z (10 mm)

Fig. 2. The curve of the temperature (a) ionization (b) and electron density (c) with z axis along the longitudinal direction before the main pulse arrive. The delay time is 4ns other conditions are same as fig.1. (d) The curve of the temperature with different density along z axis at the end time of the main pulse. Here the solid line is for n0=1.0×1019 cm-3 the dash line is for n0=4.0×1019 cm-3 the dot line is for n0=8.0×1019 cm-3 the dash-dot line is for n0=1.2×1020 cm-3 the dot-dot line is for n0=4.0×1020 cm-3 the short dash line is for n0=8.0×1020 cm-3.

density through choosing different longitudinally incident position in the experiment. It is noted that the electron temperature changes obviously with z in different electron density. It also shows that the electron temperature varies only from 88.11 eV to 83.62 eV when the density is lower 1.0×1019 cm-3 for instance while the electron temperature decreases rapidly to the initial value of 5.37 eV in the 8.0×1020 cm-3. Therefore it is more effective method to choose the proper element of which the requirement of the density in the gain region is lower.

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4 Conclusions A similarity model is developed for the longitudinally pumping x-ray lasers. The results are in agreement with the experimental results. The hydrodynamics of the scheme are investigated using the model. The results show that (1) The pedestal of the longitudinal pumping pulse play an important role in the Ni-like ionization state (2) The absorption of longitudinally pumping laser in the plasma result in the asymmetry of the temperature and the density in the laser propagation direction so that the gain length is limited. (3) It is an effective method to choose the proper element of which the required density is low in the gain region.

References 1. P. V. Nickles et al. Phys. Rev. Lett 78 2748 1997. 2. R. Li et al. Phys. Rev. E 57 7093 1998. 3. T. Ozaki et al. Phys. Rev. Lett 89 253902 2002. 4. Y. J. Li et al. 9th International conference of x-ray lasers page 333 Beijing May 24-28 2004. 5. Y. J. Li et.al. Phys. Rev. E 63 036410 2001.

Numerical Analysis of Plasma Medium of a Fully Coherent X-Ray Laser N. Ohnishi1, M. Nishikino2 and A. Sasaki2 1

Department of Aerospace Engineering Tohoku University 6-6-01 Aramaki-Aza-Aoba Aoba-ku Sendai 980-8579 Japan 2 Kansai Photon Science Institute Japan Atomic Energy Agency 8-1 Umemidai Kizu Souraku Kyoto 619-0215 Japan

Summary. Two-dimensional (2D) radiation hydrodynamics simulations have been performed to investigate the generation and the refraction influence in the plasma medium of a fully coherent x-ray laser at 13.9 nm by the double-target configuration. The local energy deposition of the main laser pulse generates a blast wave near the critical density surface and the density dip structure is gradually formed behind the blast wave. The size of the density dip structure is about 10 μm after 50 ps of the main pulse. The three-dimension (3D) ray-trace calculation using the result of the 2D simulation shows the x-rays pass through the density dip with less refraction. The size and the position of the density dip area are similar to the light source of the fully coherent x-ray laser.

1 Introduction The development of the brilliant x-ray source has been progressed for the material science and the biological science and the soft x-ray free-electron lasers (XFELs) [1 2] will open up possibilities of the new scientific area. The laser-driven x-ray lasers (XRLs) [3–9] with highly spatial and temporal coherence are applicable light sources as a scientific tool for the purpose of the practical application of the XFEL. Since the first demonstration of the laser-driven soft XRL [10] the improvements of the beam properties have been demonstrated by a number of the groups [11– 15]. The significantly improvement of the beam quality such as spatial and temporal coherence is the important issue for the practical applications. Recently soft-XRLs with small divergence and highly spatial coherence have been demonstrated by the double-target amplification [16–18] and the longitudinal pumping [19]. In contrast to the transient-collisionalexcitation (TCE) XRL [20 21] the highly spatial coherent XRL is

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developed with discharged capillary plasma [22] and the amplification of the high-order harmonic generation [23]. A fully coherent XRL has firstly demonstrated at a wavelength of 13.9 nm by the double-target amplification [16–18]. In the double-target amplification the XRL from the first target is used as a seeding light and a coherent portion of the seeding XRL is amplified in the gain medium of the second target. Since the spatial coherence of the TCE XRL is limited by the short length of the gain medium the amplifier of the second target was separated from the first target by a sufficient distance with the condition of the Fresnel number N < 1. When the delay time between two pumping pulse is optimum condition the highly directional XRL is generated. The total gain of the amplification of the second target is about 1000 with the gain coefficient of about 8 cm−1 and the output energy is achieved about 1 μJ [24 25]. In this configuration the gain medium of the second target works as an active spatial filter. From the first experimental result and the simple analysis the spatial position of the gain medium of the second target is generated in a lower density area for avoiding the influence of the x-ray refraction. Then the position of the gain medium is about 100 μm from the target surface. However the gain region is about 20 μm distance from the target surface and the source size of the gain medium is about 20 μm in the 2D imaging experiment [26]. It turns out that there is a difference between the simple estimation and the experimental result. Therefore we have performed the 2D radiation hydrodynamics simulation to investigate the generation and the refraction influence of the gain medium plasma. In this paper we present the numerical analysis of the gain medium plasma of the fully coherent XRL using a 2D radiation hydrodynamics code and the 3D ray-tracing of x-ray laser has been conducted with arranging flow-fields of the 2D simulation result. We have carried out the comparison of the gain medium between the experimental result and the simulation one. The effects of hydrodynamic properties of the gain medium plasma have been investigated for finding the optimal pumping laser condition.

2 Numerical Methods and Conditions The computational code for plasma medium of x-ray laser should be able to properly reproduce high-temperature dense plasma. In the preset paper we have developed a 2D radiation hydrodynamics code based on the RAICHO code [27] which was originally developed for inertial fusion

Numerical Analysis of Plasma Medium of a Fully Coherent X-Ray Laser

337

plasmas with some modifications for including the effects of thermal nonequilibrium realistic equation of state and laser refraction. The governing equations consist of inviscid compressible hydrodynamic equations with the additional terms due to electron/ion thermal conduction x-ray radiation and laser absorption in energy equation. Also radiative transfer equation is simultaneously solved to estimate the radiation source term. Numerical fluxes due to inviscid compressible flow are estimated by AUSM-DV approximate Riemann solver [28] with second-order spatial accuracy. The radiative transfer equation is approximated by the multigroup diffusion with variable Eddington factor. Non-LTE (CRE) emissivity and opacity is tabulated before the simulation based on the averaged ion model [29]. The electron and ion thermal conductions are modeled with the assumption of the flux-limited diffusion with classical conductivities. The flux-limiter was set to be 0.1 in the present simulation. In our code two-temperatures for electrons and ions are adopted with the relaxation term because they must be in thermally non-equilibrium in a corona. The laser absorption of inverse-bremsstrahlung is calculated by the ray-tracing manner including the refraction due to the electron density gradient [30].

Fig. 1. Simulation conditions for plasma medium of the second target.

The computations are conducted to investigate the density effect of the plasma medium of the second target in the oscillator-amplifier configuration. Figure 1-(a) shows the simulation area of the second target. The simulation domain with 50 _m long and 150 _m wide is calculated on the center of the target with 301 x 51 computational grids. This number of grids is sufficient for capturing the plasma features. The target material is silver. The laser wavelength is 1.06 _m. Input laser pulses consist of the Gaussian shaped pulses shown in Fig. 1-(b) which are pico-sec prepulse 100-ps prepulse and pico-sec main pulse. The pulse widths are 12 ps 100 ps and 12 ps at FWHM respectively. The pulse energies are 1J, 3 J and 12 J respectively. Since the pedestal of the laser pulse affects the plasma condition [7] we performed the calculation including the pedestal with 1012

338

N. Ohnishi, M. Nishikino and A. Sasaki

W/cm2. The timing of t = 0 ps is the peak of the main pulse. The silver target is irradiated from right hand side of Fig. 1-(b) by the line focused laser whose spatial width is 20 μm (10 μm in the computational domain) at the focal position. In the present study the spatial distribution of the laser intensity is uniform in that width. The laser is divided into 100 computational rays and the rays are parallel to each other without divergence.

3 Results and Discussion Electron temperature is rapidly increased by the main pulse near the critical densisy and exceeds 2 keV in the preformed plasma. Then pressure becomes very high while density gradient is relatively gradual. This leads the formation of a blast wave. The blast wave formation depends on the geometrical condition. Figure 2 shows the typical profiles of electron number density and electron temperature with different dimensions at 50 ps after the main pulse. In 1D (planar) geometry we cannot find the formation of the blast wave. However the propagation of the shock wave towards the corona region and the low density dip (circled region in Fig. 2(b)) can be found with 2D simulation. This density dip may affect on the refraction of the incident x-ray laser from the first target.

Fig. 2. Profiles of electron number density and electron temperature by (a) 1D planar simulation and (b) 2D simulation (in axis of symmetry) at 50 ps after the main pulse.

In order to confirm this density dip effect we have performed 3D raytracing of injected x-ray laser in the variable flowfield along the incident direction. The flowfield felt by the injected rays was constructed with arranging the time series of 2D simulation. Figure 3-(c) shows the contours of electron number density at 50 ps after the main pulse. The rays in the

Numerical Analysis of Plasma Medium of a Fully Coherent X-Ray Laser

339

density dip around X = 20–30 μm and Y = 0–10 μm meander though the dip while the other rays are refracted to the expansion direction. Figure 3-(b) shows the ray positions at the cross section of the second target (6 mm from the incidence). In the present study a gain length for each ray is defined by the light path integrated over the assumed gain region where 1020 < ne < 1021 cm−3 and 0.25 < Te < 1.0 keV. The length for the rays in the density dip can be longer than that for the other rays because that dip is in the condition of the gain region. In this timing the length is about 5 mm. The size of the ray passed through the density dip is about 10 and 20 μm for the horizontal and vertical direction respectively. The non-refracted rays are located at X = 20–30 μm. Figure 3-(a) shows the near-field pattern (NFP) of the second target of the double-target amplified XRL in the case of the gain length of about 6 mm. The NFP was measured using a near-field imaging system with magnification of 8.5[26]. The size and the position of transmitted rays where the non-refracted rays are found are similar to those of intense area of the NFP.

Fig. 3. (a) The NFP of the 6-mm length second target of the double-target amplified XRL. (b) The ray positions in the cross section of the second target at 6 mm from the incidence. (c) The contours of electron number density at 50 ps after the main pulse.

4 Conclusion We have performed 2D radiation hydrodynamics simulations and 3D raytracing for investigating the plasma medium of the fully coherent x-ray

340

N. Ohnishi, M. Nishikino and A. Sasaki

laser. The results suggest that the density dip behind the blast wave near the critical density suppresses the refraction of the injected x-ray laser from the first taget. We are planning the coupling computation with unsteady atomic process for detailed analysis of the fully coherent x-ray laser.

References [1] J. Arthur Rev. Sci. Instrum. 73 1393 (2002). [2] V. Ayvazyan et al. Phys. Rev. Lett. 88 104802 (2002). [3] M. Kalachnikov et al. Phys. Rev. A 57 4778 (1998). [4] A. Klisnick et al. J. Opt. Soc. Am. B 17 1093 (2000). [5] J. Dunn et al. Phys. Rev. Lett. 84 4834 (2000). [6] R. Tommasini J. Nilsen and E. Fill Proc. SPIE 4505 85 (2001). [7] T. Kawachi et al. Phys. Rev. A 66 033815 (2002). [8] S. Sebban et al. Phys. Rev. Lett. 89 253901 (2002). [9] B. M. Luther et al. Opt. Lett. 30 165 (2005). [10]D. L. Matthews et al. Phys. Rev. Lett. 54 110 (1985). [11]C. L. S. Lewis et al. Opt. Commun. 91 71 (1992). [12]R. E. Burge et al. J. Opt. Soc. Am. B 14 2742 (1997). [13]H. Daido et al. J. Opt. Soc. Am. B 16 2295 (1999). [14]G. Cairns et al. Appl. Phys. B 58 51 (1994). [15]R. Kodama et al. Phys. Rev. Lett. 73 3215 (1994). [16]M. Tanaka et al. Opt. Lett. 28 1680 (2003). [17]M. Nishikino et al. Phys. Rev. A 68 061802(R) (2003). [18]M. Nishikino et al. IEEE Journal of Selected topics in quantum electronics 10 1382 (2004). [19]T. Ozaki et al. Phys. Rev. Lett. 89 253902 (2002). [20]P. V. Nickles et al. Phys. Rev. Lett. 78 2748 (1997). [21]J. Dunn et al. Phys. Rev. Lett. 80 2825 (1998). [22]Y. Liu et al. Phys. Rev. A 63 033802 (2001). [23]Ph. Zeitoun et al. Nature 431 426 (2004). [24]T. Kawachi et al. Proc. SPIE 5919 1 (2005). [25]M. Nishikino et al. AIP Conf. Proc. 827 499 (2006). [26]M. Tanaka et al. Surface Rev. Lett. 9 641 (2002). [27]N. Ohnishi et al. J. Quant. Spectrosc. Radiat. Transf. 71 551 (2001). [28]Y. Wada and M. S. Liou AIAA Paper 94-0083 (1994). [30]H. Takabe and T. Nishikawa J. Quant. Spectrosc. Radiat. Transf. 51 379 (1994). [31] A. L. Edwards and J. A. Fleck Jr. J. Appl. Phys. 50 4307 (1979).

Longitudinally Pumped Ne-Like Titanium X-Ray Laser Simulation with a Post-Processor Code Coupled to EHYBRID A. Demir, E. Akman, S. Bilikmen*, P. Demir*, S. İnce*, E. Kacar, E. Yurdanur* and S. Yaltkaya** University of Kocaeli Laser Technologies Research and Application Center Aslanbey Campus Kocaeli / Turkiye * Middle East Technical University Department of Physics Ankara / Turkiye ** Akdeniz University Department of Physics Antalya / Turkiye

Summary. Longitudinal pumping with a grazing incidence scheme of Ne-like Ti has been modeled by using the EHYBRID and a post-processor code. The atomic data that are required in the simulation are obtained by using the Cowan code. The variation of the Ne-like Ti x-ray laser gain at 32.6 nm is calculated for a fixed delay time with a variation in the incidence angle and a fixed incidence angle with a variation in the delay time. The post processor code has been used to simulate the x-ray resonance lines between 17 and 29 Å.

1 Introduction The first x-ray laser was put into practice in the LLNL Novette laser facility in 1984 [1]. In this first demonstration kilo joule scale optical pump energy with a transverse scheme was used to ionize Ne-like Se thin foils and the output wavelength was seen at 20 nm. Since then numerous amount of experiments have been held throughout by using Li-like Ne-like Ni-like targets [2-5] with different pumping schemes [6-9]. Besides these the progress in the area has also been due to the technological improvements achieved in the laser technology. The general aim in these researches has always been to increase the gain efficiency and the repetition rate of the x-ray lasers with a shorter wavelength output and make them compact for their further usage in science and technology. In the grazing incidence pumping scheme a double irradiation is used for lasing output. The first long duration and low intensity transversely

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pumped pulse is used to ionize the target and form a plasma column. After a delay a second higher intensity shorter duration pulse irradiates the plasma column at grazing incidence. The angle of incidence is chosen so that at a preferential electron density the pulse is refracted into the gain region. In this way the beam will pass through the same density region and the absorption and therefore the efficiency will be increased. 2 Method of Calculation

During this study the modelling of Ne-like Ti has been done by using a modified version of the original EHYBRID code [10]. This modification allowed the spontaneous transition rates to be calculated from the absorption oscillator strengths which are used in the evaluation of the ionisation balance. Besides this the line intensities are calculated with a post-processor code that is coupled to EHYBRID by simulating the excited level population densities. The required atomic data are obtained by using the Cowan code [11]. 112 Ne-like 1s22s22p6 - 1s22s22p5 nl and 214 F-like 1s22s22p5 - 1s22s22p4 nl resonance line intensities have been calculated for the simulation of the spectral emission from the titanium plasma. 3 Results and Discussion

In the simulations firstly a 4 mm slab target is irradiated by a pre-pulse of 70 mJ energy and 200 ps pulse duration to form a plasma column. Afterwards a main pulse of 80 mJ energy and 1.2 ps duration has been sent with a grazing incidence for observing x-ray lasing (Fig.1.). The pulses have a 800 nm wavelength. The optimum delay time between the pulses and the incidence angle are searched for.

Fig. 1. Grazing Incidence Pumping Scheme

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The variation of the gain of the 32.6 nm Ne-like Ti laser line as a function of the incidence angle of the main pulse to the normal of the target surface for a 500 ps delay time is shown in Fig.2. Maximum gain is obtained around 10o of incidence angle. 32.6 nm Ne-like Ti Lasing Line

50

-1

Gain( cm )

40

30

20

10

0 0

10

20

30

40

50

60

70

80

90

Incidence Angle

Fig. 2. Variation of the gain of the 32.6 nm Ne-like Ti laser line as a function of the incidence angle of the main pulse to the normal of the target surface. Data was obtained using a 70 mJ 200 ps duration pre-pulse followed by an 80 mJ 1.2 ps duration grazing incidence short pulse separated by a 500 ps time delay.

Simulation is performed to determine optimum delay time between the two pulses. Pre heating pulse has 70 mJ energy and 200 ps pulse duration in the simulation. The main pulse has 1.2 ps pulse duration and 80 mJ of energy. Fig.3. shows the variation of the gain as a function of the time delay with a grazing incidence angle of 10o. 70 32.6 nm Ne-like Ti Lasing Line 60

Gain (cm-1)

50

40

30

20

10

0 200

250

300

350

400

450

500

550

600

650

700

Delay Time (ps)

Fig. 3. Variation of the gain of the 32.6 nm Ne-like Ti laser beam as a function of the delay time between the two pulses. Data was obtained using a 70 mJ 200 ps duration pre-pulse followed by a 80 mJ 1.2 ps duration grazing incidence shot at 10o to the normal.

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Fig.4. shows the simulated time integrated Ne-like and F-like Ti resonance line spectrum for total pulse energy of 150 mJ. The Ne-like resonance lines are more intense than the F-like resonance lines. Ne-like 3d-2p

3.0E+15

Ne-like 3s-2p

F-like 3s-2p

F-like 3s-2p

1.0E+15

F-like 4s-2p

Ne-like 4s-2p

2.0E+15

F-like 3d-2p

Intensity (photons/Å)

4.0E+15

0.0E+00 17

19

21

23 Wavelength Å

25

27

29

Fig. 4. The time integrated Ne-like and F-like resonance line spectrum emitted from Ti plasma.

Fig.5. shows the Ne-like plus F-like resonance line intensity and gain of the Ne-like Ti lasing lines at 32.6 nm as a function of time. The FWHM of the gain is ~64 ps for 32.6 nm. 45

1.4E+22

40

1.2E+22

30 8.0E+21

25

6.0E+21

20

Gain (cm-1)

Intensity (photons/Å)

35 1.0E+22

15 4.0E+21 10 2.0E+21

0.0E+00 710

Ne-like and F-like Resonance Line 32.6 nm Gain Line

720

730

740

750

760 770 Time (ps)

780

790

800

5 0 810

Fig. 5. Variation of the gain and the intensity of the 32.6 nm Ne-like Ti laser beam as a function of time. Data was obtained using a 70 mJ 200 ps duration prepulse followed by a 80 mJ 1.2 ps duration grazing incidence shot at 10o to the normal. The time delay between the two pulses is 500 ps.

Longitudinally Pumped Ne-Like Titanium X-Ray Laser Simulation

345

Ti(I) 3d 4s4p-3d 4s5s

3

2

430

480

530 580 Wavelength (nm)

Ti(III) 3p 3d5d-3p 3d5f

6

6

630

6

6

3

750

0 380

Ti(III) 3p 3d5s-3p 3d5p

3

Ti(I) 3d 4p-3d 4d

3

Ti(I) 3d 4s4p-3d 4s5s

2

3

3

Ti(I) 3d 4s-3d 4p

2 2 2 3

3

1500

Ti(I) 3d 4s -3d 4s4p

6 6

Ti(II) 3d -3d 4p

6

2250

6

Intensity (Au)

3000

Ti(III) 3p 3d4f-3p 3d5g 3 3 + Ti(I) 3d 4s-3d 4p

6

3750

Ti(III) 3p 3d5p-3p 3d5d 3 3 + Ti(I) 3d 4s-3d 4p

6

4500

Ti(II) + Ti (III) 3p 3d4f-3p 3d5g 3 3 + Ti(I) 3d 4s-3d 4p

Fig.6. shows the visible line spectrum emitted from Titanium preplasma created using pre-pulse laser conditions. The energy of the laser pulse is 200 mJ and the pulse duration is approximately 6 ns. The pre-pulse has created low ionized plasma and the main pulse interacts with the preformed plasma to create lasing action. The focus width is 100 μm.

680

730

Fig. 6. Experimentally observed visible spectrum of Titanium under pre-pulse condition.

4 Conclusions

During the simulations firstly the optimum incidence angle corresponding to the irradiation of a Ti target with a 70 mJ 200 ps pre-pulse which is followed by a 80 mJ 1.2 ps main pulse after 500 ps of time delay has been investigated and the optimum incidence angle is found at 10o. The pulses have an 800 nm wavelength. After this at 10o the optimum time delay is searched between 200-700 ps for the data given above and it is seen that 500 ps is near to the optimum case. The FWHM of the gain and the resonance lines between 17 and 29 Å for these optimum cases have been investigated.

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Acknowledgements This project has been supported by DPT under the contract number K120710.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

Matthews D.L. et al.: Phys. Rev. Let. 54 110 1985 Nickles P.V. et al.: Phys. Rev. Let. 78 2748 1997 Zhang J. et al.: Phys. Rev. A 53 3640 1996 Zhang J. et al.: Phys. Rev. Let. 78 3857 1997 Zhizhan Xu et al.: App. Phys. Let. 63 1023 1993 Kolacek K.: Proc. National Laser Symposium Indore India 2001 Sebban S. et al.: Phys. Rev. Let. 86 3004 2001 Ruxin Li et al.: Phys. Rev. E 57 7093 1998 Keenan R. et al. : Phys. Rev. Let. 94 103901-1 2005 Pert G.: J. Fluid. Mech. 131 401 1983 Cowan R.D.: J. Opt. Soc. Am. 58 808 1968

Simulation of Longitudinally Pumped Ni-Like Molybdenum X-Ray Laser Medium Using PostProcessor Code Coupled to EHYBRID E. Kacar, P. Demir, P. Demir*, A. Demir and S. Yaltkaya** Laser Technologies Research and Application Center University of Kocaeli Aslanbey Campus Kocaeli / TURKEY * Department of Physics METU Ankara/TURKEY ** Department of Physics University of Akdeniz Antalya/TURKEY

Summary. Longitudinally pumped Ni-like Mo x-ray laser media is modeled using EHYBRID and a post-processor code. The required atomic data are obtained using the Cowan code. In this study the pre-formed plasma is pumped on longitudinal direction with a grazing angle. Variation of the x-ray laser gain of the 18.9 nm and 18.2 nm Ni-like Mo lines according to the incidence angle of the main heating pulse normal to the target surface is calculated for different main pulse energies. X-ray resonance lines between 26 and 37 Å emitted from molybdenum plasma have been simulated using post-processor coupled with EHYBRID.

1 Introduction A longitudinal Ni-like Mo x-ray laser at 18.9 nm was proposed in 1998 [1] and it was demonstrated by using a short pulse which pumps the inversion along a pre-formed plasma column [2-5]. The pump energy required to produce a saturated Ni-like Mo x-ray laser can be reduced by pumping preplasma column from a longitudinal direction. An 18.9 nm Ni-like Mo x-ray laser operating close to saturation at 10 Hz repetition rate have been reported to be produced by pumping with 14° grazing incidence angle and 150 mJ of total pumping energy [3]. A plasma column is preformed by irradiating a slab target transversely with a long pulse. Then the short pulse is sent with a grazing angle to the target surface through the laser-produced plasma after a delay and refracted back into the gain region from a predetermined electron density. Refraction of the short pulse in the plasma depends on the incidence angle of the short pulse relative to the target surface. Path length and absorption of the short pulse is increased by

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refraction [3]. In experimental investigations dependencies of the longitudinally pumped Ni-like Mo x-ray laser intensity on parameters such as delay time heating pulses’ energy ratio intensity of the main pulse have been observed and the optimal conditions have been obtained [6]. In this paper longitudinally pumped Ni-like Mo x-ray laser is modelled by using EHYBRID code [7]. The modelling was performed for different parameters such as delay time between pulses heating pulses’ energy incidence angle of the main pulse.

2 Method of Grazing Incidence Pumping Simulations Longitudinally pumped Ni-like Mo x-ray laser is modelled using EHYBRID code [7]. Line intensities are calculated in a post-processor coupled with the EHYBRID using the simulated excited level population densities. The orginal EHYBRID code was modified to calculate the spontaneous transition rates from the absorption oscillator strengths used in the evaluation of the ionisation balance. The required atomic data are obtained using the Cowan code [8]. 128 Ni-like 1s22s22p63s23p63d10 1s22s22p63s23p63d9 nl and 230 Co-like 1s22s22p63s23p63d9 1s22s22p63s23p63d8 nl resonance line intensities have been calculated for the simulation of the spectral emission from the molibdenium plasma. In our simulations laser pulses of 0.8 µm wavelength focused on 4 mm target have been simulated. Molibdenium has been pumped with a prepulse and a short pulse. The pre-pulse has 70 mJ energy and 200 ps pulse duration and the following short pulse has 80 mJ energy and 1.2 ps pulse duration. The pre-pulse and the main pulse are separetad by 300 ps.

3 Results and Discussion

A plasma column is preformed by irradiating a slab target transversely with a long pulse. Then the short pulse is sent with a grazing angle to the target surface through the laser-produced plasma after a delay and refracted back into the gain region from a predetermined electron density. Refraction of the short pulse in the plasma depends on the incidence angle of the short pulse relative to the target surface. Variation of the gain of the 18.9 nm and 18.2 nm Ni-like Mo laser lines as a function of the incidence angle of the main heating pulse normal to the target surface is shown in Fig. 1. Maximum gain is obtained around 20° of incidence angle. And also

Simulation of Longitudinally Pumped Ni-Like Molybdenum X-Ray Laser

349

Fig. 1 shows the plasma gain widths for each incidence angle of the main pulse . Gain for 18.9 nm Gain for 18.2 nm

400

Gain width

10

350

-1

Gain (cm )

250 6 200 4

150

Gain width (µm)

8

300

100 2 50 0

0 0

10

20

30

40

50

60

70

80

Incidence Angle

Fig. 1. Variation of the gain of the 18.9 nm and 18.2 nm Ni-like Mo laser lines as a function of the incidence angle of the main heating pulse normal to the target surface. Data was obtained using a 70 mJ 200 ps duration prepulse followed by a 80 mJ 1.2 ps duration grazing incidence short pulse separated by a 300 ps.

90 -1

18.2 nm 18.9 nm

350

80

300 70 250

60

200

50 40

150

30 100 20 50

10

0

Gain of 18.9 mn Ni-like Mo line (cm )

-1

Gain of 18.2 mn Ni-like Mo line (cm )

Simulation is performed to determine optimum energy level of pumping in the range of 18.9 nm and 18.2 nm. Pre heating pulse has 70 mJ energy and 200 ps pulse duration in the simulation. Delay time between the pre-pulse and the short pulse is 300 ps and the main pulse duration is 1.2ps. Fig. 2. shows the variation of gain as a function of the main pulse energy at 20° of incidence angle.

0 0

30

60

90

120

150

180

210

240

Main pulse energy (mJ)

Fig. 2. Variation of the gain of the 18.9 nm and 18.2 nm Ni-like Mo laser beam as a function of the main heating pulse energy at 20o of incidence angle. Data was obtained using a 70 mJ 200 ps duration prepulse followed by a 1.2 ps duration grazing incidence short pulse separated by a 300 ps.

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Fig. 3. shows the simulated time-integrated Ni-like and Co-like Mo resonance line spectrum for total pulse energy 150 mJ. The Co-like resonance lines are more intense than the Ni-like resonance lines. Co-like 4f - 3d

5.0E+15

Ni-like 4p - 3d

Ni-like 4f - 3d

Ni-like 5f - 3d

1.0E+16

Co-like 4p - 3d

1.5E+16 Co-like 5f - 3d

Intensity (photons/Å)

2.0E+16

0.0E+00 26

28

30

32

34

36

38

Wavelength (Å)

Fig. 3. The time integrated Ni-like and Co-like resonance line spectrum emitted from Mo plasma.

Fig.4. shows the Ni-like plus Co-like resonance line intensity and gain coefficient of the Ni-like Mo lasing lines at 18.9 nm and 18.2 nm as a function of time from the start of the short pulse interaction time. The FWHM of the gain coefficient duration is ∼ 23 ps for 18.9 nm and for 18.2 nm. Ni-like and Co like resonance line

4.0E+19

300

18.9 nm Gain line 250

200 -1

Gain (cm )

Intensity (photons/Å)

18.2 nm Gain line 3.0E+19

150

2.0E+19

100 1.0E+19 50

0.0E+00 495

0 515

535

555

575

595

Time (ps)

Fig. 4. The time variation of the resonance lines for Ni-like plus Co-like lasing lines and gain coefficient for 18.9 nm and 18.2 nm Ni-like Mo lasing lines.

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351

4 Conclusion Longidutinally pumped Ni-like Mo x-ray laser medium is modelled to determine optimum grazing incidence angle of the main heating pulse normal to the target surface and optimum main heating pulse energy. Optimum grazing incidence angle of the main pulse is found around ∼ 20° under the explained simulation conditions in the text. X-ray laser output at 18.2 nm and 18.9 nm and intensity of resonance lines between 26 Å and 37 Å emitted from molibdenium plasma has been simulated using the EHYBRID. Acknowledgements

This project is supported by DPT under the contract number K120710.

References 1. 2. 3. 4. 5.

Li R. et al. Phys.Rev.A 66 047402 2002. Ozaki T. et al. Phys.Rev.A 66 047402 2002. Keenan R.et al. Phys.Rev.Lett. 94 103901 2005. Tümmler J. et al. Phys.Rev.E 72 037401 2005. Larotondo M.A. et al. IEEE J. of Selected Topics in Quant. Electronics 10 6 1363 2006. 6. Kuroda H. et al. 29th EPS Conf. On Plasma Phys. And Contr.Fusion Monterux ECA 26B D-5.005 2002. 7. Pert G.J. Fluid. Mech. 131 401 1983. 8. Cowan R.D. J.Opt.Soc.Am. 58 808 1968

X-Ray Laser at 10–15 nm in Pd-like Ions Er XXIII – Re XXX. E.P. Ivanova, A.L. Ivanov and T.E. Pakhomova Institute of Spectroscopy of Russian Academy of Sciences

Summary. The intensive output radiation at 10-15 nm is possible by the use of the Pd-like scheme of X-ray laser. We have performed the calculations of spectroscopic constants kinetics of level populations in plasmas and gains for eight Pd-like ions ErXXIII – ReXXX. The laser action proved to be efficient at the optically self-pumping transition 4d95f 1P1 – 4d95d 1D1 and at the conventional transition 4d95d 1S0 – 4d95p 3P1. The optimum plasma parameters for lasing and time evolution of gain are calculated. The experimental scheme is implied which use an ultra-short laser pulse pumping.

1 Introduction. The first observations of the Pd-like X-ray laser [1-2] have proved that it is most efficient in compare with the Ne-like either Ni-like schemes. The first reason: the ionization of the electron shells with n=6 occurs at relatively smaller electron energy; thus smaller energy of pumping source is necessary. The second: the optimal electron density (ne=neopt) for X-ray lasing is relatively smaller (ne ~3·1018 - 4·1020 cm-3 for Pd-like ions with Z=54 - 75); hence the recombination and bremstraulung radiation plasma losses are negligible. In [3] we have interpreted the results of experiments [1-2] and suggested the improvements for the pumping and target parameters in order to increase the X-ray radiation yield. During last decade the spectra of Pd-like ions with Z = 52-60 were carefully analyzed (see [4] and references herein) however the spectroscopic data for the heavy ions (Z > 65) are known from the only work [5]. Recently in several independent experiments investigating the interaction between the optical field of intense laser pulse and a xenon cluster beam an anomalously high quantum yield in the plasma radiation in the range 10-15 nm was recorded [6-7]. In our work [8] the nature of this phenomenon was interpreted high conversion efficiency is shown to be possible when producing plasma with optimum parameters for the

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amplification of spontaneous radiation on the definite transitions in Xe XXVII. At present nanowires grow by electro-deposition using nonporous template have attracted much attention due to the simplicity of this technique for preparing nano-scaled materials. For instance a standard way to fabricate lead or tin nanowires arrays is suggested in [9]. The production of nanowires arrays of other heavy elements is quite possible. In the present work we imply the experimental scheme similar to that described in [6-7] but nanowires (or dust) array of heavy element (Z = 68-75) is used instead of Xe clusters. Recently the method of relativistic perturbation theory with model potential of zero approximation (RPTMP) was used for the calculation of energy levels of Ag- Rh- and Pd- like ions with Z≤86 [10]. The results of [10] are used here for the calculation of the spectroscopic constants and gains of the Pd-like ions Er XXIII – Re XXX. Optimal plasma parameters for the X-ray lasing at 10-15 nm are determined. The method of gain calculation may be found elsewhere ([8] see the references herein).

2. X-ray laser in Pd-like ions. There are two principal X-ray laser transitions in Pd-like ions; i) 4d3/25d3/2 [J=0]–4d3/25p1/2 [J=1] (5d-5p 0-1); the amplification of this line emission was observed in [1-2]; ii) 4d3/25f5/2 [J=1] – 4d3/25d3/2 [J=0] (5f–5d 1-1). The amplification on the 5f-5d 1-1 optically self-pumping transition is weak in the light Pd-like ions and was not observed experimentally yet. However the amplification grows significantly along the sequence. The kinetics of level population is calculated here with the following assumptions: i) Plasma is produced in the shape of cylinder with diameter d = 100 μm and length L. ii) The pumping pulse parameters are such that plasma with initial temperature Te (at the moment τ = 0) in which the Pdlike ions constitute 90% of the plasma and are in the ground state is produced immediately after the interaction of the optical field laser with array of nanowires or dust). iii) Plasma parameters: electron density (ne) temperature (Te) and diameter (d) are not varying with time. iv) The electron and ion energy distribution are Maxwellian and the shape of the distribution plays no significant role in calculating the rates of the transitions induced by electron-ion collisions. v) The ion temperature Ti = Te/10. For each ion Er XXIII – Re XXX we calculate the gain g(neTed|τ) with unchanged d = 100 μm. For each transition at given Te the optimal value

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X-Ray Laser at 10–15 nm in Pd-like Ions Er XXIII – Re XXX.

355

ne= neopt is determined by the condition that the time averaged ĝ = g(neoptTed|τ) is maximum value. Figure 1 shows the time dependences of the gains for the 5d-5p 0-1 (a λ = 107.8 Å) and 5f-5d 1-1 (b λ = 139.5Å) transitions in W XXIX. The decay of the gain of the 5d-5p 0-1 transition is conditioned predominantly by ionization of the W XXIX into higher stages while the decay for 5f-5d 1-1 transition is due to collisional mixing of level populations ⎯ as a result the gain disappears on a shorter time interval than it does on the 5d-5p 0-1 transition. The gain is presented for three values of Te and ne = 1020 cm-1 for the 5d-5p 0-1 transition (Fig.1a) ne = 3·1020 cm-3 for the 5f-5d 1-1 transition (Fig.1b). 120

100

a) g (cm-

80

60 40

20 0 0.01

0.1

1

τ

10

100

1

τ

10

100

300

b) g (cm250 200

150 100

50 0 0,01

0,1

Fig. 1. Time evolution of the gain (g) in W XXIX for two transitions at Te = 0.5 (open circles) 1 (black circles) 1.5 (triangles) keV; d = 100 μm; a) 5d-5p 0-1 transition (λ = 10.78 nm); ne = 1020 cm-3; b) 5f-5d 1-1 transition (λ = 13.95 nm) ne = 3·1020 cm-3.

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E.P. Ivanova, A.L. Ivanov and T.E. Pakhomova

a)

b)

λ [Å] Fig. 2. Model W XXIX spectra calculated with accounting for theamplification at Te=1.5 keV d=100 μm λ = 100 Å - 160 Å a) ne = 1020 cm-3 L=0.4 cm b) ne = 3·1020 cm-3 L=0.15 cm.

The model spectra in the region 10 – 16 nm with accounting for the amplification are shown in Fig.2 ab. One can see also the second strong 5d-5p 0-1 laser transition at 12.08 nm and the second strong 5f-5d 1-1 transition at 14.48 nm. We used the time-averaged values of g(τ)=ĝ to compute the spectra. In Fig.2 the plasma length L corresponds to the saturation of the amplification. At relatively low Te≤ 700 eV amplification saturation is conditioned by the time duration of lasing. At high Te ≥ 1000 eV time-averaged ĝ is more than 100 cm-1 in this case the saturation is

X-Ray Laser at 10–15 nm in Pd-like Ions Er XXIII – Re XXX.

357

caused by too high inversion value. In this case Lsat determination should be based on the model that accounts for the interaction between X-ray laser field and Pd-like ions. Table 1. Characteristics of X-ray laser on the transition 5d-5p 0-1 in the Pd-like ions.

Z λ [nm] Aul· 1010 Al0· 1011 neopt 1019 R· 10-10 Δν· 1012 I0· 1029 g0 cm-1

68

69

70

71

72

73

74

75

14.61

13.84

13.15

12.49

11.88

11.32

10.78

10.29

4.70

5.52

6.44

7.45

8.57

9.80

11.2

12.7

2.69

3.30

3.94

4.65

5.44

6.31

7.26

8.29

4.0

4.0

5.0

5.0

6.0

6.0

7.0

7.0

9.18

8.75

8.00

7.09

6.56

6.06

5.65

5.02

1.4

1.4

1.4

2.2

1.7

2.0

2.1

2.3

0.8

0.9

1.0

1.2

1.7

2.0

2.6

2.1

32.0

30.4

40.1

17.4

42.9

35.9

44.4

24.6

To make an estimate of Lsat the condition ĝ·Lsat ≈ 15-16 might be used. The results of spectroscopic constants and gain calculations for Er XXIII – Re XXX are summarized in the Tables 1 and Tables 2. For all Pd-like ions the calculations have been performed with the same values Te = 1000 eV d = 100 μm. In the table 1 time-averaging for g(τ) I0(τ) is performed on the interval 0 - 21 ps in the table 2 - on the interval 0 – 5.2 ps. One can see that radiative and collisional transition probabilities as well as time averaged emissive power I0 change gradually along this piece of the sequence. However ĝ value exhibits abrupt jumps along Z what is meant by the inversion sensitivity to a mixing of level populations due to the multitude of transitions induced by electron collision.

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Table 2. Characteristics of X-ray laser on the transition with a short-lived inversion 5f-5d 1-1 in Pd-like ions.

Z λ [nm] Aul · 1010 Au0· 1012 neopt 1020 R· 10-11 Δν· 1012 I0· 1030 Ĝ cm-1

68

69

70

71

72

73

74

75

17.64

16.92

16.24

15.61

15.02

14.47

13.95

13.47

7.41

7.92

8.43

8.96

9.50

1.00

1.06

1.12

1.06

1.33

1.64

2.00

2.39

2.83

3.31

3.85

1.4

1.8

2.2

2.6

3.0

3.2

3.6

3.9

2.74

2.71

2.68

2.63

2.57

2.56

2.57

2.28

2.2

2.8

3.1

3.7

3.4

4.1

3.8

5.2

0.3

0.4

0.5

0.5

0.7

0.9

1.0

1.1

186.0

120.8

115.9

76.9

116.3

104.9

125.3

68.5

Note: Wavelengths λ (nm) radiative transition probabilities (RTP) from upper to low active level Aul(s-1). RTP from the low active level 4d3/25p1/2 [J=1] to the ground level Al0(s-1) RTP from the upper active level 4d3/25f5/2 to the ground level Au0(s-1). The rates of level excitation by electron collision from the ground state per unit volume R(cm--3s-1) the Voight line width Δν(s-1) the time-averaged transition emissive power (without accounting for an amplification) I0(eV/cm3s) and the time-averaged gain ĝ (cm--1) were calculated at ne=neopt Te=1000 eV d=100μm.

3. Conclusion This investigation allows drawing the following principal conclusions: a. In all ions ĝL ≥ 14 is possible at Te ≥ 800 eV. b. The time it takes for the gain decay (τlas) reduces at larger ne.τlas = 30 – 60 ps for the 5d-5p 0-1 transition; τlas = 6 – 10 ps for the 5f – 5d 1-1 transition. In each ion the value neopt for the transition 5d-5p 0-1 is few times smaller than for the optically self-pumping transition 5f-5d 1-1. c. Amplifications on the 5f-5d 1-1 transitions with a short-lived inversion are possible only with the use of an high intensity ultra

X-Ray Laser at 10–15 nm in Pd-like Ions Er XXIII – Re XXX.

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short laser pulse pumping. Amplifications on the 5d-5p0-1 transitions are possible with either ultra short or long lasting laser pulse pumping. This investigation confirmed beyond any reasonable doubt that the Pd-like X-ray laser scheme is promising to attain the most efficiency as compared to the Ne-like either Ni-like scheme. The other models of an X-ray laser derived from the Pd-like scheme are under development.

References 1. Lemoff B.E. Barty C.P.J. Harris S.E.: Opt. Let. 19 569-572 1994. 2. Sebban S. et.al. : Phys. Rev. Lett. 86 3004-3007 2001. 3. Ivanova E.P. Ivanov A.L.: ‘Theoretical search for optimal pump parameters for observing spontaneous radiation amplification on the λ=41.8 nm transition of Xe IX in plasma’ Quantum Electronics 34 1013-1017 2004. 4. Churilov S.S. et al: ‘Analysis of the spectra of Pd-like Praseodymium and Neodymium’ Physica Scripta 71 589-598 2005. 5. Sugar J. Kaufman V. Rowan W.: ‘Observation of Pd-like resonance lines through Pt32+ and Zn-like resonance lines of Er38+ and Hf42+’ J. Opt. Soc. Am. 10 799-801 1993. 6. Ter-Avetisyan S. Schnürer M. Stiel H. et.al. ‘Absolute extreme ultraviolet yield from femtosecond-laser excited Xe clusters’ Phys. Rev. E 64 0364041-8 2001. 7. Mori M. et. al. ‘Extreme ultraviolet emission from Xe clusters excited by high- intensity lasers’ J. Applied Physics 60 3595-3601 2001. 8. Ivanova E.P. Ivanov A.L. ‘A Superpower Source of Far-Ultraviolet Monochromatic Radiation’ J. Exp. Theor. Phys. 100 844-856 2005. 9. Michotte S. ‘Standard manufacture and properties of arrays of Pb and Sn nanowires’ Int. J. of Modern Physics B 17 4601-4618 2003. 10. Ivanova E.P. ‘Energy levels of the ions of the isoelectronic sequences Silver and Rhodium’ Optics and Spectroscopy (Russian)

Temporal Characterization of Attosecond Harmonic Pulses C. H. Nam and K. T. Kim Department of Physics and Coherent X-ray Research Center, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 305-701, Korea

Summary. Techniques to characterize attosecond harmonic pulses based on the cross-correlation between harmonic and IR laser pulses are presented. The selfcompression of an attosecond harmonic pulse in the harmonic generation itself has been demonstrated, obtaining near transform-limited attosecond harmonic pulses.

1. Introduction High harmonic x-ray sources possess unique features suitable for attosecond physics and science [1,2]. High harmonics from atoms driven by intense femtosecond laser pulse can form an attosecond pulse train or a single attosecond pulse when properly controlled and selected. For proper understanding of the interactions between attosecond pulses with matter, the temporal structure of attosecond pulses should first be well characterized. Since efficient nonlinear material for two photon processes is difficult to realize in the xuv wavelength region, autocorrelation techniques, normally used for the characterization of femtosecond pulses, can be applied only to limited cases of low-order harmonic pulses. Cross correlation techniques based on the photoionization of atoms by high harmonic and femtosecond laser pulses, acting simultaneously, are thus useful for the characterization of attosecond pulses. As a realization of the cross correlation technique, the reconstruction of attosecond beating by interference of two-photon transition (RABITT) method was demonstrated by Paul et al. [3]. An attosecond pulse train with 250-as duration was measured, and attosecond intrinsic chirp structure was revealed as theoretically predicted [4,5]. For complete characterization of attosecond pulses, the frequency resolved optical gating method for the complete reconstruction of attosecond bursts (FROG CRAB) was proposed by Mairesse et al. [6]. The demon-

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stration of FROG-CRAB would provide the detailed temporal structure of attosecond harmonic pulses. Here we present techniques to characterize attosecond harmonic pulses, especially the FROG-CRAB method, and the self-compression of an attosecond harmonic pulse to generate near transform-limited attosecond harmonic pulses.

2. Temporal characterization of attosecond harmonic pulses Attosecond pulses obtained from high harmonic generation contain a complex chirp structure. In single atom calculations, each single pulse in an attosecond pulse train is positively chirped [5], while each harmonic is negatively chirped [7]. For rigorous temporal characterization of such complex attosecond harmonic pulses, one needs to precisely determine the spectral phase and amplitude of the attosecond pulses. In the RABITT method, photoionization of atoms by attosecond harmonic pulse and IR laser pulse is used for the temporal reconstruction of the attosecond pulse. The photoelectron spectrum shows sidebands due to the interference between photoelectrons with same energy but generated through different two-photon transitions. The sideband is modulated as the time delay between the harmonic and IR probe pulses changes. The phase information of the attosecond pulses can then be found in the side band modulation as A cos ( 2ω0τ + Δϕq ) .

Here, A is the amplitude of the modulation, ω0 is the laser frequency, τ is the time delay between harmonic and laser pulses, and Δϕ0 is the phase difference between (q+1)th and (q-1)th harmonics. The spectral amplitude can be obtained from the photoelectron spectrum obtained only with the harmonic pulse. The reconstruction of the attosecond harmonic pulse is possible from those phase and amplitude information. However, this technique has some drawbacks because the attosecond harmonic pulses are assumed to be the sum of the discrete harmonics, separated by 2ω0. It cannot be used for the reconstruction of a single attosecond pulse having continuum spectrum. Furthermore, the reconstruction result is always an attosecond train with identical individual pulses which is the average of the real pulse train. The chirp information on individual pulses is not available. The FROG CRAB method can provide the complete information on attosecond pulses. In this technique, the photoelectron spectra obtained with harmonic and laser pulses with time delay τ can be represented by

Temporal Characterization of Attosecond Harmonic Pulses S ( ω ,τ ) =

∫

+∞

−∞

2

dt G ( t ) E X ( t − τ ) eiωt .

363

(1)

Here E X ( t ) is the harmonic electric field to be measured and G(t) is the phase gate function defined by +∞ G ( t ) = exp ⎡i ∫ dt ′ { v ⋅ A ( t ′ ) + A 2 ( t ′ ) / 2}⎤ , ⎣⎢ t ⎦⎥

(2)

where v is electron velocity and A(t) is the vector potential of IR laser pulse. Since Eq. (1) is the spectrogram expressed in frequency and time delay, a conventional FROG inversion algorithm, such as the principal component generalized projection algorithm (PCGPA), may be used to reconstruct the attosecond harmonic pulse [6]. However, slight modification is necessary to overcome the problem that the gate function does not have same values at both ends. Consequently, one can retrieve the harmonic electric field containing the detailed information of the attosecond harmonic pulse.

3. Experiment setup The schematic of the experimental setup is shown in Fig. 1. A 1-kHz Ti:sapphire laser, generating pulses of 30-fs duration, was used to obtain high harmonics. The laser beam was split into two parts by a beam splitter; the first beam was focused into a gas cell for high harmonic generation. The second beam was used as a probe laser beam. After harmonic generation, the transmitted laser beam was blocked by a 200-nm aluminum filter

Fig. 1. Schematics of the experiment setup.

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to completely eliminate the laser light. The harmonic and the probe beams were combined using a mirror having a hole in the center, and both beams were then focused together, using a gold-coated toroidal mirror, into an effusive atomic beam and generated photoelectrons were measured with a time-of-flight photoelectron spectrometer.

4. Results

Intensity (arb. units)

First, applying the RABITT technique, we achieved the generation of selfcompressed attosecond harmonic pulses. A 30-fs laser pulse with intensity of 2.5×1014 W/cm2 was applied to an argon gas cell with length of 12 mm. Photoelectron spectra were obtained for harmonics from 17th to 41st orders. As the argon pressure was increased from 15 torr to 40 torr, the harmonics below 25th order were severely absorbed, and the intrinsic positive chirp was compensated by the negative group delay dispersion of argon itself. The reconstructed temporal profile of the attosecond harmonic pulse is shown in Fig. 2. The measured pulse width of 206 as is slightly longer than the transform-limited width of 200 as. 1.0 0.8 0.6 0.4 0.2 0.0 -600

-400

-200

0

200

Time (as)

400

600

Fig. 2. Self-compressed attosecond harmonic pulse measured using RABITT.

Second, FROG CRAB measurements were carried out using the same experiment setup, but with different harmonic conditions due to the poor energy resolution of the spectrometer at high photoelectron energy. Attosecond harmonic pulses, consisting of harmonics up to 31st order, were generated with a 6-mm-long 25-torr argon gas cell. Photoelectron spectra obtained by changing the time delay between the harmonic and IR laser pulses is shown in Fig. 3 (a). The temporal reconstruction of the harmonic pulses was carried out using a modified principal component generalized

Temporal Characterization of Attosecond Harmonic Pulses

365

a)

b) Fig. 3. (a) Photoelectron spectra obtained by applying harmonic pulse with IR laser pulse with time delay. (b) Temporal profile of an attosecond harmonic pulse reconstructed using the FROG CRAB technique.

projections algorithm (PCGPA). Figure 3(b) shows the temporal reconstruction of the attosecond harmonic pulse. The envelope width of the pulse train is 11 fs and the width of the single attosecond pulse at the center of the train is 230 as. In this case, the intrinsic attosecond chirp at the center of the train and the harmonic chirp of the 17th order are estimated to be 1.4×10-32 s2 and -2.3×10-28 s2, respectively. Since the modified PCGPA

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is a blind FROG technique, the FROG CRAB measurement provides the information on both harmonic pulse and laser pulse.

5. Conclusion We have demonstrated the temporal characterization of attosecond harmonic pulses using both RABITT and FROG CRAB techniques. The 206as self-compressed attosecond pulses was reconstructed using RABITT. And the FROG CRAB technique has been applied for the complete reconstruction of attosecond harmonic pulses, obtaining an attosecond pulse train of 11-fs envelope width and 230-as width at the pulse peak.

References [1] M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, Nature 414, 509 (2001). [2] M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, F. Krausz, Nature 419, 803 (2002). [3] P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, Ph. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001). [4] Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovacev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, Science 302, 1540 (2003). [5] K. T. Kim, C. M. Kim, M.–G. Baik, G. Umesh, and C. H. Nam, Phys. Rev. A 69, 051805(R) (2004). [6] Y. Mairesse and F. Quéré, Phys. Rev. A 71, 011401(R) (2005) [7] J.-H. Kim and C. H. Nam, Phys. Rev. A 65, 033801 (2002).

Nonlinear Interaction of Intense Attosecond XUV Pulses with Atoms and Molecules K. Midorikawa, T. Shimizu and Y. Nabekawa Laser Technology Laboratory, RIKEN

Summary. We have observed nonlinear optical processes such as two-photon double ionization and above threshold ionization of rare gases in the xuv region with intense high-order harmonics. Using two-photon double ionization in He, the pulse width of the 27th (42 eV) harmonic was measured by an autocorrelation technique, and found it to be 8 ns. A train of attosecond pulses was also characterized directly by the energy-resolved autocorrelation of the above threshold ionized electrons.

1 Introduction The progress of chirped pulse amplification and femtosecond Ti:sapphire laser enables the study of the interaction of strong optical fields with atoms and molecules. A variety of interesting phenomena, including highharmonic generation, high energy radiation/particles emission, and Coulomb explosion of molecules, have been investigated intensively. The underlying physics of these extremely nonlinear optical phenomena have been explored through the interaction with low-frequency radiations such as infrared or visible light; however, little has been understood concerning the interaction of intense high-frequency radiation. Great interest has been aroused recently in the interaction of intense high-frequency radiation with matters. Yet no one could observe it because of the lack of an intense coherent light source in this spectral region. The induced phenomena are expected to be much different from those caused by low frequency radiation because the electron quiver energy—the cycle averaged electron energy in the optical field—is proportional to a square of the wavelength. In this paper, we report on the generation of intense soft X-ray pulses and its application to nonlinear multiphoton processes. Using such nonlinear processes, the temporal width of the 42-eV soft x-ray pulse was meas-

368

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ured directly by an autocorrelation technique. A train of attosecond pulses was also characterized by frequency-resolved autocorrelation. Intense high harmonics produced by the phase-matching technique enable the observation of these nonlinear optical processes.

2 High-Power High Harmonic Generation For application of high harmonics to nonlinear optics in the XUV region, high focused intensity is crucial because the cross section of nonlinear processes in atoms or molecules tends to decrease rapidly with decrease of the pump wavelength. To increase high harmonic energy by improving conversion efficiency from the pump energy, phase matching is essential. It is, however, not easy to satisfy the phase matching condition along the interaction length, because in contrast to low-order harmonic generation in the perturbative regime, the atomic dipole phase is dependent on the driving laser intensity [1]. This means that the atomic phase varies rapidly around the focus when the pump pulse is tightly focused in the nonlinear medium. Furthermore, in addition to the medium’s dispersion, nonlinear phenomena such as self-focusing and plasma defocusing accompanied by a high-intensity pump pulse also make the experimental achievement of the phase matching quite difficult. Overcoming such difficulties, the energy scaling of high-order harmonics under the phase-matched condition has been achieved using a long interaction length and a loosely focused pumping geometry [2]. This method shows a linear increase in harmonic energy with respect to the geometrical focusing area of the pump pulse, while keeping an almost perfect spatial profile of the harmonic output. Peak powers of 130 MW at 62.3 nm in Xe [3], 10 MW at 29.6 nm in Ar [2], and 1 MW at 13.5 nm in Ne [4] are obtained with femtosecond, high-power Ti:sapphire laser pulses.

3 Focusing Property of High Harmonics Although the advent of high harmonics having excellent beam quality and spatial coherence, together with high output energy, opens up the possibility of focusing XUV beams as intensity sufficient for inducing nonlinear optical processes, a technique for focusing an intense, coherent soft x-ray beam and its characterization should be established before the observation of nonlinear phenomena. Figure 1(a) shows the 1/e2 beam spot size of the 27th harmonic beam as a function of distance from the off-axis parabolic

Nonlinear Interaction of Intense Attosecond XUV Pulses with Atoms

369

mirror. In this measurement, the 27th harmonic wave was selected and focused to a Ce:YAG scintillator by an off-axis parabolic mirror with a SiC/Mg multilayer coating having 40% reflectivity. A set of image relay optics transferred the visible light image onto an image-intensified chargecoupled device (CCD) camera. The red circles and blue squares correspond to the horizontal and vertical spot sizes, respectively. There is little difference between the horizontal and vertical diameters, showing that circularity is maintained during focusing. The best-fit curve provided a figure of M2 = 1.4, indicating nearly perfect spatial beam quality [5]. The focusing property was also investigated by an ablation pattern produced on a gold-coated mirror placed at the focal position. Figure 1(b) shows the atomic force microscope image of the ablation pattern. Note that the pattern was produced by a single shot irradiation of the focused 27th harmonic pulse. The diameter of the circular hole is approximately 2 μm, which agrees well with the scintillator experiment. Because the high-order harmonics have excellent spatial coherence and beam quality, the focusability might be dominated by the performance of the mirror. The focused intensity of the 27th harmonic wave was estimated from those experimental results of the energy, spot size, and pulse width. Assuming that the pulse width of the 27th harmonic wave was the same as the fundamental pulse, the maximum focused intensities of 1.0 x 1014 W/cm2 were obtained. 20 Horiz. Vert. 15 μm

p o

0 .5

10

0 - 0 .5 - 10

5

-5

0

5 μm 60

60.5

0

61

61.5

62

5 1 0 μm

Distance from focusing mirror [mm]

(a)

(b)

Fig. 1. Focusing property of the 27th harmonic pulse: (a) spot size as a function of middor distance and (b) ablation pattern produced on a gold coated mirror surface by a single-shot irradiation.

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4 Two-Photon Double Ionization in He at 42 eV As the first step in investigating the interaction of intense high-frequency radiation with matter, the He atom has been selected as a target. At the very high frequency and low intensity limit, double ionization by single photon absorption has been investigated in detail using synchrotron radiation; this process has been understood as “shake off.” On the other hand, in the low-frequency and high-intensity regime realized by femtosecond high intensity Ti:sapphire lasers, the occurrence of double ionization has also been reported and the process was explained by a rescattering model. Between these two extreme experimental conditions, the occurrence of twophoton double ionization by intense XUV lights was theoretically predicted about 20 years ago. Particularly, two-photon double ionization in He has attracted much interest and has been studied theoretically in a number of papers because it provides insight into the electron-electron interaction (that is, electron correlation) and paves the way for unexplored aspects of the three-body problem [6, 7]. Figure 2(a) shows the ion spectrum produced by the interaction between the focused 27th harmonic pulses and 3 He. The production of 3He2+ results dominantly from the one-photon absorption of 3He. The strongest peak of 1.8 μs can be assigned to 3He2+. The signal of 3He2+ clearly appears between the H+ signal and H2+ signal. The generation of doubly charged He2+ confirms the observation of a nonlinear optical process (two-photon absorption) in the soft x-ray region. To further confirm that the He2+ ions are produced via the two-photon process, the 27th harmonic intensity dependence of the He2+ yield was investigated. As shown in Fig. 2(b), the result clearly showed the slope of two, giving more evidence of the occurrence of the two-photon double ionization. This is the first observation of a nonlinear optical process in the soft x-ray region [8, 9]. The XUV nonlinear optical process is not only interesting in the field of atomic or molecular physics, it is also of importance for the direct measurement of the pulse width by autocorrelation method in the ultrafast optics field. With the two-photon double ionization in He, the pulse duration of the 42-eV soft x-ray pulse was measured by means of autocorrelation. For the autocorrelation measurement, an autocorrelator splits a measured pulse equally into two pulses and spatially overlaps the separated delayed pulses at the focus point. The construction of the autocorrelator for the XUV light is, however, not straightforward because no beam splitter or high reflectance-/transmittance optics are available. Therefore, a novel autocorrelator using a split beam separator was designed [10]. The delayed pair of harmonic pulses is produced by spatially dividing the harmonic

Nonlinear Interaction of Intense Attosecond XUV Pulses with Atoms

371

8 6

3

He2+

(a)

3

H2

H+

He+

+

He2+ yield

4

(b)

2

0.01

8 6

Slope = 2

4 2

0.001 1.0

1.2

1.4

1.6

1.8

2.0

Time of flight ( μs)

2.2

2.4

2

3

4

5 6 7 8 9

1

2

+ He yield Harmonic Intensity

Fig. 2. (a) The time of flight ion spectrum and (b) doubly charged helium ion yield as a function of the 27th harmonic intensity.

beam with two beam separators of SiC substrates. One of the divided pulses is delayed or advanced to another pulse by moving one of the separators placed on a translation stage with a piezo-actuator. The measurement principle using this split beam separator is the same as an allreflective interferometric autocorrelator. With this autocorrelator and twophoton double ionization in He, a pulse width of the 42-eV soft X-ray radiation was measured for the first time and it was determined to be 8 fs [8].

5 Temporal Characterization of XUV Attosecond Pulse Train by Autocorrelation Although the temporal width of the soft X-ray pulse was measured directly by an intensity autocorrelation technique, the pulse width is limited by the bandwidth of the 27th harmonic wave. The narrow bandwidth of a SiC/Mg multilayer mirror has high reflectivity only for the 27th harmonic wavelength. If several harmonics are simultaneously focused with a broadband mirror, a train of extremely short pulses would be observed. As is well known, Fourier synthesis of harmonic wave fields exhibits a train of ultrashort pulses. The pulse width decreases in inverse proportion to the number of harmonics. The optical field in the XUV region generated as high order harmonics of a femtosecond laser pulse is one of the most significant examples of the Fourier synthesis because it can serve an attosecond pulse train. For characterization of an attosecond pulse train, several harmonics should be simultaneously measured and the information of individual harmonic phase should be determined. But the phase information can hardly

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be obtained from ion signals. Therefore, a new method to reconstruct an attosecond pulse train was proposed [11]. This method uses electrons produced by the above threshold ionization (ATI) process, another type of nonlinear mutlitphoton process. In the ATI process, an ejected electron absorbs the photons in excess of the minimum required for ionization. The ejected electrons carry the information of the phase of the XUV pulse used for ionization.

Fig. 3. Mode-resolved autocorrelation trace of two-photon above threshold ionization in Ar and the reconstrcuted train of attosecond pulses.

In the experiment, the electron energy spectra produced by the two-photon ATI process in Ar are utilized as mode-resolved signals of the autocorrelation measurement for the pulse train and its envelope [11, 12]. To simplify the analysis of the ATI electron spectra, only three harmonics from 11th to 15th were selected by passing through a Sn thin-foil filter.

Nonlinear Interaction of Intense Attosecond XUV Pulses with Atoms

373

When these three harmonics are simultaneously focused to Ar gas, five peaks form the lowest-order mode at 22nd (11th + 11th) to the highest order mode at 30th (15th + 15th) are expected to appear in the photo-electron spectrum. Among these five processes, the 24th (11th + 13th) and the 28th (13th + 15th) processes show beating due to interference of two harmonics, while only the 26th (13th + 13th, 11th + 15th) process contains the phase information between the three harmonics. The three-dimensional image of the mode-resolved autocorrelation with two-photon ionization electrons is shown in Fig. 3. From the spectral analysis, the chirp among the three harmonic fields was specified and it was found that a pulse duration should be shorter than 450 as, which is the first determination of the chirp in the attosecond pulse train with an autocorrelation technique [11]. Conforming to the custom that a method characterizing ultrashort pulses is named after creatures like FROG (frequency resolved optical gating) or RABITT (resolution of attosecond beating by interference of two-photon transitions) in the ultrafast optics field, this method is called PANTHER (photoelectron analysis of nonresonant two-photon ionization for harmonic electric-field reconstruction). PANTHER will open the way to full characterization of an attosecond pulse train.

Acknowledgment The authors wish to thank Drs. K. Yamanouchi, H. Hasegawa, K. Furusawa, K. Ishikawa, E. Takahashi, T. Okino, A. Suda, and H. Mashiko for their experimental contribution and helpful discussions.

References 1. P. Saliéres, A. L'Huillier, M. Lewenstein: Phys. Rev. Lett. 74, 3776–3779, 1995. 2. E. Takahashi, Y. Nabekawa, T. Otsuka, M. Obara, K. Midorikawa: Phys. Rev. A 66, 021802(R), 2002. 3. E. Takahashi, Y. Nabekawa, K. Midorikawa: Opt. Lett. 27, 1920 –1922, 2002. 4. E. J. Takahashi, Y.NabekawA, K. Midorikawa: Appl. Phys. Lett. 84, 4-6, 2002. 5. H. Mashiko, A. Suda. K. Midorikawa: Opt. Lett. 29, 1927-1929, 2004. 6. H. Bachau, P. Lambropoulus: Phys. Rev. A 44, R9-R12, 1991. 7. P. Lambropoulos, L. A. A. Nikolopoulos, M. G. Makris: Phys. Rev. A 72, 013410, 2005.

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8. Y. Nabekawa, H. Hasegawa, E. J. Takahashi, K. Midorikawa: Phys. Rev. Lett. 94, 043001, 2005. 9. H. Hasegawa, E. J. Takahashi, Y. Nabekawa, K. L. Ishikawa, K. Midorikawa: Phys. Rev. A 71, 023407, 2005. 10. H. Hasegawa, E. J. Takahashi, Y. Nabekawa, K. Midorikawa: Laser Phys. 15, 812-820, 2005. 11. Y. Nabekawa, T. Shimizu, T. Okino, K. Furusawa, H. Hasegawa, K. Yamnouchi, K. Midorikawa: Phys. Rev. Lett. 96, 083901, 2006. 12. K. Furusawa, T. Okino, T. Shimizu, H. Hasegawa, Y. Nabekawa, K. Yamanouchi, and K. Midorikawa: Appl. Phys. B 83, 203-211, 2006.

Anomalous Enhancement of Single High-Order Harmonic Generation at 61 nm and 47 nm by Indium and Tin Due to Strong Resonance M. Suzuki, M. Baba, R. A. Ganeev and H. Kuroda Institute for Solid State Physics, University of Tokyo T. Ozaki Institut national de la recherché, Universite du Quebec

Summary. We have successfully demonstrated the intensity enhancement of single high-order harmonic at a wavelength of 61.26 and 46.76 nm using low ionized indium and tin ions in laser ablation plume as the nonlinear medium. The ablation plume was produced by irradiating of solid tin target with 10 mJ energy picosecond laser pulse. Using the indium target, the 13th harmonic at the wavelength of 61.26 nm was obtained with conversion efficiency of 8x10-5. Using the tin target, the 17th harmonic at a wavelength of 46.76 nm was observed with conversion efficiency of about 10-4. We attribute the strong enhancement of single high-order harmonic to multiphoton resonance with a strong radiative transition of the In and Sn II ions.

1 Introduction High-order harmonic generation (HHG) is a very attractive radiation source in the extreme ultraviolet (XUV) and soft x-ray region, with good spatial quality and femtosecond resolution. One of the most important subjects of HHG research is the enhancement of conversion efficiency. In the past, such conversion efficiency enhancement has been pursued by controlling the phase matching condition in the gas filled capillary or gas cell. The strongest output energy of harmonics were 7 μJ for the 11th harmonic at a wavelength of 72.7 nm, 4.7μJ for 13th harmonic at a wavelength of 62.3 nm, and 1μJ for 15th harmonic at a wavelength of 54 nm using xenon gas-cell.1 Very recent results have reported an enhancement of high-order harmonic conversion efficiency when a two-color (fundamental and sec-

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ond harmonic field) orthogonally polarized driving field is used.2 Using the helium from the gas-jet, the conversion efficiency of the 38th harmonic at a wavelength of 21.6 nm was 5x10-5. An alternative approach is the resonance enhancement of HHG, which has been proposed by theoretical calculations.3 Experimentally, the resonance enhancement of the 13th and the 15th order harmonics generation using the argon gas medium has been observed.4 However the enhancement in these works were a factor of two to three, and the harmonic spectrum consisted of multiple harmonics. In this proceeding, we report the first observation of the single highorder harmonic enhancement in the XUV region. In this experiments, the nonlinear medium was indium and tin ablation plumes, produced by a lowenergy laser pulse, instead of the conventional gas medium. Using the tin target, the intensity of the 17th order harmonic at the wavelength of 46.76 nm was 20 times higher than its neighbor harmonics. The output energy of only this harmonic is measured to be about 1.1 μJ. Such output energy that was obtained the maximum output energy in the XUV region. Using the indium target, the conversion efficiency of the 13th harmonic at a wavelength of 61 nm was about 10-4, which was two orders of magnitude higher than its neighboring harmonics. The output energy of the 13th harmonic was measured to be 0.8 μJ.5 The origin of these enhancements is attributed to resonance with strong radiative transitions, produced within the laserablated plume.

2 Experiments The schematic of experimental setup was described in another proceeding.6 The pump laser was a commercial, chirped pulse amplification laser system (Spectra Physics: TAS-10F), whose output was further amplified using a homemade three-pass amplifier operating at a 10 Hz repetition rate. A pre-pulse was split from the amplified laser beam by a beam splitter before a pulse compressor. The pre-pulse energy is 10 mJ with pulse duration of 210 ps. A main pump pulse output at a center wavelength of 795 nm has energy of 10 mJ with pulse duration of 150 fs. A cylindrical lens focuses the pre-pulse onto a solid tin target placed within a vacuum chamber, which generates a laser ablation plume that contains low-charged ions. The size of the line focus on the target surface was 600 μm width and 1mm long, and the intensity of the pre-pulse was varied between 1010-1011Wcm2. The main pulse is focused onto the ablation plume by a spherical lens (focus length of 200 mm), 100 ns after pre-pulse irradiation. The intensity of the main pulse at the plasma plume is 1014Wcm-2. The spectrum of the

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generated high-order harmonics was measured by grazing incidence spectrometer with a gold-coated Hitachi 1200 grooves/mm flat-field grating. A gold-coated grazing incidence cylindrical mirror was used to image the target harmonics at the ablation plume onto detector plane. The XUV spectrum was detected using a micro-channel plate (MCP) with a phosphor screen read-out (Hamamatsu, model F2813-22P), and the optical output from the phosphor screen was recorded using a CCD camera (Hamamatsu model C4880). The detail of an absolute calibration of the spectrometer was described in elsewhere6.

3 Results and discussions Figure 1 shows the spectra of HHG from tin and vanadium laser-ablated plume pumped by femtosecond laser pulse. The plateau and cut-off of the harmonics have observed in these experiments. The second ionization potential of tin and vanadium are 14.63 eV and 14.65 eV, respectively. Therefore, the cut-off order for both targets should be the same, since the cut-off order has been shown to depend on the ionization potential. Though the signal is weak, high-order harmonics up to the 23rd (wavelength: 34.56 nm) order was observed in these experiments with both tin and vanadium. However, a strong 17th order harmonic at a wavelength of 46.76 nm was observed using tin laser ablation plume, as shown in Fig. 1(a). The intensity of the 17th harmonics was 20 times higher than those of its neighbors. The conversion efficiency of the 17th harmonic was measured to be about 1.1x10-4, and this output energy of 1.1 μJ was obtained from the pump laser energy of 10 mJ. For vanadium ablation plume, the strong single HHG was not observed, as can be seen in Fig. 1(b). To confirm the nature of this strong emission at the wavelength of 46.76 nm, we investigated the effect of pump laser polarization on HHG. Figure 2 shows the intensity of the 46.76 nm line as a function of the laser polarization ellipticity. A quarter-wave plate was installed after the focusing lens to change the pump laser polarization from the linear to circular. The line intensities shown in Fig. 2 are normalized to that generated using linearly polarized pump laser, corresponding to the zero position. The intensity of emission at the wavelength of 46.76 nm decreased after 10-degree rotation of the quarter-wave plate, which completely disappeared after 50-degree rotation of the quarter-wave plate. This tendency is consistent with that of HHG, which leads us to conclude that the strong emission at 46.76 nm should be generated by HHG.

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To investigate the mechanism of enhancement for the 17th harmonic, the central wavelength of the pump laser pulse was changed from 795 nm to 778 nm. Figure 3 shows the HHG spectra from the laser-ablated tin laser with three different laser wavelengths of 795 nm, 782nm, and 775 nm. In Fig. 3(a), one sees that the intensity of the 17th harmonic using 795 nm wavelength pump dominates the harmonic spectrum. The intensity of the 17th harmonic is 20 times higher than that of other harmonics. However, in Fig 3(b), the intensity of the 17th harmonic using 782 nm wavelength pump is decreased, and is almost same as that of other harmonics. In Fig. 3(c),

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the intensity of the 17th harmonic with 775 nm wavelength pump is further decreased. In the case, the 17th harmonic intensity is weaker than that of the 13th and 11th harmonics. The above results show that the intensity of the 17th harmonic gradually decreased as the wavelength of the pump laser become shorter. In the past work, the strong Sn II ion has been shown to posses a strong transition of the 4d105s 25p2P3/2-4d95s25p2 (1D) 2D5/2 at the wavelength of 47.256 nm.7 The gf-value of this transition has been calculated to be 1.52 and this value is 5 times larger than other transition from ground state of Sn II. Therefore, the enhancement of the 17th harmonic with 795 nm wavelength laser pulse can be explained be due to resonance with this transition driven by AC-Stark shift. By changing the pumping laser wavelength from 795 nm to 778 nm, the wavelength of the 17th harmonic is changed from 46.76 nm to 45.76 nm. Therefore, the wavelength of 17th harmonic pumped by laser wavelength of 775 nm is farther away from the 4d105s 25p2P3/2-4d95s25p2 (1D) 2D5/2 transition, at the wavelength of 47.256 nm. As a result, the resonance condition of the 17th order harmonic is weaker when pumped by a 778 nm, compared with the case for 795 nm pump.

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Figure 4 shows the typical spectra of HHG from the laser ablation indium plume. For indium, the 4d105s2 1S0-4d95s25p (2D) 1P1 transition of In II, which have an absorption oscillator strength (gf–value) of 1.11,8 can be driven into resonance with the 13th order harmonic by AC-Shark shift. The intensity of 13th harmonic for indium is attributed to such resonance of the harmonic wavelength with that of a strong radiative transition. By changing the laser wavelength from 796 nm to 782 nm, the 15th harmonic at the wavelength of 52.13 nm increased, and the intensity of 13th harmonic decreased at the same time. The reason of 15th harmonic enhancement is due to resonance with the 4d105s5p 3P2-4d95s5p2 (2P) 3F3 transition of In II, which has a gf-value of 0.30. The enhancement of 15th order harmonic intensity is lower than that of 13th harmonic because the gf-value of 4d105s5p 3 P2-4d95s5p2 (2P) 3F3 transition is lower than that of the 4d105s2 1S04d95s25p (2D) 1P1 transition. Furthermore the central wavelength of the 13th harmonic was driven away from resonance with the 4d105s2 1S0-4d95s25p (2D) 1P1 transition when using 782 nm wavelength laser, thereby decreasing the 13th order harmonics.

4 Conclusions We have observed the strong resonance enhancement of the single highorder harmonic generation at the wavelengths of 46.76 nm and 61.26 nm using tin and indium laser ablation plumes irradiated by femtosecond laser pulse. Conversion efficiencies of these harmonics were about 10-4 in the

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XUV region. We attribute the strong harmonic intensity to resonance with a strong oscillator strength transitions of Sn and In.

References 1. 2.

3. 4. 5. 6. 7. 8.

Takahashi, E., Nabekawa, Y., Midorikawa, K.: 'Generation of 10-μJ coherent extreme-ultraviolet light by use of high-order harmonics', Opt. Lett., 27, 1920-1922, 2002. Kim, I.J., Kim, C. M., Kim. H. T., Lee, G. H., Lee, Y. S., Park, J. Y., Cho, D. J.,Nam, C. H.:'Highly Efficient High-Harmonic Generation in an Orthogonally Polarized Two-Color Laser Field ' Phys. Rev. Lett. 94, 243901 2005. Gaarde, M B., Schafer. K. J.: 'Enhancement of many harmonics via a single multiphoton resonance ' Phys.Rev. A 64, 013820 2003. Toma, E. S., Antoine, Ph., Bohan, A. de., Huller, H. G.: 'Resonanceenhancement high-harmonic generation ' J. Phys. B 32, 5843-5852 1999. Ganeev. R. A., Suzuki. M., Baba, M., Kuroda, H., Ozaki, T.: 'Strong resonance enhancement of a single harmonic generated in the extreme ultraviolet range' Opt. Lett. 31, 1699-1701 2006. Ganeev, R. A., Baba, M., Suzuki, M., Kuroda: 'High-order harmonic generation from silver plasma', Phys. Lett. A, 339, 103-109, 2005. Duffy, G., Kampen, P. van.,Dunne, P: ' 4d-5p transitions in the extreme ultraviolet photoabsorption spectra of Sn II and Sn II' J. Phys. B 34, 3171-3178 2001. Duffy,G.,Dunne, P.: ' The photoabsorption spectrum of an indium laser produced plasma ' J. Phys. B34, L173-L178 2001.

Enhanced High Harmonic Generation from Ions Using a Capillary Discharge Plasma

M. Grishama, D. M. Gaudiosib, B. Reagana, T. Popmintchevb, M. Berrilla, O. Cohenb, B. C. Walkerc, M. M. Murnaneb, H. C. Kapteynb and J. J. Roccaa

NSF ERC for Extreme Ultraviolet Science and Technology a Electrical and Computer Engineering Department, Colorado State University, Fort Collins, CO b JILA and Physics Department, University of Colorado at Boulder c Department Physics and Astronomy, University of Delaware.

Summary. We demonstrate a significant extension of the high harmonic cutoff observed in xenon, up to 150 eV, by generating harmonics from ions in a capillary discharge plasma. The pre-ionized plasma generated by the capillary discharge dramatically reduces ionization-induced defocusing and energy loss of the driving laser due to ionization, allowing higher photon energies to be generated from xenon ions. We also demonstrate enhancement of the harmonic flux of nearly two orders of magnitude at photon energies around 90 eV when the capillary discharge is used to ionize xenon, compared with harmonic generation in a hollow waveguide. The use of a capillary discharge plasma as a medium for high harmonic generation shows great promise for extending efficient harmonic generation to much shorter wavelengths.

The extension of high harmonic generation (HHG) to higher photon energies from neutral atoms is not limited by the laser intensity, but is rather limited by the intensity at which all the neutral atoms are ionized. Ionization of the gas by the driving laser pulse leads to ionization-induced defocusing and beam attenuation, therefore limiting the peak intensity and cutoff photon energy. Generation from ions removes this limitation by reducing ionization-induced defocusing and beam attenuation and allows for extension of the cutoff harmonic [1]. A preformed plasma waveguide has been suggested as an advantageous media in which to generate efficient high harmonics [2,3]. Capillary discharges can conveniently produced elongated plasma waveguides suitable for guiding high intensity

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light pulses [3,4]. In this work, we demonstrate a significant extension of the high harmonic cutoff observed in xenon using a capillary discharge plasma waveguide. We have extended the cutoff by 60 eV, and have enhanced the harmonic flux at 90 eV photon energy by an order of magnitude.

Fig. 1. Schematic of the experimental setup for generating high-order harmonics from a capillary discharge created plasma

The experiment (fig. 1) made use of a 10-Hz, two stage Ti:sapphire laser system capable of generating 12 mJ pulses with a 28 fs duration. The laser pulses were focused into the entrance of a 175 um diameter, 5 cm long capillary discharge plasma. The capillary was filled with 2-4 Torr of xenon and simmered with a small DC current of ~10 mA. A main current pulse with a peak amplitude of ~5A and duration of ~5 µs generates a plasma with a density profile that is minimum on-axis, constituting in an index waveguide. The discharge was operated at 10 Hz matching the repetition rate of the laser used in this experiment. The high harmonic spectrum was measured using a flat field EUV spectrometer with an X-ray CCD camera.

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A comparison of typical spectra obtained in the capillary dicharge and in a hollow-core fiber is shown in figure 2. In both situations 5 mJ, 28 fs laser pulses were focused into the waveguides filled with 2.8 Torr of xenon. The laser pulses were injected into the discharge 2 μs after the intiation of the current pulse. The use of the discharge clearly extends the highest observable harmonic from 90 eV to ~ 150 eV. Above photon energies of 75 eV the discharge enhances the HHG signal. Harmonics around 85 eV are enhanced by an order of magnitude. Both the flux enhancement and cutoff extension are due to a reduction in the losses in the waveguide by the discharge plasma. The reduction of laser induced-ionization by the discharge also results in spectra with more distinct harmonic peaks as shown in Fig. 3. This is due to a reduction of the severe SPM broadening of the driving laser resulting from the rapid ionization of neutral Xenon. Time-resolved visible spectroscopy of the discharge plasma shows that the plasma is completely ionized at the time delay that corresponds to the observation of the highest harmonics. At this time, the spectrum is dominated by Xe II and Xe III lines, with Xe I lines (dominant before the onset

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of the discharge pulse) practically unobservable. The temporal evolution of typical lines of each species is shown in Fig. 4. These spectra confirm 4

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the results of hydrodynamic / atomic physics simulations of the capillary discharge plasma which predict that the plasma is fully ionized. This is also in agreement with ADK ionization rate calculations that show harmonics greater than 80 eV could only be generated at an intensity where the plasma is fully ionized. For a particular photon energy of 120 ev, figure 4 shows delays between the rise of the current pulse and injection of the laser as well as a complete current profile. Before the current pulse there is no signal at this photon energy. The flux then rises to a peak 2 μs after the initiation of the current pulse and then slowly returns to zero. This clearly demonstrates the advantages of HHG in a capillary discharge created plasma. Spectroscopy measurements of the plasma show that at the time of maximum high harmonic emission the plasma is completely ionized. It is possible that the delay of the maximum HHG signal is due to the presence of plasma nonuniformities caused by the fast rise time of the current pulse.

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Fig. 4. (a) Time evolution of the harmonic signal at 120 eV in Xe (diamonds). The current pulse is shown for reference (solid). (b) time evolution of the visible emission lines from Xe I (823.16 nm) (dotted), Xe II (418.01 nm) (dashed), and Xe III (410.92 nm) (solid).

In conclusion, we have demonstrated that a capillary discharge plasma waveguide can be used to extend high harmonic generation to shorter wavelengths. We have obtained high harmonic generation from Xenon to a photon energy of 150 eV. This is an increase of more than 70 eV over the highest previously published cutoff observed in xenon. Preliminary experiments in krypton and argon show similar enhancement. The capillary discharge overcomes the limitations imposed by ionization-induced defocusing, allowing for much higher laser intensities and harmonic generation at shorter wavelengths. This technique combined with quasi-phase matching methods promises to achieve efficient high harmonic generation at high photon energies.

Acknowledgement Work supported by the U.S. Department of Energy, Chemical Sciences, Geosciences, Biosciences Division of the Office of Basic Energy Sciences and by the NSF ERC for Extreme Ultraviolet Science and Technology under NSF Award No. 0310717. BCW acknowledges support from the JILA Visiting Fellows Program.

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References 1. EA Gibson et al., “High-Order Harmonic Generation up to 250 eV from Highly Ionized Argon”, Phys. Rev. Lett. 92, 033001 (2004) 2. H. M. Milchberg, C. G. Durfee III, and T. J. McIlrath, “High-Order Frequency Conversion in the Plasma Waveguide”, Phys. Rev. Lett. 75, 2494–2497 (1995) 3. A Butler, DJ Spence, and SM Hooker, “Guiding of High-Intensity Laser Pulses with a Hydrogen-Filled Capillary Discharge Waveguide”, Phys. Rev. Lett. 89, 185003 (2002) 4. Y. Wang, et al., “Capillary discharge-driven metal vapor plasma waveguides”, Phys Rev. E 72, 026413 (2005)

Generation of High-Order Harmonic Continuum Supporting Single Attosecond Pulse in Argon Driven by Intense 7 fs Laser Pulse Y. H. Zheng 1, H. Xiong 1, Y. Peng 2, H. Xu 2, X. Yang 2, Z. N. Zeng 1, X. W. Chen 1, R. X. Li 1, H. P. Zeng 2 and Z. Z. Xu 1 1

State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China

2

Key Laboratory of Optical and Magnetic Resonance Spectroscopy of Ministry of Education, Department of Physics, East China Normal University, Shanghai 200062, China

Summary. High-order harmonic continuum in the cutoff is demonstrated with an argon gas cell driven by 0.4 mJ/7 fs (FWHM) ultrashort intense laser pulse. We find that the spectral structure, the modulation depth and the continuum bandwidth of the high-order harmonic spectra vary when the carrier-envelope phase (CEP) of driving laser pulse is stabilized at different values. At some CEP values, a continuous spectrum of <17% modulation depth and 10 eV continuum bandwidth is achieved, supporting a transform-limited 300 attosecond single pulse in time domain.

1 Introduction Attosecond pulses are important tools for studying and controlling the motion of electrons inside atoms [1]. The discrete nature and broad envelope spectrum of high-harmonic emission implies that appropriate phase locking of different harmonics can result in a train of pulses of attosecond duration as was predicted in Ref. [2, 3] and shown experimentally in Ref. [4]. The successful generation of isolated attosecond pulses is an important step towards attosecond physics since single attosecond pulses are more promising for applications in time-resolved spectroscopy. To obtain single attosecond pulses remains, however, a major physical challenge. The main

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problem to generate isolated attosecond pulses is to confine the harmonic emission to less than one half optical cycle of the IR pump laser field. The first method that achieved this goal is to rapidly modulate the polarization of the fundamental pulse and use the strong ellipticity dependence of HHG for confinement [5-8]. Recently, I. J. Sola et al. use two birefringent (quartz) plates in conjunction with CEP-stabilized 5 fs pulses to create a polarization gate shorter than T0/2 (T0 is an optical cycle) and obtain chirped isolated pulses of 205 attosecond in experiment [9]. An alternative way to generate isolated XUV attosecond pulses requires linearly polarized, phase stabilized short enough laser pulses and a subsequent spectral filtering of cut off harmonics [10, 11]. Isolated 650 attosecond pulses in the high-order harmonic cutoff region have been achieved in experiment firstly by Hentschel et.al. [10]. But the 7 fs driving laser field they used was not phase stabilized. In fact, for pulses that have a duration equal to or shorter than 2.5T0, the dependence of the spectral structure of the cut-off radiation on phase is found to be robust within a broad range of parameters [12]. In this work, High-order harmonic continuum in the cutoff is demonstrated with an argon gas cell driven by 0.4 mJ/7 fs (FWHM) ultrashort intense laser pulse. We find that the spectral structure, the modulation depth and the continuum bandwidth vary when the CEP of driving laser pulse is stabilized at different values. At some special CEP values, a continuous spectrum of <17% modulation depth and 10 eV continuum bandwidth is achieved, supporting a transform-limited 300 attosecond isolated pulse in time domain.

2 Experimental results and discussions The experimental setup consists of a laser system, a focus light path, a target chamber and a flat-field soft x-ray grating spectrograph, where the spectrograph [13] consists of a gold-coated spherical mirror, a gold-coated mirror, a slit, a Hitachi flat-field grating (1200 grooves/mm) and a soft Xray CCD (Princeton Instruments, 1340×400 imaging array PI-SX: 400). In the experiment, we use a commercially available all-solid-state femtosecond laser system with kHz repetition rate, 800 nm wavelength, 40 fs (FWHM) pulse duration and 2.5mJ pulse energy (Spectra Physics Spitfire® Pro Ti:Sapphire regenerative amplifier). Pulses generated by this laser system are spectrally broadened by self-phase modulation in a hollow fiber filled with argon and subsequently compressed in a broadband highthroughput dispersive system. Gauss Pulses as short as 7 fs (after the window at the entrance of target chamber) with energy 0.4 mJ/pulse (after the

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window at the entrance of target chamber) and spot diameter 6.5 mm are obtained finally. Focused by a silver-coated concave mirror (f/40cm), the Gauss laser beam fight its way into a gas cell fixed in a vacuum chamber and cause high-order harmonic emission of argon atoms. The generated highly collimated coherence harmonic radiation propagates through one ~500 nm aluminum foil which blocked the driving laser, goes into the soft x-ray spectrograph and is recorded by the soft x-ray CCD. In the experiment, the intensity of driving laser in the focus spot is ~3×1014W/cm2. In order to minimize the broadening of driving laser in the propagation, the window at the entrance of target chamber is 0.6-mm-thick fused silica. The gas cell is 5-mm-long, sealed by two 0.1-mm-thick stainless steel plate. And the gas pressure in the cell is controlled by a precision valve.

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Fig. 1. shows the high-order harmonic spectra obtained as the driving laser is stabilized at two different CEP values, denoted in blue dotted line and red solid line, respectively. The accumulating time for the collected signal in CCD is 10s and the backing pressure of argon in the gas cell is 1.27×103 Pa. In the experiment, variation of the CEP of driving laser is achieved by stabilizing the output pulses of oscillator at different CEP positions at random. The position where the signal appears a sharp drop presents the absorption edge of aluminum (73eV in the picture, blue line). One can see from this figure that the spectral distribution, the modulation depth (the ratio of the peak to the valley of signal) and the continuum bandwidth of the spectra vary when the CEP of driving laser pulse is stabilized at different values. The modulation depths in the 57.0-59.5eV region are 41% and 17% for the blue dotted line and red solid line, respectively,

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which have 24% difference. The continuum of 10eV bandwidth appears around the absorption edge in the red solid spectral line. Although the accurate CEP value of the driving laser pulse has not been measured, the strong dependence of the spectral structure of the cut-off radiation on phase is presented in the picture. For some CEP, good continuum is obtained and discrete spectra for others, however. In the absence of phase stabilization the harmonic structure of the near-cut-off soft x-rays is almost completely smeared [12], thus the spectrum is not a real continuum. After selecting all of the harmonics in the 52.6-73.0eV region of the red spectral line and performing an inverse Fourier transform, this analysis gives us the temporal shape of the XUV pulse. One can obtain a transform-limited 300 attosecond single pulse under our experimental conditions.

3 Conclusion High-order harmonic continuum in the cutoff is demonstrated with an argon gas cell driven by 0.4 mJ/7 fs ultrashort intense laser pulse. We find that the spectral structure, the modulation depth and the continuum bandwidth of the high-order harmonic spectra vary when the CEP of driving laser pulse is stabilized at different values. For some special CEP, a continuous spectrum of <17% modulation depth and 10 eV continuum bandwidth is achieved, supporting a transform-limited 300 attosecond single pulse in time domain. It is the first time that the high-order harmonic continuum supporting a single attosecond pulse is achieved in a long gas cell, not in a gas jet. Using a gas cell is possible to control the interacting length of the driving pulse and further control the phase match conditions in the highorder harmonic generation.

Acknowledgments This work is supported by the National Science Foundation of China under Grant Nos. 19974058, 69925513 and 10525416 and the Major Basic Research Project of Shanghai Commission of Science and Technology under Grant No. 04dz14001.

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References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

Drescher, M.: 'Time-resolved atomic inner-shell spectroscopy', Nature (London), 419, 803-807, 2002. Farkas, G.: 'Proposal for attosecond light pulse generation using laser induced multiple-harmonic conversion processes in rare gases', Phys. Lett. A, 168, 447-450, 1992. Harris, S. E.: 'Atomic scale temporal structure inherent to high-order harmonic generation', Opt. Commun. 100, 487-490, 1993. Paul, P. M.: 'Observation of a train of attosecond pulses from high harmonic generation', Science, 292, 1689-1692, 2001. KovaŎev, M.: 'Temporal con-finement of the harmonic emission through polarization gating', Eur. Phys. J. D, 26, 79-82, 2003. Altucci, C.: 'Frequency-resolved time-gated high-order harmonics', Phys. Rev. A, 58, 3941-3934, 1998. Chang, Z. H.: 'Single attosecond pulse and xuv supercontinuum in the highorder harmonic plateau', Phys. Rev. A, 70, 043802(8), 2004. Huo, Y. P.: 'Single attosecond pulse generation using two-color polarized time-gating technique', Optics Express, 13, 9897-9902, 2005. Sola, I. J.: 'Controlling attosecond electron dynamics by phase-stabilized polarization gating', Nature Physics, 2, 319-322, 2006. Hentschel, M.: 'Attosecond metrology', Nature, 414, 509-513, 2001. Kienberger, R.: 'Atomic transient recorder', Nature, 427, 817-821, 2004. Baltuška, A.: 'Attosecond control of electronic processes by intense light fields', Nature, 421, 611-615, 2003. Li, R. X.: 'Space resolved spectrograph for laser induced plasma diagnostics', J. Opt.(Paris), 25, 143-150, 1994.

High-Order Harmonic Generation From LaserAblated Plasma Plume Pumped by Femtosecond Laser Pulse M. Suzuki, M. Baba, R. A. Ganeev and H. Kuroda Institute for Solid State Physics, University of Tokyo T. Ozaki Institut national de la recherché, Universite du Quebec

Summary. We have demonstrated a generation of 71st harmonic at a wavelength of 11.20 nm using low ionized vanadium ions in a laser ablation plume as a nonlinear medium. The conversion efficiency of this harmonic was about 0.8x10-6. Further the 61st harmonic at a wavelength of 13.03 nm with conversion efficiency of 2.6x10-6 have been obtained using the laser ablation titanium plume. Such high harmonics generation appears to an interaction between a femtosecond laser pulse and double charge ions.

1 Introduction Since the first demonstrations of high-order harmonic generation (HHG) by short pulse lasers [1], the coherent and ultrashort pulse radiation have achieved in the extreme ultra-violet (XUV) and soft x-ray region. An advantage of HHG is a very good spatial quality and femtosecond resolution. Attosecond pulse (several hundreds) generation in the process of HHG with irradiating the few-cycle laser pulse has recently been reported [2]. Furthermore the maximum cut-off energy has reached to the 1.3 keV (wavelength: 1.03 nm) [3]. On the other hand, the maximum output energies were 7 µJ for the 11th harmonic at a wavelength of 72.7 nm, 4.7 µJ for the 13th harmonic at a wavelength of 62.3 nm, and 1 µJ for 15th harmonic at a wavelength of 54 nm using xenon gas cell [4]. For an application experiment of HHG, the motion of bound electron control in molecular [5], the observation of mapping attosecond electron wave packet motion [6], and the nonlinear phenomena in the XUV region [7] have been demonstrated.

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To obtain the highest possible photon energy, the higher ionisation potential nonlinear medium has a big advantage. In the past [8,9,10], as the ionisation energy of alkali material is higher than any other gas medium, the HHG has been demonstrated using the rare-gas like ions from alkali material laser plasma instead of rare-gases. However the maximum photon energy of the harmonic was 64.92 eV using the laser plasma potassium ions with irradiating the subpicosecond KrF excimer laser at the wavelength of 248 nm [8]. Using laser plasma lead ions, the maximum cut-off energy was 105 eV with irradiating the high energy KrF laser pulse [9]. On the other hand, the maximum cut-off order of HHG were 27th harmonic at the wavelength of 29.4 nm using laser plasma sodium and potassium ions [10]. Furthermore the plateau was not observed using the rare-gas-like ion from laser plasma. We have recently obtained the 63rd harmonic at a wavelength of 12.63 nm (photon energy: 98 eV) using laser ablation boron ions with irradiating the femtosecond laser pulse [11]. The 63rd harmonic occurred from the interaction of femtosecond laser pulse with the single charged ion or atoms. In this proceeding, we report the observation of the 71st harmonic generation at the wavelength of 11.20 nm (photon energy: 110 eV) with conversion efficiency of 0.8x10-6 using a laser ablation vanadium plume. Using the laser ablation titanium plume, the 61st harmonic at the wavelength of 13.03 nm have been obtained. The maximum cut-off order depends on the second ionisation energy from our previous results. Although the second ionisation potential of vanadium is 14.65 eV, such a high harmonic have obtained in this experiment. The reason of the observation of the 71st harmonic was due to an interaction between the femtosecond laser pulse and double charge ions

2 Experiments The schematic of experimental setup was described in elsewhere [12]. The pump laser was a commercial, chirped pulse amplification laser system (Spectra Physics: TAS-10F), whose output was further amplified using a homemade three-pass amplifier operating at a 10 Hz repetition rate. A prepulse was split from the amplified laser beam by a beam splitter before a pulse compressor. The pre-pulse energy is 10 mJ with pulse duration of 210 ps. A main pump pulse output at a center wavelength of 795 nm has energy of 10 mJ with pulse duration of 150 fs. A cylindrical lens focuses the pre-pulse onto a solid target placed within a vacuum chamber, which generates a laser ablation plume that contains low-charged ions. The size

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of the line focus on the target surface was 100 µm width and 3 mm long, and the intensity of the pre-pulse was 1010 Wcm-2. The main pulse is focused onto the ablation plume by a spherical lens (focus length of 200 mm), 100 ns after pre-pulse irradiation. The intensity of the main pulse at the plasma plume is 1014 Wcm-2. The spectrum of the generated high-order harmonics was measured by grazing incidence spectrometer with a goldcoated Hitachi 1200 grooves/mm flat-field grating. A gold-coated grazing incidence cylindrical mirror was used to image the target harmonics at the ablation plume onto detector plane. The XUV spectrum was detected using a micro-channel plate (MCP) with a phosphor screen read-out (Hamamatsu, model F2813-22P), and the optical output from the phosphor screen was recorded using a CCD camera (Hamamatsu model C4880). The detail of an absolute calibration of the spectrometer was described in elsewhere [13].

3 Results and discussions Figure 1 shows the typical spectra of HHG from laser ablation silver and vanadium plumes with irradiating femtosecond laser pulse. Only odd harmonics were observed in this experiment. The high-order harmonics up to 71st order at a wavelength of 11.20 nm was observed using the laser ablation vanadium plume. By changing the polarization of the femtosecond laser pulse from the linear to circular, these signal disappeared. The tendency shows that these signals are generated from HHG. The conversion efficiency of the 71st harmonic was 0.8x10-6. Using laser ablation silver plume, the 59th harmonic at a wavelength of 13.47 nm with conversion efficiency of 6x10-6 have been observed. The plateau and cut-off were observed in both spectra. The appearance of plateau on these harmonics shows that these harmonics occurs from the non-pertubative regime. Therefore the cut-off energy of HHG from the laser ablation plume depends on the 3-step model [14]. By using the 3-step model, the cut-off energy rule is given by Ecut-off =Ip+3.17Up, [eV] where Ip is the ionisation potential of nonlinear medium and Up is the ponderomotive potential. Up=e2E2/4mω2=9.33×10-14Iλ2, where e and m are electron charge and mass, and E, ω, I, λ, are the field’s amplitude, frequency, laser intensity and laser wavelength, respectively. In previous our works, the maximum cut-off energy depends on the second ionisation potential of laser ablation plume. Therefore the maximum cutoff energy was 98 eV (wavelength: 12.6 nm) using the laser ablation boron target because the second ionisation energy is 24.124 eV. As well as bo-

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Intensity (a.u.)

3000 2500

10 shots

Ag

45

1800

th

1600

100 shots

V

45

th

1400

2000

1200

1500

59

1000

71

st

th

1000

500 0 10 11 12 13 14 15 16 17 18

800 10 11 12 13 14 15 16 17 18

Wavelength (nm)

Wavelength (nm)

Fig. 1. Typical HHG spectra from the laser ablation silver and vanadium plumes in the soft x-ray region.

-ron, the second ionisation potential of silver is 21.04 eV, therefore the cutoff energy of the laser ablation silver was 95 eV (wavelength: 13.03 Using vanadium, the 71st harmonic have obtained.nm) in this experiments. Although the second ionisation energy of vanadium is 14.65 eV, the 71st harmonic at a wavelength of 11.20 nm have been obtained. The photon energy of this harmonic was 110 eV. The second ionisation potential of vanadium is lower than that of silver, however the cut-off energy of vanadium is higher than that of silver. The estimation of the maximum cut-off energy of vanadium was 96 eV by using the cut-off rule equation.

Intensity (a.u.)

3500

10 shots

3000

45

th

2500 2000 61

1500

st

1000 500 8

10

12

14

16

18

Wavelength (nm)

Fig. 2. HHG spectra from the laser ablation titanium plume

In these experiments, the cut-off energy of our results is higher than that of our estimation value. As the reason for observation of the 71st harmonic,

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this harmonic occurred from the interaction between double charged ions and femtosecond laser pulse. The third ionisation potential of vanadium is 29.31 eV. The third ionisation potential value of vanadium is higher than the second ionisation potential value of silver. Therefore the observation of cut-off energy by using vanadium is higher than that of silver. Figure 2 shows the spectra of HHG from the laser ablation titanium plume. Using the laser ablation titanium plume, the 61st harmonic at the wavelength of 13.03 nm have obtained. The second ionisation potential of titanium is also lower than that of silver, however the maximum cut-off energy is higher than that of silver. As well as vanadium, the 61st harmonic from the laser ablation titanium plume occurred from the interaction between the femtosecond laser pulse and double charged ions.

4 Conclusions We have observed the 71st harmonic at the wavelength of 11.20 nm with the conversion efficiency of 0.8x10-6 using the laser ablation vanadium plume with irradiating femtosecond laser pulse. Furthermore the 61st harmonic at the wavelength of 13.04 nm with the conversion efficiency of 2.6x10-6 have been obtained using the laser ablation titanium plume. Such a high harmonics generations occurred from the interaction between the femtosecond laser pulse and double charged ions. Using another high third ionization potential material as use for nonlinear medium, the higher harmonic may be obtained.

References 1.

McPherson, A., Gibson, G., Jara, H., Luk, T. S., McIntyre, I. A., Boyer, K., and Rhodes, C.: 'Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases', J. Opt. Soc. Am B., 4, 595-601, 1987. 2. Drescher, M., Hentschel, M., Kienberger, R., Tempea, G., Spielmann, C., Reider, G. A., Corkum, P. B., Krausz, F.:'X-ray Pulse Approching the Attosecond Frontier', Science, 291, 1923-1927. 4. Seres, J., Seres, E., Verhoef, A. J., Tempea, G., Streli, C., Wobrauschek. P., Yakovlev, V., Scrinzi, C., Spielmann, C., Krausz, F.:'Source of coherent kiloelectronvolt X-rays', Nature, 433, 596, 2005. 5. Takahashi, E., Nabekawa, Y., Midorikawa, K.: 'Generation of 10- J coherent extreme-ultraviolet light by use of high-order harmonics', Opt. Lett., 27, 19201922, 2002.

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5. Kling, M. F., Siedschlang, Ch., Vnerhoef, A. J., Khan, J. I., Schultz, M., Uphues, Th., Ni, Y., Uiberacker, M., Drescher, M., Krausz, F., Vrakking M. J. J.: 'Control of Electron Localization in Molecular', Science, 312, 246-248, 2005. 6. Niikura, H., Villeneuve, D. M., Corkum, P. B.: 'Mapping Attosecond Electron Wave Packet Motion', Phys. Rev. Lett., 94, 083003-1-4, 2005. 7. Nabekawa, Y., Hasegawa, H., Takahashi, E. J., Midorikawa, K.: 'Production of Doubly Charged Helium Ions by Two-Photon Absorption an Intense Sub10-fs Soft X-Ray Pulse at 42 eV Photon Energy', Phys. Rev. Lett., 94, 043001-1-4, 2005. 8. Akiyama, Y., Midorikawa, K., Matsunawa, Y., Nagata, Y., Obara, M., Tashiro, H., Toyoda, K.: 'Generation of High-Order Garmonic Using LaserProduced Rare-Gas-Like Ions' Phys. Rev. Lett. 69, 2176-2179, 1992. 9. Kubodera, S., Nagata, Y., Akiyama, Y., Midorikawa, K., Obara, M., Tashiro, H., Toyoda, K.: 'High-order harmonic generation in laser-produced ions', Phys. Rev. A, 48, 4576-4582, 1993. 10. Wahlstrom, C.-G., Borgstrom, S., Larsson, J., Pettersson, S.-G.: 'High-order harmonic generation in laser-produced ions using a near-infrared laser', Phys. Rev. A, 51, 585-591, 1995. 11. Ganeev, R. A., Suzuki, M., Baba, M., Kuroda, H., Ozaki, T.: 'High-order harmonic generation from boron plasma in the extreme-ultraviolet range', Opt. Lett., 30, 768-770, 2005. 12. Kuroda, H., Suzuki, M., Ganeev, R. A., Baba, M., Zhang, J., 'Highly brilliant soft X-ray higher harmonics based on new scheme of ablated controlled plasma and intense single higher harmonics due to strong resonance enhancement' in these proceedings. 13. Ganeev, R. A., Baba, M., Suzuki, M., Kuroda: 'High-order harmonic generation from silver plasma', Phys. Lett. A, 339, 103-109, 2005. 14. Corkum, P. B.: 'Plasma perspective on strong-field multiphoton inonization', Phys. Rev. Lett., 71, 1994-1997, 1993.

Development of Multilayer Optics for EUV, Soft X-Ray and X-Ray Regions in IPOE Z.S. Wang* , J.T. Zhu, F.L. Wang, Z. Zhang, H.C. Wang, S. J. Qin and L.Y. Chen Institute of Precision Optical Engineering (IPOE), Tongji University, Shanghai 200092, China

Summary. In EUV and X-ray regions, multilayer mirrors are the essential and necessary optics elements. The good prospects of the EUV and X-ray optics for next generation lithography system, microscopy in the “water windows”, astronomy telescope, spectroscopy, plasma diagnostics, and X-ray laser have impelled the development of multilayer. This report introduced the recent results of the multilayer optics elements in institute of precision optical engineering (IPOE), Tongji University, China, including beam splitters, broad band/angular polarizers, supermirrors, and high-reflectance mirrors. The product of reflectivity and transmittance is above 4% for the Mo/Si multilayer beam splitter at 13.9 nm. Over the 15-17 nm wavelength range, the s-reflectivity of the non-periodic Mo/Si broadband multilayer polarizers is reasonably constant, as high as 36.6%, and the degree of polarization is more than 97.8%. The experimental results of some X-ray supermirrors and high-reflectance mirrors in our lab were also presented.

1. Introduction The EUV and X-ray optics has been regarded as one of the important fields in modern optics, and produced many promising applications in next generation lithography system, astronomy telescope, spectroscopy, plasma diagnostics, and X-ray laser. However, in the EUV and X-ray regions, the nature of the complex optical constants of all materials makes the realization of the ideal optical elements like ones working in visible region impossible. The development of EUV and X-ray optics has been retarded for long time by the absence of optical elements, for example, mirrors, beam splitters, and polarizers. Various schemes have been proposed and demonstrated utilizing multilayer interference structures to function as optical elements in EUV, soft X-ray and X-ray regions. Multilayers are presently *

Corresponding author: Tel/fax: 86-21-65984652, [email protected].

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used in many optical components for these regions. This report will introduce the recent results of the multilayer optics elements in institute of precision optical engineering (IPOE), Tongji University, China, including beam splitters, broad band/angular polarizers, supermirrors, and highreflectance mirrors. All these multilayers were fabricated by an ultra high vacuum direct current magnetron sputtering system made in China.

2. Beam splitter for soft X-ray laser Soft X-ray transmission optics allows new investigations of soft X-ray interferometer to probe the electron density of laser-produced plasma. The maximum electron density and the size of the probed plasmas are severely limited by absorption and refraction of the probe beam. There are two types of soft X-ray laser interferometers. One is Mach-Zehnder interferometer. The other is Michelson interferometer. Da Silva and his colleagues developed an amplitude-division soft X-ray laser Mach-Zehnder interferometer, and successfully probed dense plasma at 15.5 nm in 1995 [1]. High temporal and spatial coherence and saturated output of 13.9 nm Nilike silver X-ray laser has been obtained in China. And the soft X-ray laser Mach-Zehnder interferometer working at 13.9 nm has been successfully developed in 2003 [2]. The design, fabrication and characterization of beam splitter multilayers for Ni-like Ag X-ray laser working at 13.9 nm have been carried out in IPOE. Figure 1 shows the measured reflectivity and transmittance of the beam splitter. At the wavelength of 13.9 nm, the reflectivity and transmittance are as high as 20% or higher. The product of reflectivity and transmission is about 4%. Two beam splitters were needed at the same time for accomplishing the interferometer. Three sizes of 5 mm × 5mm, 10 mm × 10 mm and 14mm × 14 mm have been fabricated in IPOE.

3. Broadband multilayer polarizer and phase retarder For polarization-sensitive studies, accurate evaluation of the states of polarization of light is crucially important, such as circular dichroism spectroscopy, spin-polarized photoelectron spectroscopy, spectroscopic ellipsometry [3], and so on. Various schemes have been proposed and demonstrated utilizing multilayer interference structures to function as polarizers and retarders for soft X-ray and EUV [4]. A linear polarizer based on Mo/B4C/Si multilayer that achieved almost 99.9 % polarization with

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Fig. 1. The reflectivity and transmission of the beam splitter measured by synchrotron radiation (NSRL) at the wavelength of 13.9 nm.

s-component reflectivity at 13.5 nm has been realized [5]. However, the property of narrow-band of soft X-ray multilayer polarizers loses polarizing power and limits their applications. In order to solve this problem, Yanagihara et al. [6] developed the double-multilayer polarizer, which re quired a complicated experimental arrangement and sacrificed the throughput. To overcome these disadvantages, the non-period Mo/Si multilayer polarizers working in wide spectral and angular range were designed and fabricated in IPOE, which is convenient in the experiment measurement. The main feature of the method is the use of non-periodic multilayer as broadband polarizer and the use of an analytical solution as a starting point for direct computer calculation. Figure 2(a) shows the measured s- and p-reflectivity of aperiodic multilayer polarizer design for the grazing incidence angle of 50º. The measured s-reflectivity is as high as ≈37% and almost keeps constant in the wavelength rang of 15-17 nm, and the measured p-reflectivity was rather low, 0.24%.The aperiodic polarizer not only exhibits broad spectral widths at their design angle, but can also be used at nearby angles. To demonstrate this, the multilayer was also measured at grazing incidence angles of 45º and 48º. The measured s- and p-reflectivities are shown in Fig. 2 and com-

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pared with those at 50º. It can be seen that the reflectivity shifts to shorter wavelengths when the grazing incidence angle is decreased. The range is 15–17nm for a grazing incidence angle of 50º (as designed), shifts to 14.5– 16.5nm at 48º and to 13.8–15.8nm at 45º, in keeping with the Bragg equation.Besides the high reflective broadband multilayer polarizer, the broadband phase retarders were also designed and fabricated using direct current magnetron sputtering on the 100 nanometers silicon nitride substrate. Figure 3 shows the measurement and fitting results of the Mo/Si broadband phase retarder designed for the grazing incident angle of 47 º.

Fig. 2. The s- and p-reflectivities of the Mo/si multilayer polarizer measured by synchrotron radiation (BESSY-II) at grazing incidence angles of 50º, 48º and 45º.

3. X-ray supermirror Joensen et al. [7] proposed the concept of X-ray supermirrors from the depth-graded multilayer based on neutron supermirrors. Theoretically, Xray supermirror is a non-periodic multilayer structure satisfying the Bragg condition in wide energy or angle range to get flat and high response reflectivity. Using the local optimization method of simplex algorithm and the simulated annealing algorithm with different initial multilayer structures [8] the broad angular supermirrors with broad grazing incidence an-

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gle ranges at the energy of 8.0 keV (Cu Kα line) and the wide energetic bands supermirrors at fixed grazing incidence angles were designed. Fig ure 4(a)

Fig.3. The s- and p-transmittance of Mo/Si broadband phase shift measured by synchrotron radiation (BESSY-II) at the grazing incident angle of 47 degree (a), and the calculated and fitting phase shift (b).

shows the W/Si supermirror has the reflectivity of above 30% in the angle range of 0.4-0.85° at the fixed energy of 8 keV. The W/B4C supermirror has the reflectivity of about 20% in the angle range of 0.9-1.2°, and the reflectivity of W/C supermirror working in the grazing incident angle range of 0.9-1.2° is about 20% (not shown here). We also designed and fabricated the dual-path supermirror. Fig. 4(b) shows the design and measured reflectivities of W/C dual-path supermirror at 8.0 keV in the grazing angle regions of 0.7o~0.85o and 1.09o~1.3o.

4. High reflective multilayer mirror In this section, the experimental results of some multilayer mirrors in our lab were listed in table 1, such as Mo/Si, Mo/Y, Cr/C, La/B4C, Si/C, Mg/SiC, and so on.

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Table 1. The experimental results of some multilayer mirrors in IPOE. Incident angle(°)

Wavelength (nm)

Reflectivity (%)

Measurement place

Mo/Si

5.0

13.20

65.0

BESSY-II

Mo/Si

5.0

17.10

47.1

NSRL

Mo/Si

5.0

19.50

38.7

NSRL

Mo/Si

5.0

28.40

22.4

NSRL

Mo/Si

5.0

30.40

19.8

NSRL

Mo/Si

33.50

19.0

Si/Mo/B4C

5.0 5.0

30.40

32.5

NSRL NSRL

Si/B4C

5.0

30.73

25.4

NSRL

Si/C

5.0

30.74

16.8

NSRL

Si/SiC Mg/SiC

5.0

15.6 37.4

NSRL

10.0

30.16 30.36

Mg/SiC

16.4

30.41

47.3

NSRL

Mg/SiC

29.0

30.46

41.5

NSRL

Mg/SiC

40.0

25.60

48.0

NSRL

Cr/C

45.0

6.10

17.6

BESSY-II

Cr/C

46.0

4.48

13.6

BESSY-II

Cr/C

5.0

4.48

7.5

BESSY-II

Cr/Sc

5.0

4.48

6.1

BESSY-II

Mo/Y

45.0

7.80

18.4

BESSY-II

La/B4C

45.0

6.80

17.6

BESSY-II

NSRL

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Normalized intensity

1.0

(a)

(b)

Design Measure

0.8 0.6 0.4 0.2 0.0 0.0

0.2

0.4

0.6

0.8

1.0

Grazing incident angle,θ (degree)

1.2

Fig. 4. The design and measured reflectivities of W/Si supermirror at 8.0 keV in the grazing angle regions of 0.4o~0.9o (a), and W/C dual-path supermirror at 8.0 keV in the grazing angle regions of 0.7o~0.85o and 1.09o~1.3o.

5. Summary In this report, the design and fabrication of multilayers for EUV, soft Xray, and X-ray regions in our group were described, including the beamsplitter multilayers designed for Mach-Zehnder interferometer, broad band/angular multilayer polarizers and phase retarders, X-ray supermirrors, and some high-reflective multilayer mirrors working in different wavelengths. Small d-spacing multilayers are also studied now.

Acknowledgement The authors are indebted to Prof. Alan G Michette, Dr. IV Kozhevnikov, Dr. Franz Schäfers, and Dr. Andreas Gaupp for their useful discussions and kindly help. This work is supported by NNSFC (60378021, 10435050), 863-804 Sustentation Fund, and NCET (04-0376).

Reference 1. L.B.Da Silva, T.W.Barbee, Jr., R.Cauble, P.Celliers, et al. “Electron density measurements of high density plasmas using soft X-ray laser interferometry”. Phys. Rev. Lett. 74, 3991-3994,1995,. 2. Z. S. Wang, Y.G. Wu, W.X Tang, et al. “Fabrication of the beam splitter for soft x-ray laser application”, Chinese Science Bulletin, 48, 1930, 2003.

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3. Y. Wu, S. S. P. Parkin, J. Stöhr, et al. “Direct observation of oscillatory interlayer exchange coupling in sputtered wedges using circularly polarized Xrays”. Appl. Phys. Lett.63,263, 1993. 4. J. B. Kortright, M. Rice, et al. “Optics for element-resolved soft X-ray magnetooptical studies”. J. of Magnetism and Magnetic Materials 191,79, 1999. 5. B. Kjornrattanawanich, Saa Bajt, and John F. Seely. “Mo/B4C/Si multilayercoated photodiode with polarization sensitivity at an extreme-ultraviolet wavelength of 13.5 nm”. Appl. Opt. 43,1082, 2004. 6. M. Yanagihara, T. Maehara, H. Nomura et al. “Performance of a wideband multilayer polarizer for soft x rays”. Rev Sci Instrum. 63,1516, 1992. 7. Joensen K D, Chrstensen F E, Schnopper H W, et al. “Medium-sized grazing incidence high-energy X-ray telescopes employing continuously graded multilayers” Proc. SPIE. 1736, 239, 1992. 8. I V Kozhevnikov, I N Bukreeva, E Ziegler, “Design of x-ray supermirrors”. Nucl Instrum Methods in Physics Research. A460,424,2001.

Chirped Multilayer Soft X-Ray Mirrors for Attosecond Soft X-Ray Pulses U. Kleineberg1,2, W. Hachmann3, U. Heinzmann3, S. Hendel3, N. Kabachnik3, F. Krausz1,2, U. Neuhäusler3, M.Uiberacker1, Th.Uphues3, A. Wonisch3, V. Yakovlev2 1

Ludwig Maximilians University Munich, Am Coulombwall 1, D-85748 Garching, Germany; 2 Max Planck Institute for Quantum Optics, Hans Kopfermannstr. 1, D85748 Garching, Germany; 3 University of Bielefeld, Faculty of Physics, Universitaetsstr. 25, D-33615 Bielefeld, Germany

Summary. Aperiodic XUV multilayer coatings with broad spectral bandwidth and flat dispersion characteristics have been developed and fabricated as reflecting and spectrally filtering optical elements for attosecond XUV pulses. Based on a genetic computational optimization algorithm aperiodic Mo/Si multilayer structures exhibiting up to 40 eV spectral bandwidth and pulse responses down to about 100 attoseconds at 80 eV center photon energy could be simulated. An experimental multilayer design exhibiting about 15 eV spectral bandwidth at 93 eV photon energy was realized and tested in an attosecond XUV pump – IR probe photoionization experiment (attosecond streak camera) utilizing single attosecond pulses from a High Harmonic Generation source. The results display the enhanced spectral bandwidth filtered by the aperiodic mirror which holds the potential for the extraction of single XUV pulses shorter than 200 attoseconds.

1 Introduction The generation, measurement and utilization of ultrashort electromagnetic pulses are at the frontier of modern physics. Time-resolved pump-probe experiments studying the evolution of fundamental ultrafast electronic processes in atoms, molecules and on surfaces over time are limited by the pulse duration1, 2. Over the last decade serious progress has been reported worldwide in the development of single isolated attosecond pulses or pulse trains based on High Harmonic Generation (HHG) with pulse durations ranging down to about 250 asec3-6. Attosecond pulses are inevitably at

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short wavelengths in the Extreme Ultraviolet (XUV) or even Soft X-ray (SXR) spectral range. Besides the sources, multilayer-coated EUV/SXR optics plays a key role for spectrally filtering those pulses from the comb of the harmonic spectrum as well as spatially guiding and controlling the pulse in a pump-probe experiment without deteriorating the pulse duration7, 8. We report on the development, optimization, realization and characterization of aperiodic multilayer soft-X-ray mirrors with tailored spectral bandwidth properties as well as smooth broadband dispersion characteristics. Those chirped multilayer mirrors hold the potential to conserve the time structure of subfemtosecond pulses or even compress chirped pulses and, in this way, to achieve pulse durations as short as 50 asec. In the present paper we discuss the development, fabrication and characterization of chirped Mo/Si multilayers which were specially designed for use in generation of single isolated 100-150 asec pulses at a photon energy of about 93 eV from High Harmonics produced by a 5 fs Ti:Sa laser pulse. The theoretical development and optimization procedure of the chirped Mo/Si multilayer stack has been performed by using a genetic algorithm technique. The mirrors have been fabricated by UHV electron beam evaporation as well as Ion Beam Deposition. Characterization of the multilayer structure and the spectral reflection bandwidth has been performed by hard X-ray and soft X-ray reflectometry, respectively. Finally, first results on electron streak measurements in a photoionization experiment by using this chirped multilayer mirror are reported. Measuring the photoelectron spectrum of the Ne-2p photoelectrons generated by the EUV pulse and cross correlated with the phase stabilized IR laser carrier field provides us with information about the time structure of the EUV pulse after reflecting off the multilayer. The results point to a multilayer time response supporting a pulse duration of approximately 155 asec in accordance with our theoretical design goal.

2 Chirped Mo/Si multilayer coatings The optical reflection of attosecond XUV pulses by an XUV mirror requires the control of the spectral phase over a bandwidth exceeding 10 electron volts (~25 eV required for 100 asec pulse). The requirements of large bandwidth, flat spectral dispersion and optimized high reflectance cannot simultaneously be achieved by a standard periodic multilayer XUV

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mirror which usually tends to be optimised for small bandwidth and high peak reflectance. We have thus simulated the reflectivity amplitude r(ω) and phase φ(w) of non-periodic multilayer stacks based on a recursive Fresnel equation code and a genetic algorithm. The time response of such a mirror can then be described by multiplying the electrical field amplitude E(ω) of the incoming pulse with the calculated complex reflectivity of the mirror : R(ω) = r(ω)*exp(iφ(ω))

E(ω)out = E(ω)in*R(ω)

The calculated reflectivity and spectral phase of an aperiodic Mo/Si multilayer mirror consisting of 10 layers and optimised for a gaussian shaped reflectivity profile with a bandwidth of approximately 15 eV FWHM is displayed in Fig. 1.

Fig. 1. Reflectivity and phase of the aperiodic XUV multilayer mirror (left) and time response to an (unchirped) XUV pulse (right)

The simulated data (dashed lines) display an almost linear development of the spectral phase over the reflectivity peak bandwidth with a small phase jump due to the secondary reflectivity maximum, the peak reflectivity of the main Bragg maximum reaches 8 % at 93 eV photon energy. In comparison, the solid lines display the reflectivity and phase of a fabricated Mo/Si multilayer mirror (details of the fabrication procedure see Ref. 7), as extracted from measurements of the multilayer stack by Grazing Incidence X-ray Reflectometry (GIXRR). It is clearly shown, that besides a small absolute shift of the reflectivity peak towards a slightly higher photon energy the complex reflectivity matches very well to the theoretical simulation. Based on the data displayed in Figure 1 (left), the time response of the multilayer mirror was calculated by Fourier backtransforming E(ω) after reflexion into E(t) assuming an incoming unchirped Fourier-limited electromagnetic pulse with a pulse duration of about 70 asec. As is displayed in Fig. 1 (right), the time response reaches 155 asec FWHM for both cases,

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the simulated model mirror (dashed) as well as the experimentally realized multilayer mirror (solid).

3 Attosecond Streak Camera Experiment The aperiodic Mo/Si multilayer mirror was utilized to spectrally filter an attosecond XUV pulse from the plateau area of the High Harmonic comb and to refocus (f = 120 mm) the pulse in a Ne gas jet for an XUV pump/ IR probe photoionization experiment (attosecond streak camera, see Ref. 3 for experimental details). The Ne-2p photoelectrons (binding energy 21.6 eV) ionized by the XUV pulse interact with the delayed IR few-cycle pulse of the Ti:Sa driver laser (λ = 750 nm, T =< 5 fsec, 0,4 mJ, 1 kHz), thus accelerating and decelerating the electrons according to the vector potential of the linearly polarized laser carrier field. 15 eV chirped mirror, non phase stabilized, 1xsmoothed 0

time delay (*200 asec)

10

20

30

40

50

575

600

625

650

675

700

725

750

775

800

825

photoelectron energy (arb. units)

Fig. 2. Attosecond streaking of Ne-2p photoelectrons with the Ti:Sa laser (non phase stabilized) for two different XUV mirrors, 9 eV BW (left), 15 eV (right) both spectra equally scaled in time delay (y) and kinetic electron energy (x)

The kinetic energies of the electrons (measured by a TOF spectrometer) as a function of the time delay between the XUV pulse and the (non CE phase stabilized) IR pulse are displayed in Fig. 2. These electron streaking spectra are displayed for an ionising XUV pulse reflected off a 9 eV

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bandwidth mirror (left spectrum) in comparison to the aperiodic 15 eV bandwidth mirror described above (right spectrum). While in both measurements the electron streaking is temporally confined to a time interval of about 5 fsec given by the pulse duration of the few cycle Ti:Sa laser, the measured kinetic energy spread of the Ne-2p photoelectrons outside the streaking area is different in both cases representing the different spectral bandwidth of the ionizing XUV pulse. It is clearly demonstrated that the electron energy spread of the unstreaked Ne-2p photoelectron peak is widened by about 40 % for the 15 eV mirror compared to the 9 eV mirror (note, that an XUV pulse of 250 asec FWHM pulse duration has been measured after reflecting off the 9 eV bandwidth mirror in previously published attosecond streak measurements). This value is somewhat smaller than the widening purely expected due to the designed bandwidth difference of both mirrors. The partially modulated HH spectrum below the plateau regime may result in a spectral clipping and thus in the smaller than expected gain in photoelectron energy width.

Fig. 3. High Resolution attosecond streaking of Ne-2p photoelectrons with the Ti:Sa laser (CE phase stabilized) for the 15 eV bandwidth XUV mirror.

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Higher resolution attosecond streaking measurements of the Ne-2p photoelectrons interacting with a carrier envelope (CE) phase stabilized Ti:Sa laser pulse are displayed in Fig. 3. The measurement clearly resembles the kinetic energy variation of the photoelectrons by the carrier field of the laser. Besides the exact reconstruction of the temporal waveform of the laser field, the measurement also encodes temporal information about the pulse duration and spectral chirp of the ionizing XUV pulse. A more detailed analysis of Fig. 3 displays a significant modulation of the photoelectron intensity within the streaking spectra with intensity maxima separated by about 3 eV , which is most probably a “finger print” of the modulated part of the High Harmonic spectrum collected by the bandwidth of the XUV multilayer. Furthermore, the occurrence of attosecond double-pulses cannot be excluded, when a large HH spectrum is filtered.

4 Summary and Outlook Summarizing, we have designed, fabricated and characterized an aperiodic Mo/Si multilayer mirror with a center photon energy of E = 93 eV and a spectral bandwidth of approximately 15 eV FWHM for the reflection of single attosecond XUV pulses. The aperiodic XUV mirror significantly enhances the useful spectral bandwidth from the Harmonic comb to about 13 eV, as is displayed by the kinetic energy spread of the Ne-2p photoelectrons ionised by the XUV pulse. This spectral bandwidth combined with the flat spectral dispersion holds the potential for the extraction of High Harmonic pulses with less than 200 asec pulse duration. The aperiodic XUV mirror was used in an attosecond streak camera experiment resolving the electron streaking of Ne-2p photoelectrons while interacting with a delayed phase stabilized IR laser pulse. These measurements encode information about the waveform of the few-cycle infrared laser field as well as about the time duration and spectral chirp of the generated attosecond XUV pulse. Further experimental improvements towards even shorter (<= 4 fsec) Ti:Sa laser pulses by advanced pulse compression schemes are required and under development in order to generate single attosecond pulses in the order of 100 asec or less. Financial support by the German “Volkswagenstiftung” under grant number AZ I/79 227 is gratefully acknowledged.

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References 1. Drescher, M., Hentschel,M., Kienberger, R., Uiberacker, M., Yakovlev, V., Scrinzi, A., Westerwalbesloh, Th., Kleineberg, U., Heinzmann, U., Krausz, F.: 'Time-resolved atomic inner-shell spectroscopy', Nature, 419, 803-807, 2002. 2. Drescher, M., Hentschel, M., Kienberger, R., Uiberacker, M., Westerwalbesloh, Th., Kleineberg, U., Heinzmann, U., Krausz, F.: 'Time-resolved electron spectroscopy of atomic inner-shell dynamics', J. Electron. Spectrosc. Rel. Phenom., 137-140, 259-264, 2004. 3. Hentschel, M., Kienberger, R. Spielmann, Ch., Reider, G.A., Milosevic, N., Brabec, T., Corkum, P., Heinzmann, U., Drescher,M., Krausz, F.: 'Attosecond metrology', Nature, 414, 509-513, 2001. 4. Kienberger, R., Goulielmakis,E., Uiberacker, M., Baltuska, A., Yakovlev, V.,Scrinzi, A., Westerwalbesloh, Th., Kleineberg, U., Heinzmann, U., Drescher, M., Krausz, F.: 'Atomic transient recorder', Nature, 427, 817-821, 2004. 5. Gouliemakis, E., Uiberacker, M., Kienberger, R., Baltuska, A., Yakovlev, V., Scrinzi, A., Westerwalbesloh, Th., Kleineberg, U., Heinzmann, U., Drescher, M., Krausz, F.: 'Direct measurement of light waves', Science, 305, 1267-1269, 2004. 6. Mairesse, Y., de Bohan, A., Frasinski, L.J., Merdji, H., Dinu, L.C., Monchicourt, P., Breger, P. Kovacev, M., Taieb, R., Carre, B., Muller, H.G., Agostini, P., Salieres, P.: 'Attosecond synchronization of high-harmonic soft X-rays', Science, 302, 1540-1543, 2003. 7. Wonisch, A., Neuhäusler, U., Kabachnik, N.M., Uphues, T., Uiber acker, M., Yakovlev, V., Krausz, F., Drescher, M., Kleineberg, U., Heinzmann, U.: 'Design, fabrication and analysis of chirped multilayer mirrors for reflection of extreme-ultraviolet attosecond pulses', Applied Optics, 45(17), 4147-4156, 2006. 8. Morlens, A.-S., Lopez-Martens, R., Boyko, O., Zeitoun, P., Balcou, P., Varju, K., Gustavson, E., Remetter, T., L´Huillier, A., Kazamias, S., Gautier, J., Delmotte, F., Ravet, M.-F.: 'Design and characterization of extremeultraviolet broadband mirrors for attosecond science', Optics Letters, 31(10), 1558-1560, 2006.

Nano-Scale Imaging With Tabletop Soft X-Ray Lasers: Sub-38 nm Resolution C. S. Menoni1,2, G. Vaschenko1,2, F. Brizuela1,2, C. Brewer1,2, Y. Wang1,2, M. A. Larotonda1,2, B. M. Luther 1,2, M. C. Marconi1,2, and J. J. Rocca1,2, W. Chao1,3, J. A. Liddle1,3, Y. Liu1,3, E. H. Anderson1,3, and D. T. Attwood1,3,4 A. V. Vinogradov5, I. A. Artioukov5, Y. P. Pershyn6 and V. V. Kondratenko6 1

NSF ERC for Extreme Ultraviolet Science and Technology Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO 80523 3 Center for X-ray Optics, Lawrence Berkeley National Laboratory, 4 University of California, Berkeley, CA 94720 5 P. N. Lebedev Physical Institute, Russia 6 National Technical University “KhPI”, Ukraine 2

Summary. We report the demonstration of soft x-ray microscopes with resolution down to sub-38 nm using tabletop soft x-ray laser illumination. One of the compact microscopes combines the 46.9 nm wavelength output from a capillary discharge Ne-like Ar laser with a reflective condenser and a free standing zone plate objective. High quality images were acquired with this microscope in transmission mode and reflection mode. The latter includes images of an integrated circuit pattern containing polysilicon features on silicon. The spatial resolution for this microscope is between 120-150 nm. Increased resolution was demonstrated in another microscope using 13.2/13.9 nm wavelength illumination from Ni-like Cd/Ag transient soft x-ray lasers in combination with diffractive zone plate optics for both the condenser and objective. Using an objective zone plate with a 50 nm outer zone width, this optical system achieved a record sub-38 nm spatial resolution. These results demonstrate the feasibility of using compact high repetition rate soft-x-ray laser sources in nanometer-scale microscopy.

1. Introduction The development of practical imaging tools with nanometer-scale spatial resolution are of importance for many applications ranging from material science and microelectronics to biology. A direct pathway to realize mi-

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croscopy with tens of nanometers resolving power is to use soft x-ray (SXR) light. The best spatial resolution for photon-based microscopes to date, 15 nm, was obtained using soft x-ray illumination from a synchrotron source [1]. Aside from the experiments conducted at synchrotron facilities, a variety of imaging experiments have been carried out using both coherent and incoherent short wavelength sources. Early imaging work with soft x-ray lasers demonstrated submicrometer resolution in reflection mode with a SXR recombination laser at λ=18.2 nm. [2] A resolution of 75 nm was reported using the λ=4.48 nm output from a SXR laser pumped by the very large fusion-driver NOVA which was limited to firing several shots a day. [3] In the last several years smaller-scale short wavelength sources including high order harmonics [4], and incoherent laser-plasma-based sources [5,6], have been used for submicron resolution imaging. Of these experiments, the best performance in terms of spatial resolution, reported as sub-100 nm, was obtained with a laser-created incoherent plasma source emitting at λ = 3.37 nm [6]. In this paper we discuss the implementation and demonstration of soft x-ray microscopy with compact high repetition rate laser sources. We present imaging results in transmission and reflection modes obtained with a microscope that combines the output from a λ = 46.9 nm capillary discharge pumped Ne-like Ar laser with a reflective condenser and objective zone plate. This instrument is capable of acquiring high quality images with a large field of view in exposure times of ~10 - 20 seconds and with a spatial resolution between 120-150 nm. Another transmission mode microscope was developed using a similar geometry but with Fresnel zone plate (FZP) optics for both the condenser and the objective in combination with shorter 13.2/13.9 nm wavelength illumination from laser-pumped Nilike Cd or Ag collisionally excited soft x-ray lasers. This compactable-top photon-based imaging system is shown to have a spatial resolution better than 38 nm.

2. λ=46.9 nm imaging system based on a table-top capillary discharge laser The tabletop soft x-ray microscope implemented using a capillary discharge Ne-like Ar laser as the illumination source is configured to operate either in transmission or in the more versatile reflection mode. In transmission mode, illustrated in Fig. 1a, the laser output is collected and focused onto a sample using a Sc/Si multilayer coated Schwarzschild con-

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denser. A free standing FZP objective then forms the image onto a backilluminated CCD detector.

Fig. 1. (a) Schematic diagram of the 46.9 nm soft x-ray laser microscope in its transmission mode implementation. (b) Photograph of the inside of the vacuum chamber that houses the microscope.

The Sc/Si multilayer coated Schwarzschild condenser contains a primary convex mirror of 10.8 mm in diameter and a 50 mm diameter secondary concave mirror. [7] Together these two mirrors produce a hollow cone of λ = 46.9 nm light that is focused onto the sample, which is positioned at ~ 5 cm from the output of the condenser. The Schwarzschild condenser has a numerical aperture (NA) of 0.18 and a throughput of ~ 1%, due to the less than optimum reflectivity of the coatings at λ = 46.9 nm The FZP objective was fabricated to be “freestanding,” as the use of any substrate material would significantly attenuate the λ = 46.9 nm light. The zone plate, manufactured onto a thin nickel foil attached to a silicon frame, contained pseudo-random bridges connecting the different zones to provide structural stability. [8] The FZP objective has a diameter of 0.5 mm, an outer zone width of 200 nm, a NA of 0.12 and a focal distance of 2.13 mm. To achieve high magnification (~ 750×) the FZP objective to CCD distance was chosen to be 1.6 m, which required the working distance of the objective be very close to its focal distance. For these experiments, the capillary discharge laser was equipped with an Al2O3 capillary 18 cm long, resulting in an average power ~ 0.1 mW. [9,10] This choice of capillary length provided a good compromise between output power and degree of coherence of the source [11]. Although a single laser shot produced discernable images, most images were acquired by accumulating several shots to improve the signal-to-noise ratio. Nevertheless, since the laser can be operated at a repetition rate of several

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Hz, the exposure time was only several seconds. The images were collected with a back-illuminated CCD camera with a 1024×1024 array of 24×24 μm2 pixels.

Fig. 2. a) Soft x-ray image of the free standing zone plate objective showing the different zones connected with pseudo-random bridges. The outermost zones of width 200 nm and the corresponding intensity cross-section are shown in (b) and (c) respectively.

The test sample used in the transmission imaging experiment was a freestanding FZP similar to the one used as the objective. Fig. 2a is an image of the central portion of this test pattern and was acquired in 20 seconds at a magnification of 250×. The resolution of the imaging system was obtained from the high magnification images of the 200 nm outer edge of the FZP sample, as shown in Fig. 2b (×750 magnification, 10 sec. exposure). From this image the intensity modulation or lineout along the outer edge portion of the FZP was obtained (Fig. 2c). An average of 100 lineout traces shows the intensity modulation is ~ 94 %. This intensity modulation is significantly higher than the 26.5% set by the Rayleigh resolution criterion, suggesting that the resolution of the instrument is significantly better than 200 nm. To estimate the spatial resolution of the imaging system, simulations were performed using the SPLAT program [12]. From the simulations a 120 - 150 nm resolution was estimated. This program assumes the use of incoherent light illumination, which is justifiable for this imaging system when using a short length capillary to ensure low coherence. [11].

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Fig. 3. Soft x-ray image of a silicon wafer patterned with 100 nm polysilicon lines (top right) and 250 nm half-period lines with equal lines and spaces (bottom right). This image was obtained with the 200 nm outer zone objective using a 20 second exposure (20 laser shots) and a magnification of 750×.

To acquire images in reflection mode the object was rotated by 45º with respect to the incoming beam, and the FZP objective and CCD were rotated by 90º. In this configuration, the depth of focus of the objective FZP limited the area of the image in focus at the CCD to 3×30 μm2. This was overcome by digitally compensating the images. We imaged a test pattern consisting of polysilicon lines on a silicon substrate. This test pattern was originally produced for optimization of the lithography process for chip manufacturing. Fig. 3 shows an image of this sample obtained with a 20 second exposure. The condenser was scanned during acquisition to ensure complete illumination of the sample and to reduce coherence effects on the image. In the upper right corner of Fig. 3, 100 nm polysilicon lines separated by 800 nm spaces are clearly discernible, and in the lower right region, 250 nm lines with 250 nm separations are well resolved. A more compact “desk-top” size version of this microscope is currently under development. It will utilize the desk-top size Ne-like Ar capillary discharge laser developed at CSU in combination with an objective FZP with a 120 nm outer-most zone to obtain sub 100 nm resolution images.

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3. Imaging at 13 nm with a laser-pumped tabletop laser We have also demonstrated the operation of a microscope at wavelengths near 13.5 nm. The shorter wavelength of the illumination coupled with aberration free zone plate optics allowed a record spatial resolution to be obtained for a tabletop photon-based full-field microscope system. The illumination is provided by either a 13.2 nm Ni-like Cd or a 13.9 nm Nilike Ag laser-pumped transient collisional laser generating highly monochromatic light (Δλ/λ < 1 × 10-4) with microwatt average power. [13,14] The condenser and objective FZPs were fabricated by electron beam lithography in a ~ 120 nm thick nickel film supported by a 100 nm Si3N4 layer that is ~ 40 % transparent to the incident 13 nm light. The condenser FZP has a diameter of 5 mm and consists of 12,500 zones of decreasing width down to 100 nm. It has a numerical aperture NA = 0.07 and a focal distance of 38 mm for the wavelength of 13.2 nm. Two different objective zone plates were used. One has a diameter of 0.2 mm and contains 625 zones with an outer zone width of Δr = 80 nm. The second one has a 0.1 mm diameter with Δr = 50 nm. Microscope magnifications of 290 – 1750× were obtained by selecting the objective working distance very close to its focal length and by selecting the distance between the objective zone plate and the CCD camera in the 0.335 to 0.635 m range. The spatial resolution of the microscope was determined by imaging a series of dense grating test patterns of period ranging from 38 to 310 nm. The sample also contains a set of 64 radial spokes decreasing in width down to ~ 40 nm as they converge towards the center of a circular pattern. Figure 4 shows an image of the radial spokes pattern obtained with the objective zone plate of Δr = 80 nm, using λ = 13.9 nm illumination and an exposure time of 20 sec (100 laser pulses at 5 Hz). The central part of the image contains 60 nm half-period lines that are clearly visible. The acquisition of images with a relatively large field of view (~ 12 × 20 µm2) is facilitated by the high brightness of the laser, which allows the condenser to efficiently collect the laser emission and focus it onto the test pattern. The spatial resolution of the microscope was experimentally determined from the images of grating patterns with different periods, all of them with nominal 1:1 line/space ratio. Figure 5 shows a soft x-ray image of gratings with 50 nm dense lines obtained with the FZP of Δr = 50 nm and λ = 13.2 nm illumination. The intensity lineout corresponding to the 38 nm grating image is also shown in Fig. 5. The ~ 70 % intensity modulation clearly demonstrates that the spatial resolution of the microscope is better than 38 nm.

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Fig. 4. Image of a pattern consisting of radial spokes of width increasing outwards obtained at λ = 13.9 nm with the Δr= 80 nm FZP and a 6 sec. exposure.

Fig. 5. Soft x-ray image of 50 nm dense lines (left) obtained at λ=13.2 nm with the Δr = 50 nm FZP. The image of the 38 nm dense lines and its lineout are shown on the right. The ~ 70% intensity modulation shows that the spatial resolution of the system is better than 38 nm.

4. Summary We have demonstrated high resolution full field imaging at soft x-ray wavelengths by combining the output from high repetition rate tabletop lasers at λ = 46.9, 13.9 and 13.2 nm with diffractive FZP optics. The λ = 46.9 nm microscope renders images in transmission and in the challenging reflection mode of operation. Its spatial resolution has been determined to

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be 120-150 nm. The best spatial resolution, 38 nm, was realized with an all zone plate imaging system at λ = 13.2 nm using an objective FZP with an outer zone width of Δr = 50 nm. The spatial resolution of these microscopes could be readily improved by using objective zone plates with smaller outer zone widths and increased numerical apertures.

5. Acknowledgments This work was supported by the Engineering Research Centers Program of the National Science Foundation under NSF Award Number EEC0310717.

References 1.

Chao, W., Harteneck, B. D., Liddle, J. A., Anderson, E. H. and Attwood, D. T., “Soft X-ray microscopy at a spatial resolution better than 15 nm.” Nature 435, 1210-1213, 2005. 2. DiCicco, D. S., Kim, D., Rosser, R. and Suckewer, S., “First stage in development of a soft-x-ray reflection imaging microscope in the Schwarzschild configuration using a soft-x-ray laser at 18.2 nm.” Opt. Lett. 17, 157-159, 1992. 3. Da Silva, L. B. et al. “Demonstration of x-ray microscopy with an x-ray laser operating near the carbon K edge.” Opt. Lett. 17, 754-756, 1992. 4. Wieland, M. et al. “Towards time-resolved soft X-ray microscopy using pulsed fs-high-harmonic radiation.” Ultramicoscopy 102, 93-100, 2005. 5. Artioukov I.A. et al., “Schwarzschild soft-x-ray microscope for imaging of nonradiating objects.” Opt. Lett. 20, 2451-2453, 1995. 6. Berglund, M., Rymell, L., Peuker, M., Wilhein, T. & Hertz, H. M., “Compact water-window x-ray microscopy.” J. Microsc. 197, 268-273, 2000. 7. Artioukov I.A., Krymski K.M., “Schwarzschild objective for soft x-rays,” Optical Engineering 39, 2163-2170, 2000 8. Anderson E.H., “Specialized electron beam nanolithography for EUV and Xray diffractive optics,” IEEE Journal Of Quantum Electronics 42, 27-35, 2006. 9. Benware B.R., Macchietto C.D., Moreno C.H., Rocca J.J., “Demonstration of a high average power tabletop soft X-ray laser,” Phys. Rev. Lett. 81, 58045807 1998. 10. Macchietto CD, Benware BR, Rocca JJ, “Generation of millijoule-level softx-ray laser pulses at a 4-Hz repetition rate in a highly saturated tabletop capillary discharge amplifier,” Opt. Lett. 24, 1115-1117, 1999.

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11. Liu Y., Seminario M., Tomasel F.G., Chang C., Rocca J.J., Attwood D.T., “Achievement of essentially full spatial coherence in a high-average-power soft-x-ray laser,” Physical Review A 63, Art. No. 033802, 2001. 12. Heck, J. M., Attwood, D. T., Meyer-Ilse, W. & Anderson, E. H., “Resolution determination in X-ray microscopy: an analysis of the effects of partial coherence and illumination spectrum,” J. X-ray Sci. Technol. 8, 95-104, 1998. 13. Wang Y., Larotonda M.A., Luther B.M., Alessi D., Berrill M., Shlyaptsev V.N., Rocca J.J., “Demonstration of high-repetition-rate tabletop soft-x-ray lasers with saturated output at wavelengths down to 13.9 nm and gain down to 10.9 nm,” Phys. Rev. A 72, Art. No. 053807, 2005. 14. Rocca J.J., Wang Y., Larotonda M.A., Luther B.M., Berrill M., Alessi D., “Saturated 13.2 nm high-repetition-rate laser in nickellike cadmium (vol 30, pg 2581, 2005)”, Opt. Lett. 31, 129-129, 2006.

A Non-Normal Incidence Pumped Ni-Like Zr XRL for Spectroscopy of Li-Like Heavy Ions at GSI/FAIR T. Kühl1,2, D. Ursescu1, V. Bagnoud1, D. Javorkova1, O. Rosmej1, D. Zimmer1, K. Cassou3, S. Kazamias3, A. Klisnick3, D. Ros3, B. Zielbauer1,2,4, K.Janulewicz4, P.Nickles4, G.Pert5, P.Neumayer5 and J.Dunn5 1

Gesellschaft für Schwerionenforschung (GSI), Darmstadt, Germany; Universität Mainz, Mainz, Germany; 3Université Paris XI, Paris, France; 4 Max Born Insitut, Berlin, Germany; 5York University, United Kingdom; 6 Lawrence Livermore National Laboratory, Livermore, USA 2

Summary. One of the unique features of the PHELIX laser installation is the combination of the ultra-high intensity laser with the heavy-ion accelerator facility at GSI and its planned extension FAIR. Due to this combination, PHELIX will allow novel investigations in the fields of plasma physics, atomic physics, nuclear physics, and accelerator studies. An important issue within the scientific program is the generation of high quality x-ray laser beams for x-ray laser spectroscopy of highly-charged ions. The long range perspective is the study of nuclear properties of radioactive isotopes within the FAIR [1] project. A novel single mirror focusing scheme for the TCE XRL has been successfully implemented by the LIXAM/MBI/GSI collaboration under different pump geometries. Intense and stable laser operation with Ni-like Zr and Ni-like Ag was demonstrated at pump energies between 2 J and 5 J from the PHELIX pre-amplifier section.

1 Motivation Although the information on nuclear ground-state properties extracted from a study of hyperfine structure and isotope shift is model-independent, it is hampered in complex neutral atoms by the accuracy with which the electron wave functions are known at the site of the nucleus. In that respect, it is highly advantageous to measure these effects in highly charged ions with one or only few electrons [2]. Since the electron wave function can be precisely calculated in such simple few-electron systems, uncertainties due to the atomic hyperfine fields at the site of the nucleus are negligible.

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This way, absolute charge radii can be determined instead of only changes in charge radii between two isotopes of the same element as accessible by conventional isotope shift measurements. In terms of atomic physics, the determination of the specific mass shift, given by a comparison of atomic and Li-like isotope shifts, provides a means to disentangle features of multi-electron correlation. Li-like ions are a favorable compromise, because here the transition energy is - with the additional help of the large Doppler shift of relativistic ions - in a range which is in reach for XRL. The 2S1/2 → 2P1/2 transition in uranium has a transition energy of 280 eV. 10

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Fig. 1. Transition energy and wavelength of the 2P1/2 → 2P1/2 transition in Li-like heavy ions

The interaction of photons with highly charged ions was one of the new fields opened by the advent of heavy-ion storage rings. The new accelerator complex at GSI will enable another important step by allowing spectroscopy on a wide variety of radioactive beams, and also will largely increase the velocity of the ions. The key feature of the present heavy-ion storage ring ESR, and the future NESR ring at FAIR is the ability for a precise and versatile preparation of ion samples by electron cooling, and bunching. Using the large Doppler shift in contra-linear excitation geometry, photon energies of around 110 eV in the laboratory frame are sufficient to induce the 280 eV 2S1/2 → 2P1/2 transition even in lithium-like uranium. This means that a method will be applicable to the full range of radioactive isotopes available at the NESR. Photon energies around 90 eV,

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as presently achieved at PHELIX [3, 4], will reach into the range of lithium-like lead.

for necessary Doppler shift

0,9 0,8 0,7 0,6 0,5 ESR rigidity 10 Tm e-cooler (240 kV) Steerer (7.2 Tm) 22 nm 13.9 nm 10 nm

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Fig. 2. Necessary Doppler shift to reach the 2s1/2 - 2p1/2 transition in Li-like heavy ions of different nuclear charge. The areas on top indicate the limitations by ESR machine parameters

2 XRL Development The XRL experiments at GSI were performed using the output from the pre-amplifier section of the PHELIX laser. As shown in Fig. 3, the preamplifier delivers chirped pulses at 1053 nm wavelength, which are normally further amplified in the following high-energy stages. The pump beam of 2 to 8 J energy is split into two parts: 75% of the energy is entering in a single grating, double-pass compressor which re-compresses the pulse down to 400 fs. The transmission of the device is slightly better than 50%. The remaining 25% of the energy are directly transported to the target. The duration of this un-compressed pulse is about 0.8 ns. It is passed through an 18 m long optical delay line in order to produce nearly the same optical path length as the travel distance in the compressor. This nanosecond pulse is focused by a spherical lens with 1 m focal length and a cylindrical lens with 250 mm focal length to a line focus of (30 μm × 6 mm) onto a Zr metal target. Here it serves to create a plasma column

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several hundreds of picoseconds before the impact of the compressed pulse.

Fig. 3. Schematic diagram of the PHELIX laser system and its use in the present XRL experiments

Fig. 4. View of the experimental set-up. The pump beams are entering from the left, the XRL emission is directed to the front

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Due to the ultra-high intensity of the short ps-pulse this plasma is rapidly heated, which leads to a non-stationary population inversion, with a high transient gain. The compressed pulse is focused onto the same position on the target by a single, gold coated, 6 inch diameter on-axis parabola. Tilted at an incidence angle of 9° this naturally generates a line focus of 30 μm - 100 μm width and over 5 mm length. The XRL experiments in Ni-like Zr at PHELIX were performed in two campaigns with similar setups. The first one was using an incident angle on target of 45° for the main pulse. In a second experimental campaign, an incidence angle on target of 72° was used. In a very recent experiment, an XRL in Ni-like silver was also demonstrated.

Fig. 5. XRL in Ni-like silver at 13.9 nm

A somewhat surprising result was the strong favoring for shorter main pulse durations at the more grazing incidence angle. While at 45 degree incidence angle the plasma emission, detected with a pinhole x-ray camera with an aluminum filter, was rising with increasing pulse duration and showed an optimum between 4 and 5 ps, there was no increase at the 72 degree configuration. The same behavior was reflected by the laser emission, which showed the maximum at 4 ps and 0.5ps, respectively. An analysis of the different situations using the EHYBRID code [5] showed good agreement with this behavior. The simulation indicates that the penetration depth at the different angles of incidence leads to a selective heating of very different plasma layers in the two cases, varying strongly in temperature, density and ionization stage.

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Fig. 6. Comparison of the observed plasma emission for different pulse durations at 45 and 75 degrees incidence angle of the main pulse onto the target. In both cases the plasma emission was detected behind a 500 nm thick aluminium filter, suppressing low energy photons.

3 Outlook The experimental results with Ni-like lasers in zirconium and silver nicely demonstrate the ability to produce lasing at moderate pump energies using the non-normal pumping geometry. For the goal of the XRL spectroscopy at GSI and FAIR the wavelength range would already be sufficient for spectroscopy of the ground state transition in lithium-like ions up to the lead region. Within this range even much higher repetition rates are in reach [6]. A further extension into the shorter wavelength range would, however, be highly interesting. In this respect the full understanding of the ionisation- and pumping process is of extreme importance. The agreement of the present results with different pump angles in Ni-like Zr with EHYBRID calculations therefore is a valuable first step in this direction. The capability of the PHELIX system to supply higher pump energies, which can be handled by similarly simple focusing systems [7], should allow for an extension to shorter wavelength.

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References 1. T. Stoehlker et al., 'Status and Perspectives of Atomic Physics Research at GSI: The new GSI Accelerator Project', Nucl. Instr. and Meth. B, 205, 156, 2003 2. P. Neumayer et al. 'X-ray laser spectroscopy on lithium-like ions', Proc. SPIE Int. Soc. Opt. Eng., 4505, 236, 2001 3. P. Neumayer et al., 'Transient collisionally excited X-ray laser in nickel-like zirconium pumped with the PHELIX laser facility', Appl. Phys. B, 78, 957, 2004 4. P. Neumayer et al., 'Status of PHELIX laser and first experiments', Laser and Particle Beams, 23, 385, 2005 5. Pert, G. J.: 'Optimizing the performance of nickel-like collisionally pumped xray lasers', Phys. Rev. A, 73, 033809, 2006 6. K. Cassou et al.: 'A 10 Hz, 3 µJ transient x-ray laser pumped in grazing incidence geometry', this conference 7. B. Zielbauer et al., 'X-ray imaging of the heating zone of non-normal incidence pumped XRL plasma', this conference 8. D. Ursescu et al., 'A focusing system for high energy TCE', this conference

Recent Progress of X-Ray Laser at Shenguang II: Diagnosing ICF Plasma by Ni-Like Ag 13.9nm X-Ray Laser C. Wang, Z. Fang, J. Sun, J. Xiong, L. Ji, B. Ma, J. Wu, J. Ye, S. Fu, Y. Gu and S. Wang Shanghai Institute of Laser Plasma, Shanghai, 201800, P.R.China

G. Zhang, W. Ye, W. Zheng, J. Wu and T. Zhang Institute of Applied Physics and Computational Mathematics, Beijing 100088, P.R.China

Summary. Plasma produced by laser irradiation of CH slab target was diagnosed by Mach-Zehnder (M-Z) interferometer, and the plasma produced by laser irradiation of plane CH modulation target which was used to study nonlinear development of ablation Rayleigh-Taylor (RT) instability, were also diagnosed by M-Z interferometer and by side-on radiography using an Ni-like Ag soft X-ray laser (XRL) at 13.9nm as probe light. Two-dimensional electronic density profile of CH slab target up to a density of 3.2×1021 cm-3 had been obtained. Furthermore, the nonlinear development of ablation RT instability also had been observed by M-Z interferometer and side-on radiography using a soft XRL as probing light. In this paper, the experiment arrangement and the experiment results were reported, and the primary analysis on it also was represented.

A soft X-ray interferometer to probe a large laser-produced plasma with micron spatial resolutions has been developed by Silver et al.[1,2] A Ne-like Y XRL at 15.5 nm was combined with M-Z interferometer to obtain electron density profiles up to a density of 3×1021 cm-3 in a plasma produced by laser irradiation of a CH target. The measured electron density profile has been compared to hydrodynamic simulation and shows good agreement near the ablation surface but some discrepancy at low density. Recently, experiment diagnoses of plasma electron density by M-Z interfer-

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ometer using an Ni-like Ag XRL at 13.9nm as probe light was been obtained by Wang et al.[3] Electron density profiles up to a density of 9.5×1020 cm-3 in a plasma produced by 1ω pre-main pulse laser with 100 ps duration irradiation of a CH target. The measured electron density profile has been also compared to hydrodynamic simulation and shows good agreement near the ablation surface but some discrepancy at low density. Plasma produced by laser irradiation of CH slab target was diagnosed by M-Z interferometer, and the plasma produced by laser irradiation of plane CH modulation target which was used to study nonlinear development of ablation RT instability, were also diagnosed by M-Z interferometer and by side-on radiography. Two-dimensional (2D) electronic density profile of CH slab target, and the nonlinear development of ablation RT instability also had been observed. In this paper, the experiment arrangement and the experiment results were reported, and the primary analysis on it also was represented.

1. Experiment principle of Mach-Zehnder interferometer At 13.9 nm, the multilayer mirror has 30-40% reflectivity, multilayer beam splitter has 20-15% in reflectivity and transmission, respectively, overall throughput of each arm is ~0.75%. First and seventh beams of Shenguang II facility were used as driven laser to produce X-ray laser. Two driving lasers have 100ps duration in Gaussian distributing, 100 J output for each beam, 1.053 μm wavelength, 3-5 % prepulse’s intensity. The interval between peaks of two pulses t12 is 3ns. Using

Fig.1. The output of Ni-like Ag XRL

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25+25 mm double Ag slab target opposite coupling, with vertical distance 260 μm and a angle between two targets 2 mrad, a saturated XRL at 13.9 nm with output energy Eout~200-400 μJ and a divergence~5-8 mrad has been got. The XRL duration is ~30 ps. In the far field，the 2D XRL output profile was been shown in Fig.1. diagonostic time

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The ninth beam of Shenguang II facility was used to produce laser plasma to be diagnosed. The ninth beam has output in double frequency with ~ 2.2 ns duration in single pulse, which used lens array to get uniform irradiation in diameter of 350 μm at power density 4~7 ×1014 Wcm-2. The output intensity of ninth beam vs. time was been shown in Fig.2. The standardization diagnostic time t0 is at descending fringe of the pulse.

Fig. 3. Dynamic interferogram at No.05081264 (part).

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Fig. 4. The electron density 2D profile

2. Diagnostic electron density of laser plasma by M-Z interferometer In the No. 05081264 shot, the ninth beam had 1682 J output, a intensity of 7.55×1014 Wcm-2 irradiated on a steel plug guage target plated with 10 μm CH in shape of rectangle with 1 mm width. The diagnostic time is at standardization diagnostic time. The XRL imaging magnification is 10, giving a pixel limited spatial resolution 2 μm. The dynamic interferogram has been shown in Fig.3. The image shows excellent fringe visibility and very little self-emission from the plasma. Analysis of the fringe pattern gives a fringe visibility of 0.4±0.1. The maximum of Nfringe is 11.6. In punctual focus, cylindrical symmetry plasma has been formed. According to the Abel transform[4,5,6], the electron density can be inversed from Nfringe. The 2D electron density profile is been put in Fig.4. The maximum electron density is higher than 3×1021 cm-3. In Fig. 5 we show the calculated electron density Ne profile obtained from 1.5D JB19 simulation with curvature radium of 700 μm and the measurement electron density profile for r=0. The maximum of electron density is 3.2×1021 cm-3. It is difficult to confirm location of the critical surface both according to simulation and dynamic interferogram. However, it shows some kind of agreement near the ablation surface but big discrepancy at low density. Due to flatness of the beam splitter, for different undisturbed fringes by plasma and far from target sur-

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face or at the back of the target, the fluctuation of angle and the fluctuation of width also are ~±5 %. The precision of Ne is ~2.7×1020 cm-3. The precision of Ne is ~2.5×1019 cm-3 by one pixel resolution. 1E22

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3. Diagnose CH modulated target ablation nonlinear RayleighTaylor instability by side-on The experiment principle is been showed in Fig.6. A M-Z interferometer experiment is been completed in No. 05080858 shot. The ninth beam had 1037 J output, a intensity of 4.65×1014 Wcm-2 irradiated on a CH modulated target with amplitude 1.52 μm, periods 54.03 μm, thickness 17.64 μm, and width 163 μm. The diagnostic time is 0.5 ns early than t0. The imaging magnification is 10, giving a pixel limited spatial resolution 2 μm. The dynamic interferogram measured by M-Z interferometer is put in Fig.7.

Fig. 6. The experiment principle of diagnose by side-on .

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Fig. 7. The dynamic interferogram at No.05080858 shot

The image shows excellent fringe visibility and very little self-emission from the plasma. Analysis of the fringe pattern gives a fringe visibility of 0.3±0.1. The 2D density profile calculated by two-dimension LARED-S is put in Fig.8. The 2D dynamic interferogram and the 2D XRL intensity profile due to absorption by plasma calculated from tow-dimension LARED_S simulation result are put in Fig.9. a) and b), respectively.

Fig. 8. The density profile simulated by two-dimensional LARED_S

Fig. 9. a) dynamic interferogram b) The XRL intensity profile

The experiment and simulation results are qualitative alike. The nonlinear development of RT instability developed obviously. But the target wasn't penetrated through in both of experiment and simulation. The area where the electron density is higher than critical density also can be seen. At back of target there are some kinds of structure. In the No. 05080656 shot, a CH modulated target side-on radiography experiment is been completed by using single arm of M-Z interferometer. The ninth beam had 889 J output, a intensity of 3.99×1014 Wcm-2 irradiated

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on a CH modulated target with amplitude 1.19 μm, periods 53.25 μm, thickness 21.45 μm, and width 167 μm. The diagnostic time is at t0. The imaging magnification is 20, giving a pixel limited spatial resolution 1μm.

Fig. 10. The density profile calculated by 2D LARED_S in one mode approximately

Fig. 11. The side-on radiography profile. at No.05080656 shot

The 2D density profile of CH modulated target in single mode calculated by two-dimension LARED-S is put in Fig.10. The CH modulated target side-on radiography experiment result is put in Fig.11. The experiment and simulation results are qualitative alike. The target also wasn't penetrated through in both of experiment and simulation.

Fig. 12. The density profile calculated by two-dimensional LARED_S

Fig. 13. The side-on radiography profile at No.05081265 shot.

In the No. 05081265 shot, the ninth beam had 1031 J output, a intensity of 4.63×1014 Wcm-2 irradiated on a CH modulated target with amplitude

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1.53 μm, periods 54.04 μm, thickness 16.92 μm, and width 175 μm. The diagnostic time is at t0. The XRL imaging magnification is 10, giving a pixel limited spatial resolution 2 μm. The 2D density profile of CH modulated target calculated by twodimension LARED-S is put in Fig.12. The CH modulated target side-on radiography experiment result is put in Fig.13. The mushroom RT instability can be seen, obviously. The experiment and simulation results are also qualitative alike. The driven intensity, target amplitude and target thickness were almost same to that of No. 05080858 shot, because the diagnostic time is 0.5 ns later than it, the nonlinear development of RT instability is developed faster than that the latter. The target was penetrated through obviously in both of experiment and simulation.

4. Conclusion The 2D electron density profile has been measured up to a density of 3.2×1021 cm-3. The magnitude of discrepancy has been observed between the experiment and simulation. It is similar to LLNL’s experiment. Due to 30 ps duration of Ni-like Ag XRL, using ninth beam from Shenguang II with 2ω, more than 4×1014 Wcm-2 as driven laser, and choosing 200 μm path length, it is possible to have been measured electron density profile up to a density higher than critical density for CH plasma. As driven laser intensity increasing, thickness of target decreasing, modulated amplitude increasing and diagnostic time advancing, the nonlinear development of ablation RT instability has been observed, in the end the target has been penetrated through obviously. The mushroom spike and bubble can be seen, obviously. It is no possible to get this picture by face-on radiography experiment. The experiment and simulation results qualitative alike, but in quantitative, the magnitude of discrepancy has been also observed between the experiment and simulation. There is a lot of information in both dynamic interferogram and side-on radiography profile. As side-on radiography probing light, the soft XRL better than the hard plasma X-ray in its 2-3 μm spatial resolution. Further more in the side-on radiography, only using soft XRL the 2D electron density profile can be got. These two factors are very important to understand nonlinear development of ablation RT nonlinear instability. Of course, for soft XRL, ununiformity in output beam affects to get quantitative results in side-on radiography experiment, and its penetration ability is less than the latter. But our experiments show that for soft XRL has ability to diagnose 100-200 μm path length as CH low-Z material.

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These experiments just demonstration! It is show that the soft XRL with short wavelength, short duration, high brightness, high spatial resolution (at least 2-3 μm) and adequate coherence can be used to measure electron density profile near the critical density, also can be used to diagnose the nonlinear development of ablation RT instability. The brightness and stability of XRL has been improved. Due to test simulation, precision of driving laser, target and optical elements have been needed, and all kinds of diagnosis method have been used to do benchmark experiment.

Acknowledgement We would like to thank Prof. Yu Min for direction this work. We would also like to thank the Shenguang II Facility Group for their assistance in these experiments. We would also like to thank Physics Department of Tongji Univ. for provided multilayer beam splitter, target and filter. We would also like to thank Changchun Institute of Optics and Fine Mechanics, CAS for provided multilayer mirror. This work was supported by National Hi-Tech ICF Committee of China.

References [1] L.B. Da Silva, T.W. Barbee, Jr., R Cauble, et al. X-ray Lasers 1996 Proceedings of the 5th International Conference on X-ray Lasers held in Lund, Sweden, 10-14 June 1996, edited by S Svanberg and C-G Wahlström, Institute of Physics Conference Seriers Number 151: 504-508,1996. [2] L.B. Da Silva, T.W. Barbee, Jr., R Cauble, et al., Phys. Rev. Lett. ,4: 90-3994, 1995. [3] Wang Chen, Wang Wei, Sun Jinren, et al., Acta Physica Sinica, 54: 202-205, 2005. [4] Bockasten K, J. Opt. Soc. Amer., 51: 943-947, 1961. [5] Barr W, J. Opt. Soc. Amer. 52: 885-888, 1962. [6] Jian Shaoen, Liu Zhongli, Tang Daoyuan, et al., Optics and Precision Engineering, 8: 181-184, 2000.

Plasma Opacity and Laser Ablation Measurements Using X-Ray Lasers G. J. Tallents1, M. H. Edwards1, D. Whittaker1, N. Booth1, H. Huang1, P. Mistry1, G.J. Pert1, B. Rus2, T. Mocek2, M. Koslovà2, J. Polan2, A. Praeg2, M. Stupka2, P. Homer2, C. McKenna3, A. Delserieys3, C. L. S. Lewis3, M. Notley4 and D. Neely4 1

Department of Physics, University of York, York, YO10 5DD, U.K. Department of X-ray Lasers, PALS Research Centre, Institute of Physics, Academy of Sciences of the Czech Republic, 182 21 Prague 8, Czech Republic 3 School of Mathematics and Physics, Queen's University of Belfast, Belfast BT7 1NN, U.K 4 Central Laser Facility, Rutherford Appleton Laboratory, Chilton, Didcot OX11 0QX, U.K. 2

Summary. The use of x-ray lasers as probes of the opacity of hot dense plasma and rates of laser ablation is considered. It is shown that x-ray lasers are sufficiently bright to overcome plasma emission and enable plasma opacity to be measured. A demonstration experiment is presented where the temporal evolution of the opacity of a thin iron plasma at high temperature (30 – 250 eV) formed from an initially 50 nm thick solid tamped with a plastic overlay after heating by a laser pulse has been measured using the transmission of a nickel-like silver x-ray laser at 13.9 nm. The experimental results are compared to transmission calculations based on the iron opacity evaluated in a post-processor from predictions of the plasma conditions using a fluid and atomic physics code (EHYBRID). In another experiment, it is shown that laser ablation of a solid iron layer that is not tamped can be determined by the change in transmission of a 21.2 nm x-ray laser.

1 Introduction The opacity of plasmas is important in radiation diffusion models of the sun and other stars, in indirect drive laser fusion and in the interaction of free-electron lasers with material. Backlighters produced by the laser irra-

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diation of solid targets emit a broad spectral output in the x-ray and EUV range and have been used to measure the opacity of plasma material over a moderate spectral range determined by the detection diagnostics. Experimental results are often compared with theory after the convolution of the detecting instrumentation spectral resolution [1 – 5]. This approach is limited in the range of plasma parameters that can be probed as it is difficult for a broad bandwidth backlighter to be sufficiently bright to ‘outshine’ the plasma self-emission. For densities close to solid, only plasma opacities at temperatures less than approximately 50 eV have been successfully measured with a broad bandwidth backlighter. There is also a well-known saturation process that effects the transmission of a broad bandwidth radiation absorbed by line radiation [6, 7]. Here measured transmissions only decrease slowly with increasing optical depth and not approximately exponentially as with a narrowband backlighter. This can result in a superficially good agreement of theory and experiment as the transmission is largely independent of the optical depth. X-ray lasers are extremely narrowband (ν/Δν > 104) and bright (saturation flux ≈ 3 × 1010 Wcm-2) and hence can overcome the difficulties of probing the opacity of high density and temperature plasmas. We have undertaken a demonstration experiment showing that opacity can be measured using x-ray lasers and appropriate targets [8]. Results of this experiment and the interpretation of the results are reviewed in this paper. We also show that x-ray lasers can be used to measure the ablation of targets and present some initial results.

2 Experiment measuring the opacity of iron The experiment was undertaken using the VULCAN Nd:glass laser at the Rutherford Appleton Laboratory. The x-ray laser was generated at 13.9 nm from a 4d-4p transition in nickel-like silver by irradiating silver slab targets. Two 18 mm long slabs of silver were aligned 500 microns apart parallel to their surfaces and 150 microns apart perpendicular to their surfaces and each irradiated by three beams of energy 40 Joules, focused to a line of 22 mm length by 100 microns width. Irradiance on the targets was approximately 2.5x1012 Wcm-2 in the pre-pulse and 2.5x1013 Wcm-2 in the main pulse. Each of the six beams used to pump the x-ray laser comprised a 4 J pre-pulse, 2.2 ns ahead of the 40 J, 80 ps main pulse. The main pulse interacts with a long scale length plasma created by the prepulse to produce the conditions for x-ray laser gain. Using two 18 mm

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lengths of target ensures that the x-ray laser output is saturated, so that shot-to-shot variations are minimized.

3 pump beams on target

Heating beam 6J, 80ps

Spherical multi-layer mirror X-ray laser

CCD detector 6.8 m from mirror

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Fig. 1. Schematic of the experimental arrangement to measure the transmission of an x-ray laser pulse through a sample target. The x-ray laser beam is imaged onto the sample target that is also heated by an infra-red ‘heating’ laser pulse. The footprint of the x-ray laser at the sample target is imaged onto a CCD detector.

The x-ray laser output was imaged by a Mo-Si multi-layer mirror onto a sample target in order to measure the sample target opacity. The multilayer mirror was positioned 86 cm from the x-ray laser source to direct the beam to the opacity target, and focus it to an approximate diameter of 200 microns. A second spherical multi-layer mirror, positioned 36 cm downstream from the opacity target imaged the transmitted x-ray laser light onto a back-thinned Andor CCD camera, located 6.8 meters away (see figure 1). Baffling was placed at appropriate points to prevent unwanted light reaching the detector which was filtered with aluminum and parylene-N, each between 100 and 300 nm thick. The relatively narrow band-width of the multi-layer mirrors (~0.8 nm) also helped to remove unwanted light from reaching the detector. 100 micron diameter alignment cross-wires were placed in front of the CCD detector and are clearly visible in the images obtained (see figure 2).

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Fig. 2. Footprint of the x-ray laser at the sample target showing the most intense component of the x-ray laser beam passing through unheated sample target (the crescent shaped image to the left of the vertical cross wire) and the high transmission component of a less intense, but more uniform x-ray laser beam where the sample target has been heated by an infra-red pulse (bright image to the right of the vertical cross wire).

The sample targets comprised a 50 (±5) nm iron layer deposited on a 0.53 (± 0.05) micron parylene-N (CH) substrate foil and buried beneath an 80 (± 10) nm layer of parylene-N. The target normal was orientated at 45O to the x-ray laser probe beam. Another ~ 6 - 9 J pulse of 80 ps duration from the VULCAN laser was focused to a spot of diameter 100 microns at 45O incidence on the sample target in order to heat the iron layer. The sample targets were designed so that energy from the heating beam would be absorbed into the outer plastic layer, conductively heating the buried iron. This tamping slows down the rate of expansion of the iron layer to provide a plasma of improved uniformity and higher density. Radiative preheating of the buried layer can be ignored as the plastic top layer, once heated, is a weak emitter. Hot electron pre-heating at the employed irradiances (~1015 Wcm-2) is also small. The opacity of the heated and high density iron was determined by measuring the transmission of the x-ray laser beam through the sample target using the transmission through the unheated portion of the target as a reference for the x-ray laser output on each shot (see e.g. figure 2). After verifying the alignment of the x-ray laser through the sample target position to the CCD detector, the self-emission of the plasma produced by

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heating the sample target was investigated by recording the self-emission output without the x-ray laser pulse. Compared with the brightness of the x-ray laser probe, the self-emission was found to be negligible at ~100 counts compared with the peak transmission (~10000 counts) at the level of filtering used. The arrival of the sample target heating beam was adjusted to enable probing of the plasma at different times in its evolution (figure 3).

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Fig. 3. The transmission of the iron layer of the sample target as a function of time relative to the arrival time of the peak of an infra-red heating pulse. Different model predictions of the transmission are superimposed on experimental data points showing that the transmission as predicted by the York post-processor code correctly predicts the iron opacity with different infra-red laser pulse energies heating the iron.

Simulations of the transmission of the x-ray laser pulse are superimposed on figure 3. Details of the simulation are published elsewhere [8, 9], but in summary, it was found necessary to consider the opacity of a large number of spectral lines to obtain agreement with the experimental results. The plasma is dense and not too hot (e.g. at 100 ps the iron layer density is simulated as varying from 0.14 – 0.005 g cm-3 with the temperature from 30 – 320 eV) so collisional line broadening is large and lines from a broad wavelength range (~ ± 1 nm) contribute to the opacity. Due to the large spectral width of the absorbing lines, the precise wavelength of the x-ray laser does not affect the opacity and, furthermore, there is no information to be gained by a continuous sweep of the wavelength as could be under-

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taken with a free-electron laser. Further useful opacity measurements could be undertaken by repeating the experiment with lasing from other nearby elements (e.g. Ni-like In or Sn at 12.6 nm and 12 nm respectively), but a rapid variation of the opacity with x-ray laser wavelength is not predicted. The high spectral density of absorbing lines also causes the total opacity to be largely independent of the magnitude of the line broadening. The uniformity of the iron layer sampled by the x-ray laser could be significantly improved by undertaking the experiment with shorter duration heating pulses (~ 1 ps) and an x-ray laser pumped with short duration pulses. Simulations have shown that thin buried layers in massive targets can be heated uniformly with pulses of ~ 1 ps [10] and x-ray lasing output pulses of 3 ps duration have been measured [11, 12]. Heating a thin buried layer with a short duration pulse ensures that the plasma produced in the layer is uniform for a short time. The plasma can be probed with a short pulse duration x-ray laser while it is still uniform before significant expansion has occurred.

3 Laser ablation of solids Our measurement of laser ablation using x-ray laser transmission is based on code calculations showing that ablated hot plasma is close to fully transparent (see figure 4). A measurement of X-ray laser transmission through a target is then determined by the absorption of the cold solid thickness of material not ablated. Using ablation rate models, we can determine the instantaneous energy absorption during laser irradiation. The experiment was undertaken at the PALS laser facility. The X-ray laser at a wavelength of 21.2 nm arising from a 3d – 3p transition in Nelike zinc was produced using the PALS infra-red (1.315 μm) laser to irradiate a 3 cm long zinc slab [13]. Two separately pumped vacuum chambers, connected by a gate valve, were respectively dedicated to the production of the X-ray laser and the transmission of that beam through a laser irradiated thin metal foil. The X-ray laser was created by irradiating with a low energy (<2 J) pulse focussed to a 500 microns wide line, followed 10 ns later by the main pulse of 400 J, focussed to a line of width 100 μm. The long scale length pre-plasma with which the main pulse interacts provides good conditions for gain by reducing refraction effects, optimising the gain volume and maximising the absorption of the pump laser [14]. To improve further the brightness and uniformity of the X-ray laser beam, a half cavity mirror was installed and the re-injection point of the beam was carefully tuned to drive the laser emission further into saturation. Accurate

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pointing of the X-ray laser beam was achieved by making adjustments to the angle of the zinc target. These adjustments were small enough not to affect the line focus geometry of the pumping beams. Previous determinations indicate that the pulse duration of the X-ray laser is 90 (±10) ps [13] 1

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Fig. 4. The transmission at 21.2 nm as a function of temperature calculated by the TOPS code for iron at various densities ρ in gcm-3 (as indicated), but keeping the density-thickness product constant as for solid iron of 0.8 μm thickness. The transmission of the sample can be seen to rise rapidly with increasing temperature and decreasing density indicating that the heating effect acts like a switch with the opacity of the whole sample being dominated by the remainder of the solid iron beneath that ablated.

The second vacuum chamber contained two near-normal incidence spherical multi-layer mirrors and a plane 45O incidence multi-layer mirror designed to focus the X-ray laser beam onto the sample target in a spot of 1 mm diameter at normal incidence and to image the sample target plane to a CCD detector (Photonic Science CCD or a Princeton Instruments PIMTE CCD camera). The sample targets were heated using a third, separate 10 J, 300 ps laser pulse at 1.315 μm, focussed to a 100 μm diameter spot producing an irradiance of 3x1014 Wcm-2. A sample image of the Xray laser transmission through a target comprising 0.75 μm thickness of aluminium is shown in figure 5. The central region corresponds to the position of the ablating laser. The otherwise approximately uniform x-ray laser beam has greater transmission through the target here. The recorded flux of the X-ray laser beam in positions away from the infra-red irradiation can be used to measure the incident X-ray laser energy incident onto the sample target after allowance for the cold target transmission at 21.3

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nm and so enable a measure of the transmission of the X-ray laser beam through the ablated target. The time of arrival of this laser pulse was advanced or delayed relative to the other laser pulses producing the X-ray laser, allowing the sample target transmission and hence ablation to be probed in time (e.g. figures 6).

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Fig. 5. The footprint of the X-ray laser after it has passed through an ablated sample target of 0.8 μm aluminium. The bright zone in the centre corresponds to a higher transmission as the X-ray laser passes through the ablated region. Around the periphery, the target is unablated and therefore its transmission remains as for the initial thickness of target. The chequered pattern in the image is due to a nickel mesh on which a 163 nm thick aluminium filter was supported.

A fit of the transmission allowing for a reduction in the thickness of the solid target using an ablation model is superimposed on figures 6. The ‘deflagration’ model [15, 16] assumes that the laser energy absorption is localised at the critical density due to resonance absorption [17, 18] or enhanced inverse bremsstrahlung with a constant plasma temperature downstream of the critical density towards the laser. If the heat release is distributed over the plasma corona due to inverse bremsstrahlung, the ‘selfregulating’ model applies [19, 20]. Both models predict a similar x-ray laser transmission through targets as they are ablated, though the results with the deflagration model with 5% laser energy absorption are shown on figure 6.

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Fig. 6. The transmission of 21.2 nm laser light through a target comprising 50 nm of iron deposited onto a 0.8 microns thick aluminium substrate as a function of time from the peak of the heating pulse of duration 300 ps and peak irradiance 3x1014 Wcm-2. The curve shown is the calculated transmission through unablated target material assuming ablation according to a deflagration model with a Gaussian shaped laser pulse.

4 Conclusion The use of x-ray lasers as probes of the opacity of hot dense plasma and rates of laser ablation has been demonstrated. A demonstration experiment has been presented where the temporal evolution of the opacity of a thin iron plasma at high temperature (30 – 250 eV) formed from an initially 50 nm thick solid tamped with a plastic overlay after heating by a laser pulse has been measured using the transmission of a nickel-like silver x-ray laser at 13.9 nm. The experimental results are compared to transmission calculations based on the iron opacity evaluated in a post-processor from predictions of the plasma conditions using a fluid and atomic physics code (EHYBRID). In another experiment, it has been shown that laser ablation of

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a solid iron layer that is not tamped by an overlay can be determined by the change in transmission of a 21.2 nm x-ray laser as material is ablated.

Acknowledgements Funding from the United Kingdom EPSRC, CCLRC and MoD and the European Laserlab Europe is gratefully acknowledged.

References 1. J M Foster et al 1991 Phys. Rev. Lett. 67, 3255. 2. T S Perry et al 1991 Phys. Rev. Lett. 67, 3784. 3. L B Da Silva et al 1992 Phys. Rev. Lett. 69, 438. 4. P T Springer et al 1992 Phys. Rev. Lett. 69, 3735. 5. C Chenais-Popovics et al 2000 Astrophys. J. Suppl Ser. 127, 275. 6. C A Iglesias 2006 JQSRT 99, 295. 7. R L Bowers and T Deeming 1984 ‘Astrophysics I’ (Wadsworth, Boston). p134. 8. M H Edwards et al 2006 Phys. Rev. Lett. 97, 035001. 9. D Whittaker and G J Tallents in preparation. 10. S J Davison, et al 2000 JQSRT 65, 151. 11. A Klisnick et al 2002 Phys. Rev. A65, 033810. 12. Y Abou-Ali et al 2003 Optics Commun. 215, 397-406. 13. B Rus, et al Phys. Rev. A 66 063806 (2002). 14. G J Tallents, J. Phys. D36, R259 (2003). 15. C Fauquignon and F Floux, Phys. Fluids 13, 386 (1970). 16. J L Bobin, Phys. Fluids 14, 2341 (1971). 17. D W Forslund, J M Kindel and K Lee, Phys. Rev. Lett. 39, 284 (1977) 18. U Teubner et al, Phys. Rev. Lett. 70, 794 (1993). 19. A Caruso, B Bertotti and P Giupponi, Nuovo Cimento 45, 176 (1966). 20. H Puell, Z. Naturforsch. 24a, 1807 (1970).

Applications of Focused X-Ray Laser at 21 nm in High-Energy Density Experiments T. Mocek1, B. Rus1, M. Kozlová1, J. Polan1, P. Homer1, M. Stupka1, L. Juha1, V. Hájková1, S. Koptyaev1, J. Chalupsky1, J. Feldhaus2, H. Wabnitz2, N. Booth3, Z. Zhai3, M. Edwards3, and G.J. Tallents3 1Institute of Physics, PALS Centre, Prague, Czech Republic 2Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany 3University of York, York, U.K.

Summary. We report on the generation of a focused X-ray laser beam with high energy density. The output of the 21.2 nm X-ray laser at PALS containing energy of 4 mJ was focused down to 20 x 40 μm2 elliptical spot. Samples of various solids were irradiated by the focused X-ray laser beam at various fluences. Feasibility of single-shot projection ablation lithography has been explored. First measurement of the XUV opacity of volumetrically heated thin foil by the focused X-ray laser has been performed.

1 Introduction Currently the most energetic X-ray laser (XRL) at 21 nm has been developed at the Prague Asterix Laser System (PALS) Centre [1]. This quasisteady-state XRL is based on collisional excitation pumping in Ne-like Zn plasma and operates in a double-pass regime using a flat Mo:Si multilayer mirror placed close to one end of the 30 mm long XRL amplifier [2]. Under optimum conditions, a highly symmetric ellipsoidal beam at 21.2 nm, with horizontal and vertical divergence of 4 mrad and 6 mrad, respectively, is generated. The combination of high output energy and narrowly collimated smooth XRL beam profile [3] gives a prospect for focusing the XRL beam to produce irradiance of about 1012 Wcm-2 which is comparable to that employed in conventional interaction experiments with optical high-power lasers, resulting in conversion of solid matter to a highly ionised plasma relevant to stellar astrophysics and warm dense matter. Recently, we focused the 21.2 nm XRL using a spherical mirror and reached energy density of about 48 Jcm2 [4]. This largely exceeds the threshold for

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ablation of various materials and opens up the way towards single-shot nano-structuring of solids by the XRL.

2 Ablation of solids at 21 nm The major motivation for studies of material ablation consists in the possibility to obtain first-ever data about the ablation rate and the processes involved in ablation in the soft X-ray spectral region, and in prospects for applications where large energy fluence is involved. These include direct nano-structuring, design of coatings of optical elements, and choice of the “first wall” materials for future fusion devices. Samples of various solid materials were irradiated by the XRL beam focused down to a spot with size of typically ~40 µm, in a setup involving a single (f = 254 mm) spherical or off-axis parabolic mirror. The irradiated surfaces were then investigated by Nomarski optical (DIC – differential interference contrast) microscopy and atomic force microscopy (AFM) using a BX51M DIC microscope (Olympus, Japan) and a Dimension 3100 scanning probe microscope (SPM) driven by a NanoScope IV controller (Veeco, USA). AFM was operated in a tapping mode. Thin Al filters were employed to appropriately adjust the intensity of the focused XRL beam. Figure 1 provides a qualitative comparison of craters ablated in different materials by single XRL pulse at the fluence of 10 J/cm2. Fig. 1(a) shows the AFM image of a ~300-nm deep crater ablated in thin (500 nm) layer of poly(methyl methacrylate)-PMMA deposited on a 315-μm thick silicon substrate (Silson, UK). The corresponding cross section is in Fig. 1(b). Besides exhibiting very good shot-to-shot reproducibility, all ablated patterns in PMMA revealed good azimuthal symmetry, high-quality surfaces, and cleanly cut walls with well developed sharp edges, not affected by thermal damage. The clean ablation is attributed to strong localization of the absorbed energy at 21 nm, i.e., both the attenuation and the thermal diffusion lengths amount to tens of nanometers only. In contrast to optical and ultraviolet radiation, at soft x-ray wavelengths the energy of a single photon is sufficient to make a significant damage in polymers. In contrast, Fig. 1(c) displays a crater produced by the XRL beam in monocrystalline Si (100, bulk), showing that the rim of the crater was formed by melted matter ejected out from the XRL impact region. This is compared to the response of a 78 nm thick layer of amorphous-Si (a-Si) deposited on a glass substrate, which has been completely blown off under identical irradiation conditions (Fig. 1(d)).

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We have also investigated radiation damage of thin films of amorphous carbon (a-C) deposited on Si substrate (Figs 1(e), 1(f)). In this case, graphitization and thermal expansion of the material occurs, i.e. no crater is generated. With increasing fluence the height of expanded material increases.

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Fig. 1. AFM images of craters ablated in various materials by the focused X-ray

laser beam at the fluence of 10 J/cm2: (a) PMMA (500 nm), (b) cross section of the crater in PMMA, (c) monocrystalline Si (bulk), (d) a-Si (78 nm), (e) a-C (890 nm), and (f) a-C (46 nm).

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To determine the ablation threshold and radiation attenuation length we have chosen the Liu’s method [5] which allows to estimate both the ablation threshold as well as focal spot diameter. Systematic analysis of the data is currently underway.

3 Feasibility test of projection ablation lithography The above results represent the first observation of material ablation with a laser at the wavelength shorter than 29 nm [6,7]. In particular, the clean ablation of PMMA gives a good prospect to obtain high aspect ratio microstructures using the 21-nm XRL radiation. Therefore we have performed a pilot experiment (Figure 2) aimed to imprint a simple lateral structure to the PMMA resists assessing the potential of a single-shot ablation lithography in the soft X-ray region.

Fig. 2. Experimental setup for single-shot projection ablation lithography at 21 nm.

The object was a 10 μm thick Ni mesh (G250, GilderGrid) with bar/gap of 30/70 μm which has been demagnified (9 x) by means of an off-axis parabolic mirror (f = 254 mm) and projected on PMMA. Figure 3 shows an AFM image of the mesh ablated in PMMA. The crater is about 60 nm deep, with high aspect ratio and cleanly cut walls. However, some imperfections can be also seen – the reason is just poor quality of the mesh itself.

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Fig. 3. AFM image of a Ni mesh projected and ablated by the 21.2 nm X-ray laser in PMMA.

4 Study of volumetrically heated plasma The nature of the interaction of intense ionising soft x-ray radiation with matter is supposed to be qualitatively different from that occurring when the target is heated by an infrared or optical laser. The critical electron density for the 21.2 nm radiation is as high as 2.5 x 1024 cm-3. This implies that the plasma generated in this interaction will be always subcritical, and the XRL radiation will interact directly with the solid target. This may be illustrated by considering thin (0.5 μm) foil of Al as a target. Assuming the extreme case in which plasma of a density equal to that of the solid state would be generated, and under complete ionisation conditions, the maximum possible electron density amounts to 7.8 x 1023 cm-3. The XRL beam will penetrate through the material, being volumetrically absorbed, and heat the foil matter (solid or ionised) to its full thickness. The foil material will thus be volumetrically converted into a plasma state having fairly uniform density profile across the foil. Such plasma and its absorption properties is completely unexplored topic both theoretically and experimentally.

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Al

Fig. 4. Experimental setup for investigation of X-ray absorption.

(a)

(b)

Fig. 5. Spatial distribution of the 21-nm laser transmitted through 500-nm thick Al foil at intensities (a) 1 x 1011 Wcm-2, and (b) 2 x 1012 Wcm-2.

Figure 4 shows schematic of the experiment aimed at direct measurement of transmission of high-intensity (up to 4 × 1012 Wcm-2) X-ray emission at 21 nm in thin foils. The XRL was focused by a spherical (f = 250 mm) Mo:Si multilayer mirror onto a sample target (aluminum or polyimide). A second spherical (f = 250 mm) multilayer mirror imaged the transmitted XRL light onto a backside illuminated CCD camera (Roper Scientific, PI MTE) with magnification of about 10. Figure 5 shows measured spatial distribution of the XRL transmitted through 500 nm thick Al foil for two different X-ray intensities. The data clearly demonstrate lower absorption

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of Al for higher X-ray intensity. Quantitative analysis is in progress. Note that the focused XRL was strong enough to burn a hole in the thin foils under investigation (Fig. 6).

Fig. 6. Hole drilled by a single shot of XRL (1 mJ) in 500-nm thick Al foil. The size of hole is 50 mm x 45 mm.

Acknowledgements This work was partially supported by the European Comission under contract No. MERG-CT-2004-011681, by the Centres of Fundamental Research projects LC528 and LC510 of the Czech Ministry of Education, and by the Grant Agency of the Czech Republic under project No. 202/05/2316. This work also benefited from the EU Transnational Access to Research Infrastructures grant HPRI-00108.

References 1. Jungwirth, K. et al.: ‘The Prague Asterix Laser System’, Phys. Plasmas 8, 2495-2501, 2001. 2. Rus, B. et al.: ‘Multimillijoule, highly coherent x-ray laser at 21 nm operating in deep saturation through double-pass amplification’, Phys. Rev. A 66, 063806, 2002. 3. Mocek, T. et al.: ‘Beam properties of a deeply saturated, half-cavity zinc soft X-ray laser’, J. Opt. Soc. Am. B 20, 1386-1391, 2003. 4. Mocek, T. et al.: ‘Focusing a multimillijoule soft x-ray laser at 21 nm’, Appl. Phys. Lett. 89, 051501, 2006. 5. Liu, J.M.: ‘Simple technique for measurements of pulsed Gaussian-beam spot sizes’, Opt. Lett. 7, 196-198, 1982.

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6. Mashiko, H. et al.: ‘Focusing coherent soft-x-ray radiation to a micrometer spot size with an intensity of 1014 W/cm2’, Opt. Lett. 29, 1927-1929, 2004. 7. Benware, B.R. et al.: ‘Focusing of a tabletop soft-x-ray laser beam and laser ablation’, Opt. Lett. 24, 1714-1716, 1999.

Mass Spectroscopy of Neutral Metal Oxide Clusters Using a Desk-Top Soft X-Ray Laser F. Dong1, S. Heinbuch2, E.R. Bernstein1 and J.J. Rocca2,3 NSF ERC for Extreme Ultraviolet Science and Technology, Colorado State University, 1 Department of Chemistry, 2 Department of Electrical and Computer Engineering, and 3 Department of Physics

Summary. We report the use of a compact 46.9 nm capillary discharge soft x-ray laser in the study of metal-oxide nanoclusters using mass spectroscopy. Transition metal oxides are widely used as heterogeneous catalysts and catalytic supports in industrial processes. There are numerous applications for transition metal oxide catalysts, and although they are widely used, there is a lack of fundamental understanding of the complicated processes that occur on the metal oxide surface during catalysis. Conventional nanocluster spectroscopy techniques have used 193 nm radiation from an ArF excimer laser corresponding to a photon energy of 6.4 eV in order to photoionize a sample. Typical metal oxide nanocluster ionization energies fall into the range of 7-12 eV while some have even higher energies. Therefore a single 6.4 eV photon can not ionize the cluster making multiphoton processes the dominant ionization method. A major problem associated with mass spectroscopy can become evident during the multiphoton ionization of clusters. Specifically, the clusters may fragment during the ionization process and the identification of the neutral parent cluster can become difficult. In the present experiment neutral vanadium, niobium and tantalum oxide clusters are studied by single photon ionization with the 26.5 eV photons produced by a capillary discharge soft x-ray laser.1 During ionization, the metal oxide clusters are observed to be almost free of serious fragmentation. The most stable neutral cluster of vanadium, niobium, and tantalum oxide growth in a saturated oxygen condition are identified as MO2, M2O4/M2O5, M3O7, M4O10, M5O12, M6O15, M7O17, M8O20, and M9O22, which can be represented as a form (MO2)0,1(M2O5)y. M2O5 is identified as a basic unit to build-up the three kinds of metal oxide clusters. In the case of niobium and tantalum oxide clusters, the oxygen-deficient clusters with a structure of (MO2)2(M2O5)y are detected for groups that contain an even number of metal atoms. For vanadium oxide clusters, the oxygen-deficient clusters are detected for every family, indicating a stable structure of (VO2)x(V2O5)y. The stoichiometry of oxygen-rich clusters can be expressed as (MO2)0,1(M2O5)yO1-3 and their structures are consistent with chemically bonded species.

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1 Introduction Transition metals, as well as their oxides, carbides, nitrides, and sulfides, are unique in their abilities to catalyze chemical reactions, primarily due to their multiplicity of low energy surface electronic states, which can readily donate and/or accept electrons in the process of making or breaking bonds at a surface.2 Transition metal oxides are employed extensively as catalysts in the chemical industry, for example, vanadium oxide catalysts are used in the generation of sulfuric acid. The microscopic properties of specific local catalytic sites and the mechanisms for catalytic activity of these metal oxide catalysts are still not elucidated. Catalytic properties of a material (activity, selectivity, and stability) are in general determined by chemical (electronic) properties of surface atoms/molecules.3,4 Metal/metal oxide clusters generated in the gas phase are considered to be an ideal model system for the local surface of the condensed/surface phase because of their relatively well defined structures, size dependent properties, and their relative ease of accessibility by theory. To explore the reactivity and behavior of metal and metal oxide clusters, one must first understand their neutral cluster distributions, growth patterns and pathways, structures, and electronic properties. Neutral metal oxide clusters tend to have high ionization energies (8 < IE < 10 or more eV) especially for oxygen rich clusters. Due to this high ionization energy, the clusters require multiphoton absorption in order to be detected by mass spectroscopy techniques. Using this technique, cluster fragmentation, and thus loss of neutral cluster distribution information, is often the end result.5,6 In the present experiment, neutral metal oxide clusters of vanadium, niobium, and tantalum are studied by single photon ionization at 26.5 eV. The structure and formation of these clusters are discussed in detail in ref. 8. Compared with 193 and 118 nm ionizations, single photon ionization by 46.9 nm radiation from the Ne-like Ar capillary discharge soft x-ray laser provides more information about the distributions and growth mechanisms of neutral metal oxide clusters with little fragmentation. Oxygen rich neutral clusters are detected for the first time and are found to have up to three attached hydrogen atoms. U

U

U

U

2 Experimental Procedures Since the experimental apparatus has been described in detail elsewhere,7 only a general outline of the experimental scheme will be presented in this

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report. Briefly, vanadium, niobium, and tantalum oxide neutral clusters are generated in a conventional laser vaporization/supersonic expansion cluster source by laser ablation of vanadium, niobium, or tantalum metal foil into a carrier gas mixed with 5% O2 at 80 psig. Pure metal clusters can also be generated by laser ablation of the metal into a pure He (99.995%) expansion gas. A 532 nm wavelength laser (second harmonic of a Nd/YAG laser, 1064 nm) is employed to ablate the metals at 5 to 10 mJ/pulse. Ions created in the metal ablation/metal oxide growth process are removed from the supersonic expansion by an electric field outside the nozzle in the vacuum system. Neutral clusters pass through a skimmer with a 4 mm aperture into the ionization region of a time of flight mass spectrometer. The clusters are ionized with a 46.9 nm capillary discharge soft x-ray laser. The soft x-ray laser (26.5 eV/photon energy) emits pulses of about 1 ns duration pulses with an energy of about 10 μJ at a repetition rate of up to 12 Hz. A time of flight (linear/reflectron) mass spectrometer (TOFMS) (Figure 1a) is employed for mass analyzer. A pair of mirrors placed in a Z-fold configuration just before the ionization region of the TOFMS provides alignment and focusing capabilities for the laser with respect to the molecular cluster beam at the focus of the TOFMS in the ionization region. The Z-fold mirror system has a transmittance of about 10%. Since the 26.5 eV photons from the soft x-ray laser (Figure 1b) are able to ionize the He carrier gas employed in the expansion, the microchannel plate (MCP) ion detector voltage is gated to reduce the gain of the MCP when He+ arrives at the mass detector in order to prevent detector circuit enclosed and saturation.

Cluster Source/Gas Nozzle

TOFMS

Soft X-ray Laser

Fig. 1. (a) Schematic of the reflectron time of flight mass spectrometer (TOFMS). (b) Schematic of the 46.9 nm capillary discharge, soft x-ray laser.

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3 Results and Discussion For the sake of brevity, a discussion of results pertaining only to tantalum will be presented. A deeper discussion, as well as a full report of all 3 cluster systems can be found in ref. 8. 3.1 Distribution of Ta Oxide Clusters Figure 2a displays a TOF mass spectrum of TamOn clusters generated with 5% O2/He expansion using two different wavelengths for ionization. In Figure 2a, only Ta+, TaO+, and TaO2+ are observed for ionization with 193 nm laser radiation. The VIE of TaO and TaO2 is about 8 and 9 eV, respectively. These ion signals must be generated through multiphoton ionization. The absence of larger clusters in this mass spectrum implies a great deal of fragmentation during the multiphoton ionization process(es).

a)

b)

Fig. 2. TOF mass spectra of tantalum oxide clusters ionized by two different wavelengths, (a) 193 nm multiphoton ionization, and (b) single photon ionization of 46.9 nm soft X-ray laser.

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Figure 2b shows a mass spectrum of TamOn clusters obtained with 26.5 eV (46.9 nm) single photon ionization from the soft X-ray EUV laser. As shown, cluster ion signals are generated for species with up to 9 Ta atoms, TaO+ and Ta+ display very small signals, and the observed features are quite sharp (ca. 10 – 20 ns). Even highly oxygen rich clusters such as TaO4,5 are detected in the low mass region. Note that Ta+ is not observed and that only very small TaO+ signal is observed. 3.2 Structure and Formation of Neutral Clusters It is observed that the most common bulk stoichiometry for group 5 (V, Nb, Ta) transition metal oxides is M2O5, indicating that the metal has an effective oxidation state of +5 with +4 also a viable state in oxides such as VO2 and V2O4. MO2 and M2O5 are thereby reasonable suggestions for the main building blocks for these metal oxide cluster series. As shown in Figure 3, stoichiometry of the most stable metal oxide clusters (that is, most intense mass spectral features) can be expressed as (MO2)0,1(M2O5)y. One can conclude that an M2O5 unit is the basic building block for the main cluster family (Mm) feature, with only at most one MO2 unit appearing in clusters of the most stable stoichiometry. Based on the premise that 26.5 eV photons do little in the way of cluster fragmentation and that 26.5 eV photons can ionize any species in the expansion, the TOF mass spectra at 26.5 eV ionization presents the important advantage of displaying all clusters and both their neutral and cation populations.

Fig, 3. Distribution of the most stable and oxygen-deficient clusters for tantalum. MO2 and M2O5 are used as basic units to build the oxide clusters.

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4 Conclusions The 26.5 eV single photon ionization made possible by a capillary discharge soft x-ray laser is shown to be an excellent diagnostic for neutral cluster distribution in general for all varieties of clusters from van der Waals, to hydrogen bonded 7 , to metal, and covalent metal oxide systems. The mass spectra suggest that during the ionization process(es) nearly all the excess energy above the VIE of the cluster is removed by the exiting photoelectron. A comparison between 10.5 and 26.5 eV ionization was made to show that the results of both methods of ionization are similar , except that 26.5 eV ionization has the significant advantage of finding all species present in the sample. Most importantly this ionization approach has found oxygen rich clusters and oxygen rich clusters with added hydrogen that have not previously been identified for laser ablation metal oxide clusters. Systematics for Nb and Ta systems can be established while V containing clusters seem to have a more varied chemistry of oxygen rich and deficient clusters for all families (Mm) of metal containing species. Nb and Ta clusters show oxygen deficient species only for Mm with m even.

Acknowledgment This work was supported by the NSF ERC for Extreme Ultraviolet Science and Technology under NSF award number EEC-0310717.

References 1. S. Heinbuch, M. Grisham, D. Martz, and J.J. Rocca, “Demonstration of a desk-top size high repetition rate soft x-ray laser”, Optics Express 13, 4050, (2005) 2. G.A. Somorjai, Introduction to Surface Chemistry and Catalysis. Wiley, New York, Chap 7. 3. D. W. Goodman, “Model catalysts: from imagining to imaging a working surface,” J. Catal. 216, 213 (2003). 4. G.A. Somorjai, “The evolution of surface chemistry. A personal view of building the future on past and present accomplishments,” J. Phys. Chem. B, 106, 9201 (2002). 5. D. N. Shin, Y. Matsuda, and E. R. Bernstein, “On the iron oxide neutral cluster distribution in the gas phase. I. Detection through 193 nm multiphoton ionization,” J. Chem. Phys. 120, 4150 (2004).

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6. M. Foltin, G. J. Stueber, and E. R. Berstein, “On the growth dynamics of neutral vanadium oxide and titanium oxide clusters,” J. Chem. Phys. 111, 9577 (1999). 7. F. Dong, S. Heinbuch, J. J. Rocca, and E. R. Bernstein, “Dynamics and fragmentation of van der Waals clusters: (H2O)n, (CH3OH)n, and (NH3)n upon ionization by a 26.5 eV soft x-ray laser,” J. Chem. Phys. 124, 224319 (2006). 8. F. Dong, S. Heinbuch, J. J. Rocca, and E. R. Bernstein, “Formation and distribution of neutral vanadium, niobium, and tantalum oxide clusters: single photon ionization at 26.5 eV, J. Chem. Phys (2006), in press.

Soft X-Ray Laser Interferometry of Colliding Al Plasmas in a Semi-Cylindrical Cavity J. Grava, M. Purvis, J. Filevich, M.C. Marconi and J.J. Rocca NSF ERC for Extreme Ultraviolet Science and Technology and Dept. of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO 80523, USA E. Jankowska Wroclaw University of Technology, 50-370 Wroclaw, Poland J. Dunn and S.J. Moon Lawrence Livermore National Laboratory, Livermore, CA 94551, USA V.N. Shlyaptsev University California Davis-Livermore, Livermore, CA 94551, USA

Summary. Soft x-ray laser interferometry was used to study the evolution of dense colliding plasmas produced by laser irradiation of semi-cylindrical targets. We present a series of interferograms that map the evolution of 1 mm long Aluminum plasmas created by irradiating 500 µm diameter semi-cylindrical targets with an intensity of ~1.1×1012 Wcm-2 from 120 ps duration laser pulses of 800 nm wavelength. The interferograms were obtained combining a 46.9 nm tabletop capillary discharge soft x-ray laser with a high throughput amplitude division interferometer based on diffraction gratings. The interferograms show that the plasma expands converging on the axis of the semi-cylindrical cavity where it reaches electron densities above 1×1020 cm-3. The code HYDRA was used to simulate the plasmas expansion and give insight on the plasma dynamics.

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1 Introduction The study of dense colliding plasmas is relevant to both fundamental plasma physics and applications. It is of particular interest in the case of the indirect drive scheme of inertial confinement fusion [1, 2], where a better understanding of plasmas created by irradiating a cylindrical cavity is important. The experimental data can also be used to benchmark computer codes. In particular, the modeling of colliding plasmas requires density data for various geometries and irradiation conditions. In this paper, we report results of an experiment designed to study the evolution of dense converging aluminum plasmas created by irradiating a semi-cylindrical target with an intensity of 1.1×1012 Wcm-2 achieved by focusing 800 nm wavelength laser pulses of 120 ps duration and ~600 mJ of energy. A series of high contrast soft x-ray laser interferograms are presented and compared with simulations performed using the 2D code HYDRA.

2 Experimental Setup The plasma was probed using a table-top 46.9 nm capillary discharge soft x-ray laser [3] combined with an amplitude division soft x-ray interferometer [4]. The interferometer uses a skewed Mach-Zehnder configuration with gold-coated diffraction gratings as beam splitters. The interferometer and its alignment procedure are described extensively in previous publications [4,5]. The probe beam is generated by a compact 46.9 nm Nelike Ar capillary discharge laser delivering pulses of ~1 ns duration and ~0.15 mJ of energy. The good spatial coherence of the soft x-ray laser assists the generation of interferograms with high fringe visibility. The pulse used to create the colliding plasma was produced by a Ti: Sapphire laser operating at 800 nm. This Ti: Sapphire laser consists of a mode-locked oscillator with three stages of amplification, yielding up to 2 J in 120 ps pulses. A vacuum spatial filter is used to smooth the beam. The pulse is then focused on target to a 310 µm spot by a 7 m focal length spherical lens, and shaped into a 1.5 mm line using a pair of cylindrical lenses (equivalent to a single cylindrical lens with variable focal distance). This line focus is monitored on every shot by a reflection from a beam splitter onto a CCD camera. The targets used in this experiment consist of semi-cylindrical cavities 500 µm in diameter machined on the edge of a 1 mm thick pure Al slab spaced by 1 mm. The target is placed in the path of the zero order arm of the interferometer between the long mirror and the second grating. The target is mounted on a motorized stage, enabling pre-

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cise positioning with respect to the probe beam. The irradiation optical laser beam is focused inside the semi-cylinder cavity while the probe beam propagates along the axis of the semi-cylindrical target.

3 Results and Discussion Figure 1 shows a sequence of soft x-ray interferograms describing the evolution of the plasmas created by irradiating the half-cylinder Aluminium cavities with an intensity of 1.1×1012 Wcm-2. Each interferogram was taken under the same conditions, moving the target to a new groove after one to two shots to minimize surface effects created by ablation. The line focus was made 1.5 mm long to overfill the target, producing a more uniform illumination and minimize edge effects. Figure 2 shows the corresponding electron density maps obtained from the fringe shift analysis assuming that the plasma is uniform along the probe axis. This assumption is justified by the smooth long line focus irradiation used to heat the plasma. We also assume that only the free electrons contribute to the index of refraction of the plasma [6]. The time is measured with respect to the peak of the 120 ps irradiation pulse. The early interferograms show the creation of the plasma close to the surface of the target. As time evolves, the plasma expands away from the wall, converging in a small region on the axis of the cavity. This collision develops as early as 1.5 ns, with electron densities increasing to above 1020 cm-3. In figure 2, in the 2.6 ns frame there exists a small region, distinguished by white shading, in which we were not able to resolve the density from the interferogram shown in figure 1, most likely due to motion blurring or very steep density gradients. The plasma was modeled with HYDRA, a 3D single fluid radiation hydrodynamics code that is currently being used to simulate targets designed for NIF [7]. We operated the code in 2D utilizing a mesh made up of arbitrary quadrilaterals. Because of our long uniform line focus we are able to use 2D simulations to accurately describe the behavior of these colliding plasmas. Inverse Bremstraung absorption is the dominant laser deposition mechanism at our irradiation conditions. Radiation transport within the plasma is treated using multi-group diffusion techniques which utilize tabular opacities and heat conduction was simulated using the conductivities of Lee and More [8]. The equations of state as well as the opacities are modeled using Lawrence Livermore National Labs LEOS. HYDRA is capable of running in Lagrangian mode or an Arbitrary Lagrangian Eulerian (ALE) hydrodynamic mode. We chose a grid motion strategy to run fully Lagrangian during the duration of the laser pulse and afterwards, when the

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Fig. 1. Sequence of soft x-ray laser interferograms describing the evolution of plasmas created by irradiating a semi-cylindrical Al cavity following irradiation by a 120 ps pulse with an intensity of 1.1×1012 Wcm-2. Time delays are measured with respect to the peak of the irradiation laser beam (incident from the right). The large number of fringe shifts close to the axis of the groove is indicative of a high density region created by the converging plasma.

laser is off, we allow the grid to ALE. This strategy helped to avoid asymmetries in the laser deposition and to deposit the laser energy uniformly. The code shows that the peak electron density and electron temperature (~50 eV) within the cavity occur a few ns after laser irradiation after the plasma has had time to expand and converge. HYDRA reveals that a peak density of 1.1x1020 cm-3 away from the wall occurs at around 2.6 ns. In the experiment we see that the peak density also occurs near this time and that the peak plasma density matches well the simulated values. In both the measurements and the simulations the electron density remains high in the region of plasma convergence for the few ns, and subsequently is observed to relax as the plasma expands and cools. The good agreement between the experimental results and the simulations with the fluid codeHYDRA, which does not model interpenetration, confirm that these plasmas collide and stagnate on axis without significant interpenetration.

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Fig. 2. Measured (left) and simulated (right) electron density maps corresponding to the interferograms of figure 1.

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Acknowledgment This research was sponsored by the National Nuclear Security Administration under the Stewardship Science Academic Alliances program through U. S. Department of Energy Research Grant #DE-FG52-06NA26152. Part of this work was performed under the auspices of the U.S. Dept. of Energy by the University of California, Lawrence Livermore National Laboratory through the Institute of Laser Science and Application, under contract No. W-7405-Eng-48. The CSU researchers also gratefully acknowledge the use of facilities from the NSF ERC Center for Extreme Ultraviolet Science and Technology, award EEC-0310717.

References 1. 2.

3. 4. 5.

6.

7. 8.

J. D. Lindl, Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain, Phys. Plasmas, 1995. 2: p. 3933. T. R. Dittrich, S. W. Haan, M. M. Marinak, S. M. Pollaine, D. R. Hinkel, D. H. Munro, C. P. Verdon, G. L. Strobel, R McEachern, R. C. Cook, C. C. Roberts, D. C. Wilson, P. A. Bradley, L. R. Foreman, W. S. Varnum, Review of indirect-drive ignition design options for the National Ignition Facility, Phys. Plasmas, 1999. 6: p. 2164. B. R. Benware, C. D. Macchietto, C. H. Moreno, J. J. Rocca, Demonstration of a high average power tabletop soft x-ray laser. Physical Review Letters, 1998. 81 (26): p. 5904-5807. J. Filevich, K. Kanizay, M. C. Marconi, J. L. A. Chilla, J. J. Rocca, Dense plasma diagnostics with an amplitude-division soft x-ray laser interferometer based on diffraction gratings, Optics Letters, 2000. 25 (5): p. 356-358. J. Filevich, J.J. Rocca, M.C. Marconi, R.F. Smith, J. Dunn, R. Keenan, J.R. Hunter, S.J. Moon, J. Nilsen, A. Ng, and V.N. Shlyaptsev, “Picosecondresolution soft-x-ray laser plasma interferometry”, Applied Optics 43, 3938, (2004). J. Filevich, J. Rocca, M.C. Marconi, S.J. Moon, J. Nilsen, J.H. Scofield, J. Dunn, R.F. Smith, R. Keenan, J.R. Hunter, Observation of a Multiply Ionized Plasma with Index of Refraction Greater than One. Physical Review Letters, 2005.94, (035005). M. M. Marinak, G. D. Kerbel, N. A. Gentile, O. Jones, D. Munro, S. Pollaine, T. R. Dittrich, and S. W. Haan, Three-dimenional HYDRA simulations of National Ignition Facility targets, Phys. Plasmas, Vol. 8, 2001 Y.T. Lee and R. M. More, An electron conductivity model for dense plasmas, Phys. Fluids 27 (1984): p. 1273

Single Photon Ionization Mass Spectroscopy of Hydrogen Bonded and van der Waals Cluster Systems Using a Capillary Discharge Soft X-Ray Laser S. Heinbuch2, F. Dong1, E.R. Bernstein1 and J.J. Rocca2,3 NSF ERC for Extreme Ultraviolet Science and Technology, Colorado State University, 1 Department of Chemistry, 2 Department of Electrical and Computer Engineering, and 3 Department of Physics3

Summary. We report the first use of a soft x-ray laser in photochemistry studies. A 46.9 nm capillary discharge soft x-ray laser was used to study hydrogen bonded and van der Waals cluster systems. The study of van der Waals cluster formation and growth in the gas phase can contribute to the understanding of solvation processes, solvation dynamics, and the nucleation and growth of small clusters. The comparative investigation of water, methanol, and ammonia clusters is of importance because these clusters demonstrate a wide range of van der Waals interactions and hydrogen bonding: water clusters are very strongly and dominantly hydrogen bonded; methanol clusters somewhat less so; and ammonia clusters perhaps not at all. Sulfur dioxide is the major contributor to acid rain and a generator of soot. The process of SO2 and water forming acid rain has been studied for some time in order to determine the atmospheric mechanism for this environmental issue. Carbon dioxide is the major gas phase pollutant responsible for the “green house effect” of the atmosphere. Many experiments employing supersonic expansion coupled with mass spectroscopic detection have been conducted in order to study monomeric and clustered structure and behavior of each of these systems. Spectroscopic and photochemical properties of the systems should be related to cluster structure. However, one of the most serious problems in the investigation of the distribution of neutral hydrogen-bonded and van der Waals clusters is the fragmentation or the intra-cluster ion-molecule reactions to the protonated cluster ions. Electron Impact (EI) ionization usually suffers considerably from fragmentation of parent cluster ions on account of the large excess energies during the ionization process. Multiphoton ionization (MPI) processes result in the predissociation of the neutral clusters before ionization. Single photon ionization is a more “gentle” way to study hydrogen-bonded and Van der Waals clusters since less fragmentation of the parent cluster ions occurs compared to EI and MPI ionization. We have used the 26.5 eV from a desk-top size Ne-like Ar capillary soft xray laser to do chemical cluster dynamics studies. A single photon from this laser is sufficient to ionize any cluster, molecule, or, even He atoms.

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1. Experimental Procedures The apparatus used in this experiment includes a time of flight (linear/reflectron) mass spectrometer (TOFMS) and a capillary discharge soft x-ray laser1 as an ionization source for the mass analyzer. Neutral clusters are generated in a supersonic expansion of desired gases (NH3, SO2, or CO2/He mixture) from a pulsed nozzle (200 μm diameter opening). During operation, saturated water or methanol vapor in He is formed by flowing He (99.9% General Air) at a pressure of 25 psi through a reservoir containing liquid distilled water or methanol (spectroscopic grade) at room temperature. Neutral clusters are ionized by the 26.5 eV soft x-ray laser photons and are accelerated toward a microchannel plate (MCP) detector in the same manner as described in ref. 2, and 3. Experiments are conducted to ensure that collision induced dissociation of clusters ion is negligible.

2. Summary of Results Protonated water clusters up to n = 60 are observed in mass spectra (figure 1). Intensity of these cluster ions decreases roughly exponentially with increasing cluster size. The parent water cluster ion does not show any special signal (“magic number”) intensity at (H2O)21H+, and the enhanced intensity at n = 21 is due to the fast dissociated of (H2O)22H+ in the drift tube. A small signal of unprotonated water dimer ion is observed if pure He is used as the carrier gas for the supersonic expansion. This unprotonated dimer signal intensity increases if the concentration of Ar in the carrier gas is increased, due to the formation of binary clusters Arm(H2O)n. These mixed clusters undergo rapid dissociation of Arm during the ionization/fragmentation process and this dissociation removes enough energy from the cluster to impede the proton transfer/fragmentation reaction. The unimolecular dissociation rate constant for protonated water cluster ions is determined to be 0.6 to 2.7 x 104 s-1 (figure 2) for clusters of 8 < n < 24. The vibrational temperatures of neutral water clusters are in the range 40 to 200 K for the clusters 10 < n < 21, based on the rate constants, excess energies, and calculated thermodynamics for (H2O)n. The major series of protonated methanol clusters is observed in the mass spectrum with no abnormal or “magic number” signals. The cluster ion signal intensity decreases roughly exponentially with increasing cluster size. The only unprotonated methanol cluster observed is the dimer. Cluster ions of the form (CH3OH)n H3O+, generated from an intracluster ionmolecule reaction and loss of (CH3)2O, are not observed in the mass spec-

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trum because only a small amount of excess energy is deposited in neutral clusters employing single photon 26.5 eV ionization. Products CH3+, CHO+, CH2O+, CH2OH+, and CH3OH+ are observed in the photolysis/ionization of CH3OH monomer. At this energy, rate constants for metastable dissociation of protonated methanol cluster ions are obtained in the range 3.6 to 6.0 x 10+3 s-1 for cluster sizes 5 < n < 10. Vibrational temperatures of neutral methanol clusters are about 50 to 100 K for the cluster range 6 < n < 10.

Fig. 1. A reflectron TOF mass spectrum of water clusters ionized by the 26.5 eV soft-x-ray laser. Pn stands for the parent ion (H2O)nH; Dn represents the daughter ion formed from Pn+1 via losing a single water molecule in the first field-free region [2].

Protonated ammonia cluster ions dominate the ammonia cluster mass spectrum, as usual for the other two systems discussed and signal intensity decreases roughly exponentially with increasing cluster size. Unprotonated clusters are observed in the range 2 < n < 22. The intensity distribution for unprotonated cluster ions exhibits a distinct minimum at n = 6. This intensity decrease implies a more rapid proton transfer reaction process for the (NH3)6+ cluster and enhanced structural stability of the (NH3)5H+ cluster ion. Products for loss of up to five H atoms in the photolysis/ionization process for the neutral ammonia dimer are observed. Loss of more than

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three H atoms is not observed in the mass spectrum of larger (n > 3) cluster ions. The unimolecular metastable dissociation rate constants for protonated ammonia cluster ions are found to be between 0.8 and 2.0 x 104 s-1 for 5 < n < 18. A cluster temperature range for (NH3)n neutral clusters could not at present be characterized (as accomplished for (H2O) and (CH3OH)n) most probably due to inconsistencies within the existing thermodynamic data set for this system.

Fig. 2. Metastable dissociation rate constants and dissociation energies for protonated water clusters.

The van der Waals clusters (SO2)n and (SO2)m(H2O)n were investigated by 26.5 eV capillary discharge soft x-ray laser single photon ionization and TOFMS detection. The distribution of (SO2)n clusters decreases roughly exponentially with increasing cluster size n. The loss of one SO2 molecule from the cluster ion (SO2)n+ is observed with a reflectron TOFMS. Metastable dissociation rate constants for (SO2)n+ to yield (SO2)n-1+ are in the range 0.6 to 1.5 x 104 s-1 for cluster sizes 5 < n < 16. This is the same range as found for similar rate constants for water, methanol, and ammonia cluster ions. A minor fragmentation path (loss of O atom) for the cluster ions is identified but this process is found to decrease with increasing cluster size. Mixed SO2•H2O clusters are studied under different cluster generation conditions and the predominant signals in the mass spectra are due to (H2O)nH+ and (SO2)n+ cluster ions as a function of conditions (concentration, expansion pressure). Mixed clusters of the form (SO2)(H2O)nH+ and

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(SO2)nH2O+ are also observed at low intensities. SO2 and H2O are not good solvents for one another. Unprotonated mixed cluster ions (SO2)nH2O+ 1 < n < 5 are observed at high SO2 concentration and (SO2)(H2O)nH+ are observed at low SO2 concentration. Proton transfer between H2O and SO2 in mixed clusters has a high activation energy. For the pure CO2 system, the dominant cluster series in the mass spectrum is (CO2)n+ which is directly generated from ionization of neutral clusters (CO2)n in the molecular beam. The distribution of (CO2)n neutral clusters decreases roughly exponentially with increasing cluster size n showing no anomalous signal intensities in the distribution. The (CO2)n-1CO+ and (CO2)n-2O2+ cluster series are observed (weakly) as the photodissociation products of the neutral (CO2)n clusters at a highly excited state of the ion. Compared to electron impact studies, much less dissociation is observed because in most instances all of the excess cluster energy above VIE is removed by the photoelectron during the ionization process. The metastable dissociation rate constants for (CO2)n+ loss of CO2 are in the range 0.2 to 1.5 x 104 s-1 for 5 < n < 16. This is the same range observed for the comparable dissociation of (SO2)n+, (H2O)n H+, (CH3OH)nH+, and (NH3)n H+ clusters. Mixed CO2-H2O clusters are studied at two different conditions of CO2 concentration in the expansion gas and two different expansion gas pressures. The predominant signals in the mass spectra are (CO2)n+ and (H2O)nH+ cluster ions for high and low parameter values, respectively. Both cluster ion series arise from pure neutral and not mixed clusters. For the high concentration condition two more cluster series, (CO2)nH2O+ and (CO2)n(H2O)2+ are observed. The X-ray laser photon does not deposit enough energy in the (CO2)n(H2O)1,2+ clusters to cause proton transfer to CO2 or H2O. CO2 acts as a good solvent for H2O molecules. At low concentration and backing pressure, many additional cluster ion series are observed. The unprotonated (H2O)n+ and (CO2)(H2O)n+ series are generated by the evaporation of CO2 molecules from the mixed cluster series (CO2)m(H2O)n+. Additional experimental results and a more in depth discussion of the results we obtained for all the systems reported above can be found in references 2, and 4-5.

3. Conclusion The very compact Ne-like Ar capillary discharge soft x-ray laser is a near ideal ionization source with which to investigate weakly bound (hydrogen

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bonded and van der Waals) clusters in the gas phase. In this work, water, methanol, and ammonia clusters are ionized by a single 26.5 eV laser photon. The advantage of single photon ionization is that it prevents or hinders cluster fragmentation after ionization. This is typically not the case for ns multiphoton ionization. Although 26.5 eV energy is initially absorbed by the neutral cluster, almost all the energy above the vertical ionization energy is removed by the ejected photoelectron. Metastable dissociation of cluster ions can thereby be understood and characterized through the internal intracluster reaction energies and neutral cluster temperature.

Acknowledgment Work supported by the NSF ERC for Extreme Ultraviolet Science and Technology under NSF award number EEC-0310717.

References 1. S. Heinbuch, M. Grisham, D. Martz, and J.J. Rocca, “Demonstration of a desk-top size high repetition rate soft x-ray laser”, Optics Express 13, 4050 (2005). 2. F. Dong, S. Heinbuch, E.R. Bernstein, and J.J. Rocca, “Dynamics and fragmentation of van der Waals Clusters: (H2O)n, (CH3OH)n, and (NH3)n upon ionization by a 26.5 eV soft x-ray laser,” J. Chem. Phys. 124, 224319 (2006). 3. F. Dong, S. Heinbuch, J. J. Rocca, and E. R. Bernstein, “Mass Spectroscopy of Neutral Metal Oxide Clusters Using a Desk-Top Soft X-ray Laser,” In these proceedings, 10th ICXRL (2006). 4. S. Heinbuch, F. Dong, E.R. Bernstein, and J.J. Rocca, “Single photon ionization of van der Waals clusters with a soft x-ray laser: (CO2)n and (CO2)n(H2O)m,”. J. Chem. Phys, in press (2006). 5. F. Dong, S. Heinbuch, E.R. Bernstein, and J.J. Rocca, “Single photon ionization of van der Waals clusters with a soft x-ray laser: (SO2)n and (SO2)n(H2O)m,”. J. Chem. Phys, in press (2006).

Soft X-Ray Laser Holographic Imaging With SubMicron Resolution P. W. Wachulak, M. C. Marconi, R. Bartels, C. S. Menoni and J.J. Rocca NSF ERC for Extreme Ultraviolet Science & Technology and Department of Electrical and Computer Engineering, Colorado State University, USA

Summary. We have demonstrated Gabor holography with a spatial resolution of ~380 nm using a table top soft X-Ray laser. The hologram was recorded in a high spatial resolution photoresist and subsequently digitized using an atomic force microscope. The final reconstruction was performed using a Fresnel propagator.

1 Introduction The possibility to record holograms in the X-ray region was suggested in the early 50s by Baez 1. However the first holographic images of simple objects were not obtained until the early 1970s 2,3. The primary barrier to achieve high resolution holographic recordings was the lack of sufficiently bright coherent sources at short wavelengths. The first demonstration of holography with a X-Ray laser was performed in Livermore National Laboratory 4 using a large laser facility and achieving a spatial resolution limited to 5 μm. The development of synchrotron facilities also allowed holographic recording at X-ray wavelengths and has been used for imaging biological samples5, nano structures6, and to study magnetic domains with nanometer resolution by the novel technique of spectro-holography7 among other applications. Compact highly coherent SXR sources8,9 have opened new opportunities for the implementation of practical coherent imaging systems with high spatial resolution. For example, 7 microns spatial resolution has been obtained in the reconstruction of a hologram recorded with a high harmonic source on a charge coupled array detector (CCD).9 Herein we present results of SXR holographic imaging with a resolution better than 400 nm using a compact 46.9 nm capillary discharge table-top laser. A detailed analysis of the factors that control the spatial resolution is

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also presented showing the necessity for high temporal and spatial coherence to realize sub-micron spatial resolution.

3 Experimental Details The experimental set up is schematically illustrated in Figure 1. The illumination is produced by a 46.9 nm table top discharge-pumped capillary Ne-like Ar laser. This compact laser when operated with 18.4 cm long capillaries is capable of producing 100 μJ pulses at repetition rates up to 10 Hz10. The SXR laser has a spectral fractional bandwidth Δλ/λ ≈ 1×10-4 corresponding to a coherence length lc ≈ 470 μm.

Fig. 1. Experimental set up used to record a Gabor’s hologram with a soft X ray laser illumination

An AFM cantilever11 served as the test object. Holograms were recorded in a 200 nm thick layer of poly methyl metacrylate (PMMA-MicroChem 950,000 molecular weight) spin-coated on a silicon wafer. The PMMA coated wafer was situated at a distance zp ≈ 4 mm away from the AFM cantilever to record the hologram. The typical resolution for photonactivated PMMA is similar to the SXR laser wavelength and thus it does not limit the spatial resolution of the holographic imaging process5. To activate the PMMA, typical exposures in the range ≈ 2×107 photons μm-2 were necessary corresponding to a dose in the range ≈ 3-4×106 Gy12. This required approximately 150 laser shots. It would be possible to significantly reduce the exposure time by using longer capillaries that provide higher energy per pulse and higher spatial coherence8. The photoresist was developed using the standard procedure.

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4 Results The hologram was imprinted in the PMMA surface and was subsequently digitized utilizing an atomic force microscope. We used a Veeco Nanoscope III model NS3a AFM in tapping mode for the reading. The maximum scan area allowed by our microscope is 100 x 100 μm2. Interference fringes in the hologram were recorded over large areas, with the

Fig. 2. Hologram read with an atomic force microscope. The image is composed by 9 sub scans to 2 cover a total area 270 x 290 μm .

Fig. 3. Numerical reconstruction of the hologram obtained with the Fresnel propagator. The inset shows details of the cantilever tip profile.

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higher frequency fringes located few hundreds of microns away from the central image of the tip. To digitize an image with the sufficient NA for recording the highest spatial frequencies we developed a procedure that consisted of scanning different partially superposed regions of the hologram and stitching the images together to cover a larger surface. The final image presented in Figure 2 is composed by 9 sub-scans and covers a total area of 270 x 290 μm2. The digitized hologram was numerically reconstructed with a Fresnel propagator13. Figure 3 is the reconstructed image obtained after processing the AFM image shown in Fig. 2 with the Fresnel propagator code. The cantilever profile is clearly displayed and the tip is obviously revealed. The inset in the figure is a magnified section of the final image where 1 pixel corresponds to 270 nm.

5. Determination of the hologram’s spatial resolution The spatial resolution of the hologram is determined by several factors: the spatial and temporal coherence of the illumination as well as the method used to digitize the image. For the geometrical conditions of the experiment, in which the object was set at a distance zs=1.7 m from the source and the object to image was zp ≈ 4mm , the temporal and spatial coherence restrict the numerical aperture of the hologram to NA≈0.342 and 0.085 and a corresponding spatial resolution of Δ≈ 84 nm and Δ≈ 338 nm respectively. However, the digitization and reconstruction could place a larger constraint if an inadequate low number of sampling points in the reading of the image are acquired. To maximize the spatial resolution in the reading and reconstruction of the hologram image, a set of 9 AFM images were stitched together as described in section 3. In addition, since the distance between the object and the recording medium zp is a critical parameter in the reconstruction code we implemented a wavelet decomposition analysis followed by correlation of the reconstructed images with the wavelet set 14. We constructed a “perfect” or “reference” which has the maximum resolution attainable, i.e. 1 pixel. From this reference image we generated a set of lower resolution wavelet components. Each wavelet component has a relative resolution to the reference given by Y = 2X, where Y is the relative resolution between the images in the wavelet decomposition and X is the scale of the wavelet. Running of the Fresnel propagator code with slightly different zp values around 4 mm generated a series of images which in turn were correlated pixel to pixel with this set of decreasing resolution wavelet components. The pixel to pixel correlation provides a quantitative relative resolution of

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these reconstructed images relative to the synthesized reference image. Simultaneously this procedure also allows for the selection of the optimum zp which is the one that maximizes the value of the correlation function. Figure 4 shows values of the correlation between the reconstructed images

Fig. 4. Coefficient obtained from the correlation between different images reconstructed with different objecthologram distances and different wavelet components as a function of the wavelet scale. Triangles: zp = 4 mm; circles: zp = 4.02 mm; stars: zp = 4.05mm; squares: zp = 4.06 mm; diamonds: zp =4.08mm.

Fig. 5. Maximum correlation coefficient for images reconstructed with different object-hologram distances. The best resolution is obtained for zp = 4.04 mm.

and the wavelet components as a function of the wavelet scale. The different curves corresponds to different object-hologram distances ranging from zp= 4 mm to zp= 4.08 mm. Although the maximum value for all zp corresponds to X = 0, a noticeable decreasing in the correlation values is observed only for values X > 1. If we take the conservative assumption that the best correlation curve corresponds to X = 0.5, this analysis indicates a resolution 20.5 = 1.41 relative to the reference image. As the synthesized reference image has by definition 1 pixel resolution (270 nm) this analysis indicates that the reconstructed image has a resolution equivalent to 1.41 pixels. This analytical method also allows to quantify the optimum value of zp. We plotted in Figure 5 the maximum value of the correlation function obtained for different object-hologram distances in the 3.8 mm to 4.3 mm range. The maximum value is obtained for zp = 4.04 mm. The position of the reference image relative to the reconstructed images also influences the

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value of the correlation. The curve shown in Figure 5 corresponds to the position of the reference image which maximizes the value of the correlation with the reconstructed images. Moving the reference image one pixel around this optimum position produces similar curves as presented in Figure 5 but with lower correlation values. From this analysis, we conclude that the optimum reconstruction corresponds to a distance zp = 4.04 mm and that the spatial resolution obtained in the reconstruction is 381 nm, which compares reasonably well with the predicted spatial coherence limited spatial resolution Δ≈338 nm.

6. Conclusions We demonstrated sub-400 nm resolution in a holographic image obtained in the Gabor’s geometry with a table top soft x-ray laser. This represents one order of magnitude improvement relative to previous holographic recordings with a table top soft x-ray source. We showed that the longitudinal and spatial coherence of the 46.9 nm capillary discharge laser do not limit the NA of the hologram easily allowing for sub 100 nm resolution. Rather the number of sampling points in the readout process is what imposes the major practical limitation in achieving sub 100 nm spatial resolution. To determine the optimum reconstruction parameters and assess the spatial resolution of the holographic recording we used a wavelet analysis followed by image correlation. Improvements for this technique will result from utilizing longer capillaries that will increase the photon flux (reducing the exposure time) and simultaneously enhance the spatial coherence. These improvements could eventually lead to single shot coherent imaging recording allowing for time resolved holographic measurements in the nanosecond scale.

7. Acknowledgements This research was sponsored by the National Science Foundation through the NSF ERC Center for Extreme Ultraviolet Science and Technology, NSF Award No. EEC-0310717.

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References 1. Baez, A.V. “A study in diffraction microscopy with special reference to Xrays”. J. Opt. Soc. Am. 42, 756, 1952 2. Giles, W.J.. “Image reconstruction from a Fraunhofer X-ray hologram with visible light”. J. Opt. Soc. Am. 59, 1179, 1969. 3. Aoki, S. and Kikuta, S. “X ray holographic microscopy”. Jpn. J. Appl. Phys., 13, 1385, 1974. 4. Trebes J.E., Brown S. B., Campbell E. M., Matthews D. L., Nilsen D. G., Stone G. F., and Whelan D. A.. “Demonstration of X-Ray holography with an XRay laser”. Science, 238, 517, 1987. 5. Lindaas S., Howells M., Jacobsen C. and Kalinovsky A.. “X-ray holographic microscopy by means of photoresist recording and atomic force microscope readout”. J. Opt. Soc. Am. A, 13, 1788, 1996. 6. McNulty I., Kirz J, Jacobsen C., Anderson E., Howells M. R., and Kern D. P. “High resolution imaging by Fourier Transform X-ray holography”. Science, 256, 1009, 1992. 7. Elsebitt S., Schlotter W. F., Lorgen M., Hellwig O., Eberhardt W., Stohr J., “Lensless imaging of magnetic nanostructures by x-ray spectro holography”. Nature, 432, 885, 2004. 8. Macchietto C.D., Benware B.R. and Rocca J. J., “Generation of millijoule-level soft-X ray laser pulses at a 4-Hz repetition rate in a highly saturated tabletop capillary discharge amplifier”. Opt. Lett., 24, 1115, 1999. 9. Bartels R.A., Green P.A., Kapteyn H., Murnane M., Bakus S., Kristov I.P., Attwood D., Jacobsen C.. “Generation of spatially coherent light at extreme ultraviolet wavelengths”. Science 297, 376, 2002. 10.Benware B.R., Moreno C. H., Burd D. J. and Rocca J. J. “Operation and output pulse characteristics of an extremely compact capillary-discharge tabletop soft-x-ray laser.” Opt. Lett. 22, 796, 1997. 11. AFM cantilever from MicroMasch with the following physical characteristics: cantilever length 230 μm, width 40 μm, thickness t = 7 μm, full tip cone angle 30°, tip height h = 20 - 25 µm, typical tip curvature radius of uncoated probe < 10 nm. 12. Beetz T. and Jacobsen C.. “Soft X-ray radiation damage studies in PMMA using a cryo-STXM”. J. Synchr. Radiation, 10, 280, 2002. 13. J. W. Goodman. Introduction to Fourier Optics. (Roberts and Company Publishers, 2005). 14. Nuňez J., Otazu X., Merino M.T. “A multiresolution-based method for the determination of the relative resolution between images: First application to remote sensing and medical images”. Inter. J. Imag. Syst. and Techno. 15, 225, 2005.

Table Top Nanopatterning Using Soft X-Ray Lasers M. G. Capelutob, P. Wachulaka , D. Patel a, M.C. Marconia , C.S. Menonia, J.J. Roccaa, E.H. Andersonc, W. Chaoc and D.T. Attwoodc a

NSF Engineering Research Center for Extreme Ultraviolet Science & Technology and Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO80523, USA b Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria. Buenos Aires, C1428EHA, Argentina c Lawrence Berkeley National Laboratory and University of California at Berkeley

Summary. In this work we demostrate a table top nanopatterning tool based on the illumination with compact Soft X-Ray (SXR) laser. Two approaches consisting of interferometric lithography (IL) and de-magnifying imaging using diffractive optics were used. Surface patterning was realized on commercial photoresists covering surfaces up to ≈50 x 50 μm2 with exposures f few seconds. Using interferometric lithography features down to ≈ 60 nm were obtained.

1 Introduction Light based incoherent lithography tools rely on reducing the wavelength of the illumination source or increase the numerical aperture of the optics to decrease the size of the printed features. Shorter wavelength illumination is also essential in coherent or interferometric printing methods to realize wavelength size periodic nanoscale imprints. We have explored the capabilities of compact SXR lasers utilized as illumination source to demonstrate a table top nanopatterning tool. The main attributes of the laser source, compactness, high photon flux and coherence are key factors for the realization of a compact and versatile nanometer scale photolithography system for research oriented applications. The SXR laser used in this work is a capillary discharge pumped laser capable of generating coherent SXR radiation at 46.9 nm with an average power in the range of few mW at repetition rates up to 10 Hz 1-2. The spatial coherence of this source was measured to increase as the capillary length increases 3-4 having a coher-

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ence radius of 550 μm at 1.5 m from the source which includes almost half of the entire laser power. The laser is also highly temporally coherent. With a spectral bandwidth of Δλ/λ ≈ 1×10-4 it has a coherence length of ≈ 470 μm, which is sufficient for most practical applications. This laser source developed at Colorado State University is the highest average power compact coherent source presently available at this wavelength. Its coherent average power per unit spectral bandwidth is similar to that generated by an undulator at a third generation synchrotron facility, while the peak coherent power exceeds that of present generation undulators by 5 to 6 orders of magnitude at this wavelength.

2 Patterning with EUV lasers One of the patterning schemes we implemented in this work consists of projecting a smaller de-magnified image from an object consisting of a periodic pattern onto a photoresist surface. The main advantages of this approach are its simplicity, capability to imprint areas of tens of square microns with extremely short exposures and the possibility to print arbitrary patterns. The whole patterning set up fits comfortably in an optical table. Figure 1 is a scheme of the patterning tool consisting of the 46.9 nm SXR laser, the vacuum line and the exposure chamber. All the components fit in a reduced space approximately 2.7 x 0.6 m2. The inset in the Fig.1 shows a detail of the sample holder. A mask with the desired pattern is illuminated

Vacuum pumps Photodiode Gate valve Laser

Chamber

1.7 m

Fig. 1. Scheme of the table top nanopatterning tool. The inset shows the sample holder located in the exposure chamber.

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with the output from the SXR laser. Its image is then formed onto the resist-coated substrate using a zone plate, as schematically shown in Fig. 2. A motorized translation stage allows for several consecutive exposures in the same substrate. This scheme offers vast flexibility in the design of the object mask as it is not restricted to regular periodic structures. The resolution in this case is limited primarily by the imaging zone plate, with a spatial resolution is determined by5

ΔrRayl = 1.22 F #λ = 1.22Δr

(1)

where ΔrRayl is the Rayleigh resolution limit, F# is the numerical aperture of the zone plate, λ is the illuminating wavelength, and Δr is the outermost zone width of the zone plate lens. Equation (1) shows the advantage of using short wavelength illumination to achieve nanometer spatial resolution. It also highlights the point that the critical component influencing the resolution is the zone plate outermost zone width Δr. In the experiments we used a self standing zone plate 500 μm in diameter, with 625 zones, with an outermost zone width Δr =200 nm. This zone plate has a focal length of 2.14 mm for λ= 46.9 nm with a depth of focus of 1.7 μm. With this focusing optics the expected spatial resolution is limited to ≈ 240 nm. We performed several tests printing a regular array of holes on the surface of a Si wafer coated with photoresists, such as polymethyl metacrylate (PMMA). This photoresist has a spatial resolution below the limit set by the diffractive optics, and provide a good sensitivity to allow short exposure times.

Fig. 2. schematic experimental set up for the de-magnifying imaging test

Fig. 3. Array of holes printed with the 47 nm EUV laser using demagnified imaging setup

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A typical pattern obtained with this set up is shown in figure 3. In this case the de-magnification factor was 6X and the pattern was obtained with 3 laser shots (3 s exposure). The size of the imprinted features is ≈370 nm. Upon the photoresist development a pattern consisting of periodic holes was obtained. This method proved to be very effective to produce arrays of holes over an area approximately 50x50 μm2 with a simple set up and extremely short exposure times (3 s).

3. Interferometric lithography The high degree of spatial coherence and the high photon flux of the λ=46.9 nm laser makes this source an interesting alternative for the interferometric lithography (IL). In a former experiment we demonstrated printing of regular lines with periods down to 52 nm using a Lloyd’s mirror configuration 6. In this work utilizing the same Lloyd’s mirror set up but now with double exposure we were able to generate crossed lines leaving small holes in the intersections. Figure 4 shows a scheme of the experimental set up. After the first exposure a regular line pattern is obtained with a period given by

d=

λ 2 sin θ

(2)

where θ is the incidence angle and λ the wavelength. In a second exposure a second identical pattern is obtained in the perpendicular direction. The

Fig. 4. Double exposure using Lloyd’s mirror set up

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Fig. 5. crossed lines printed on PMMA with a double exposure using Lloyd’s mirror set up

superposition of both patterns produces small holes in the intersections where the photoresist is activated in the two exposures. Fig. 5 shows and atomic force microscope scan of a PMMA coated wafer with the imprinted pattern. The periodicity of this structure was determined by the incidence angle, in this case 160 nm. The full width at half maximum of the imprinted holes was ≈ 60 nm.

4. Conclusions We demonstrated table top nanopatterning at SXR wavelenghts. Two approaches were implemented, de-magnified imaging of a regularly distributed array of holes and IL. With the first approach we were able to print large areas (50 x 50 μm2) obtaining holes ≈370 nm in diameter after photoresist development in very short exposure times. The second approach allowed smaller features ≈60 nm over similar areas. These results demonstrate the capability of compact SXR used in selected applications in nanopatterning for research purposes.

5. Acknowledgements This work was supported by the NSF ERC for Extreme Ultraviolet Science and Technology under NSF Award Number EEC-0310717 and NER program NSF Award DMI-0508484. MGC acknowledges the support through a fellowship from CONICET.

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References 1. Macchietto C. D., Benware B. R. and Rocca J.J. "Generation of millijoule-level soft-x-ray laser pulses at a 4-Hz repetition rate in a highly saturated tabletop capillary discharge amplifier". Opt. Let., 24, 1115, 1999. 2. Benware B. R., Moreno C. H., Burd D. J. and J. J. Rocca. "Operation and output pulse characteristics of an extremely compact capillary-discharge tabletop soft-x-ray laser". Opt. Lett., 22, 796, 1997. 3. Liu, M. Seminario, F. G. Tomasel, C. Chang, J. J. Rocca and D. Attwood, "Achievement of essentially full spatial coherence in a high-average-power soft-x-ray laser". Phys. Rev. A, 6303, art. no.-033802, 2001. 4. Marconi M.C., Chilla J.L.A., Moreno C.H., Benware B.R. and Rocca J.J. “Measurement of the spatial coherence build up in a discharge-pumped table-top soft xray laser”. Phys. Rev. Lett., 79, 2799-2802,1997. 5. D. Attwood, "Soft X-Ray and Extreme Ultraviolet Radiation, Principles and Applications". Cambridge University Press, 2000 6. Capeluto M.G., Vaschenko G., Grisham M., Marconi M. C., Luduena S., Pietrasanta L., Lu Y., Parkinson B., Menoni C. S. and Rocca J.J., "Nanopatterning with interferometric lithography using a compact l=46.9 nm laser". IEEE Transactions on Nanotechnology, 5, 3, 200

Soft X-Ray Laser Ablation of Nanometer-Scale Features G. Vaschenko1,2, F. Brizuela1,2, H. Bravo1,2, C. S. Menoni1,2, J. J. Rocca1,2, O. Hemberg3, B. Frazer3, S. Bloom3, W. Chao1,4, E. H. Anderson1,4 and D. T. Attwood1,4,5 1

NSF ERC for Extreme Ultraviolet Science and Technology Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO 80523 3 JMAR Technologies Inc., San Diego, CA 92127 4 Center for X-ray Optics, Lawrence Berkeley National Laboratory 5 University of California, Berkeley, CA 94720 2

Summary. We demonstrate single shot ablation of sub-100 nm holes using the focused output from a λ=46.9 nm capillary discharge laser. Very clean ablation craters with diameters down to 82 nm were produced in polymethyl-methacrylate (PMMA) coated substrates placed at the first and third order focus of a free standing zone plate. These results demonstrate the feasibility of using focused soft xray laser beams for the direct nanoscale patterning of materials and the development of new nanoprobes.

1 Introduction Laser ablation is a powerful tool for direct patterning of materials. The size of the smallest ablated features is limited mainly by the wavelength of the laser emission and by heat diffusion. Taking advantage of the well defined ablation threshold in materials, craters with sizes ranging from 0.7 to 1.2 μm were achieved in silicon using nanosecond ultraviolet (UV) pulses.[1] Ablation features of the order of 200 nm have been demonstrated using femtosecond laser pulses in the near-infrared [2,3], and UV [4] spectral regions. Patterning of even smaller features has been realized using the electric field enhancement created at the tip of an atomic force microscope by focused femtosecond laser pulses [5] or using optical fibers to create near-field effects [6]. In this work we demonstrate the feasibility of directly ablating sub-100 nm nanoscale holes using a focused soft x-ray laser beam. Very clean abla-

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tion craters in poly-methyl methacrylate (PMMA) were realized by focusing the 46.9 nm wavelength output from a table-top capillary discharge laser with a free-standing Fresnel Zone Plate (FZP). The smallest craters, 82 nm in diameter, were obtained by placing the sample near the third order focal plane of the FZP. This high spatial resolution coupled with the very small absorption depth of the 46.9 nm wavelength light in most materials are attractive features to exploit for nano-patterning applications.

2 Experimental details Laser ablation at λ=46.9 nm was implemented by focusing the output from CSU’s capillary discharge laser onto the sample, with a free standing zone plate, as schematically shown in Fig. 1(a). The laser, equipped with a 18 cm long capillary, produced ~ 0.1 mJ pulses of ≈1.2 ns duration with a repetition rate of up to 10 Hz. [7,8] The free-standing FZP was manufactured by electron-beam lithography [9] into a 200 nm thick nickel film attached to a silicon frame. The FZP had a 0.5 mm diameter, an outermost zone width of 200 nm, and a numerical aperture NA = 0.12. Its Rayleighlike spatial resolution in the first diffraction order focus at 46.9 nm wavelength is ~ 240 nm.[10] The FZP was mounted on an XYZ translation stage and positioned at ~ 1.8 m from the laser exit, where the laser beam diameter is ~ 16 mm. For this geometry, and considering that the FZP aperture is 0.5 mm, only a ~ 1/1000 portion of the laser beam is effectively used. When also accounting for the first order diffraction efficiency of ~ 10 %, the energy delivered to the sample’s surface is estimated to be ~ 7 nJ. The fluence at the sample was controlled by introducing argon gas into the vacuum chamber as a means of attenuating the laser beam following photoionization of the argon atoms by the 24.6 eV photons. Fig. 1(b) shows a picture of the soft x-ray ablation tool. The vacuum chamber on the left houses the FZP and sample. The sample consisted of a 500-nm layer of polymethyl methacrylate (PMMA-MicroChem, 950,000 molecular weight) spin-coated on a Si wafer. The sample was positioned perpendicular to the incident soft x-ray laser beam, whereas the translation stage was tilted at an angle of ~ 0.57º with respect to the sample’s surface to allow for precise positioning of the sample with respect to the zone plate focal plane (first order depth of focus ~ 3 μm). The ablation craters produced by the λ=46.9 nm laser beam were analyzed with a VEECO NanoScope III atomic force microscope (AFM) used in tapping mode with a 10 nm radius, 30º cone angle cantilever tip (MicroMasch, NSC16).

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Fig. 1. (a) Schematics of the soft x-ray laser ablation set up. (b) The λ=46.9 nm ablation tool showing the processing chamber on the left and CSU capillary discharge laser on the right.

3. Results and Discussion Using the set up just described, craters with diameters ranging from ~80 nm to ~ 340 nm were ablated in PMMA with single shot exposures. Figure 2(a) shows an AFM image of an ablation crater obtained positioning the sample at the FZP first diffraction order focal plane. The crater was obtained attenuating the beam by ~ 36× introducing 110 mTorr of argon into the processing chamber. Attenuation of the laser beam results in a reduction of the crater diameter and depth (Fig. 2(b)). The depth of the craters ablated without attenuation is 250 nm, which is significantly larger than the 19 nm attenuation length of the 46.9 nm light in PMMA [11]. The shot-to-shot reproducibility of the ablation was found to be very good, as illustrated by the AFM image in Fig. 2(c). The edges of the craters are very abrupt and their walls are very smooth. These high quality ablated surfaces result from the strong localization of the absorbed energy, i.e. the attenuation and thermal diffusion lengths are very short, and by the prevalence of chain scissions at soft x-ray wavelengths. [11].

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Fig. 2. (a) Typical ablation crater obtained at the first order diffraction focus. Their diameter at Full Width Half Maximum and depth varies with the degree of attenuation of the laser intensity as shown in (b). (c) Reproducible and repetitive ablation of a series of 230 nm craters in PMMA.

Fig. 3. AFM image of the smallest ablation craters, 82 nm in diameter, obtained by placing the sample at ~ 7 μm away from the third order focus of the FZP (left). Calculated intensity distribution at the third order focal plane, and at 7 μm away from it. (right) The inset shows an AFM image of a typical ablation pattern obtained outside of the focal plane without attenuation.

Smaller craters can in principle be obtained using the tighter third order focus of the zone plate. Figure 3 shows an AFM picture and corresponding cross section of the smallest crater, 82 nm in diameter, ablated in PMMA. These small features were obtained by placing the sample at ~ 7 μm from the third diffraction order focus, and by attenuating the beam. At this position, the beam intensity distribution consists of a central peak of ~

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100 nm FWHM, surrounded by less intense peaks. This intensity distribution results from uncorrected spherical aberrations in a FZP that was optimized only for first order operation, as calculation of the intensity distribution using a Fresnel propagator show (Fig. 3). [11] The ×5 attenuation of the beam provided the selectivity necessary to decrease the intensity of the secondary peaks below the ablation threshold of PMMA, thus leaving the central peak with enough intensity to ablate. The 82 nm craters had a depth of ~8 nm and excellent wall quality. These are to our knowledge the smallest ablation craters obtained by directly focusing a laser beam with a lens onto a sample surface. The use of a FZP with smaller outer zone width should produce holes of even smaller dimensions.

4. Summary We have demonstrated the feasibility of single shot ablation of sub-100 nm features using a focused soft x-ray laser beam. The smallest ablation features, 82 nm in diameter, were obtained by placing the sample near the third diffraction order focal spot and by attenuating the beam intensity by ×5. The high quality of the ablation is mainly the result of chain scissions at the soft x-ray wavelengths and strong localization of the absorbed energy. This proof-of-principle demonstration sets the path for the development of new nanoprobes and nanomachining tools. This work was supported by the Engineering Research Centers Program of the National Science Foundation under NSF Award Number EEC0310717.

References 1. 2. 3. 4.

Avrutsky I., Georgiev D. G., Frankstein D., Auner G., and Newaz G., “Superresolution in laser annealing and ablation,” Appl. Phys. Lett. 84, 2391-2393, 2004. Pronko P. P., Dutta S. K., Squier J., Rudd J. V., Du D., and Mourou G., “Machining of submicron holes using a femtosecond laser at 800-nm,” Opt. Comm. 114, 106-110, 1995. Korte F., Serbin J., Koch J., Egbert A., Fallnich C., Ostendorf A., Chichkov B.N., Towards nanostructuring with femtosecond laser pulses, Appl. Phys. A 77, 229-235, 2003. Simon P., Ihlemann J. “Ablation of submicron structures on metals and semiconductors by femtosecond UV-laser pulses,” Appl. Surf. Sci. 109/110, 2529, 1997.

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Chimmalgi A., Grigoropoulos C.P., Komvopoulos K., “Surface nanostructuring by nano-/femtosecond laser-assisted scanning force microscopy,” J. Appl. Phys. 97, Art. No. 104319, 2005. 6. Wysocki G., Heitz J., Bauerle D., “Near-field optical nanopatterning of crystalline silicon,” Appl. Phys. Lett. 84, 2025-2027, 2004. 7. Benware B.R., Macchietto C.D., Moreno C.H., Rocca J.J., “Demonstration of a high average power tabletop soft X-ray laser,” Phys. Rev. Lett. 81, 58045807, 1998. 8. Anderson E.H., “Specialized electron beam nanolithography for EUV and Xray diffractive optics,” IEEE Journal Of Quantum Electronics 42, 27-35, 2006. 9. D. Attwood, Soft X-rays and Extreme Ultraviolet Radiation, Cambridge Univ. Press, New York, 1999. 10. Henke B.L., Gullikson E.M., Davis J.C., “X-Ray Interactions - Photoabsorption, Scattering, Transmission And Reflection At E=50-30,000 eV, Z=1-92,” Atomic Data And Nuclear Data Tables 54, 181-342, 1993. 11. Juha L., Bittner M., Chvostova D., Krasa J., Otcenasek Z., Prag A.R., Ullschmied J., Pientka Z., Krzywinski J., Pelka J.B., Wawro A., Grisham M.E., Vaschenko G., Menoni C.S., Rocca J.J., “Ablation of organic polymers by 46.9-nm-laser radiation,” Appl. Phys. Lett. 86, Art. No, 034109, 2005. 12. Cao Q., Jahns J., “Comprehensive focusing analysis of various Fresnel zone plates,” J. Opt. Soc. Am. A 21, 561-571, (2004).

Ablation of Organic Molecular Solids by Focused Soft X-Ray Free-Electron Laser Radiation J. Chalupský1,2,3*, L. Juha1, J. Kuba3, J. Cihelka1,2, V. Hájková1, M. Bergh4, R. M. Bionta5, C. Caleman4, H. Chapman5, J. Hajdu4,5, S. Hau-Riege5, M. Jurek6, S. Koptyaev1, J. Krása1, A. Krenz-Tronnier7, J. Krzywinski6, R. London5, J. Meyer-ter-Vehn7, R. Nietubyc6, J. B. Pelka6, R. Sobierajski6, K. Sokolowski-Tinten8, N. Stojanovic8, K. Tiedtke9, S. Toleikis9, T. Tschentscher9, A. Velyhan1, H. Wabnitz9 and U. Zastrau10 1

Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Prague 8, Czech Republic; 2Charles University in Prague, Ke Karlovu 3, 121 16 Prague 2, Czech Republic; 3Czech Technical University in Prague, Brehova 7, 115 19 Praha 1, Czech Republic; 4 Biomedical Centre, Uppsala University, Uppsala, SE-75124 Sweden; 5 Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94550, USA; 6Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, PL-02-668 Warsaw,Poland; 7Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching, Germany; 8 University of Duisburg-Essen, D-45117 Essen, Germany; 9Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, D-22603 Hamburg, Germany; 10University of Jena, D-07743 Jena, Germany

Summary. The first soft X-ray free-electron laser has recently been put into operation at DESY in Hamburg. Tunable soft X-ray coherent radiation can be generated at the FLASH (Free-electron LASer in Hamburg; formerly known as VUV FEL or TTF2 FEL). In the interaction experiments reported here, the laser system provided ~25-fs, ~10-μJ pulses of 32-nm radiation. We irradiated thin (500 nm) layers of poly (methyl methacrylate) – PMMA deposited on a silicon substrate by single, focused FLASH pulses. The pulse energy was adjusted using a gas attenuator. PMMA ablation characteristics were determined for these unique irradiation conditions.

*

Corresponding author. E-mail: [email protected]; Fax: +420 286-890-265

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1 Introduction Laser ablation is a well-known phenomenon that is frequently used in numerous applications ranging from pulsed laser deposition of thin films to surface micro-structuring. It has been investigated for several decades and many papers have been published dealing with this topic. However, there are a few papers devoted to material ablation induced by XUV/X-ray lasers (see for example [1,2]) although there is a strong motivation to take advantage of their short wavelengths for direct nano-structuring. The ablation of PMMA has been extensively investigated with conventional UV-Vis-IR lasers (see for example [3,4]). PMMA is also widely used in electron-beam, EUV, and x-ray lithography as a resist so that its radiation-chemical and radiation-physical properties are well understood. PMMA erosion induced by high-energy photons in vacuum has already been investigated using synchrotron radiation [5,6] and coherent as well as incoherent XUV/X-ray emission from plasma-based sources [7-11]. This is why this material was chosen for the initial soft X-ray free-electron laser ablation experiments. Results of these experiments are reported here.

2 Experimental setup 500 nm layers of 495K PMMA were deposited on 315 μm-thick silicon chips fabricated by Silson, UK. The samples were positioned in an ultrahigh vacuum interaction chamber and irradiated by single FLASH pulses. The beam was focused using a grazing incidence elliptical mirror with a focal length of 2m. The operation of FLASH is described in ref. [12]. A laser-driven injector generates an electron bunch that is shot into a superconductive linear accelerator. The electrons are accelerated to relativistic energies on the order of ~100MeV. Bunch spatial properties and the electron density profile are formed by compressors before approaching a 30-m-long undulator, where the SASE (Self Amplified Spontaneous Emission) effect creates an intense beam of coherent XUV radiation. The temporal coherence is improved by using a grazing incidence monochromator, and the pulse energy is determined using a Gas Monitor Detector (GMD) [13]. The irradiated surfaces were investigated by Nomarski (DIC – differential interference contrast) optical microscopy using a BX51M DIC microscope fabricated by Olympus, Japan, and atomic force microscopy (AFM) using a Dimension 3100 scanning probe microscope (SPM) driven by a

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NanoScope IV controller (Veeco, USA). The AFM was operated in a tapping mode.

3 Data evaluation method The main goal of this contribution is to determine the ablation threshold and the radiation attenuation length for PMMA irradiated by focused FLASH pulses. We used Liu’s method [14] to obtain both the ablation threshold and the focal spot diameter. Liu’s method is based on the measured surface damage and the beam characteristics. Assuming linear behaviour of the irradiated materials and a Gaussian temporal and spatial shape of the FLASH pulses, the pulse intensity in the beam waist ( z = 0 ) can be written as (1): I ( r , t ) = I 0 exp ( − r 2 ρ 2 ) exp ( − t 2 τ 2 ) , where ρ is the laser beam radius at which the intensity drops to e-1. Integrating over time gives the spatial fluence distribution (2): F ( r ) = F0 exp ( − r 2 ρ 2 ) , and a second integration over space results in a relation of the pulse energy and the peak fluence (3): E pulse = πρ 2 F0 . Finally, we assume that the fluence (intensity) decreases exponentially

(

in

)

the

depth

of

the

material

(4):

F ( r, z ) = F0 exp − r 2 ρ 2 exp ( − z lat ) along z-axis, under the condition lat << zo,

i.e. the attenuation length lat is much shorter than Rayleigh's length z0 of the Gaussian beam. Lateral cooling can be neglected due to the ultrashort pulse duration, so that the shape of the crater can be described by equation (4). In terms of an ablation threshold (5): Fth = F0 exp ( − r 2 ρ 2 ) exp ( − z lat ) . There are two ways to determine the ablation parameters: Equation (5) can be rewritten as (6): S = S foc ln E pulse − S foc ln Eth = A + B ln E pulse , for z = 0 and (7): d = lat ln E pulse − lat ln Eth = A + B ln E pulse , for ρ = 0 . Here we used Equation (3),

S = π r 2 , S foc = πρ 2 , and Eth = πρ 2 Fth . For both cases, the parameters A and B

can be determined by means of linear regression of crater areas S or depth d as a function of ln E pulse . For the spot-area analysis, the focal spot area,

S foc , and the ablation threshold, Fth , are then linked through (8):

S foc = B ,

and (9): Fth = exp ( − A B ) S foc . For the creater-depth analysis, the attenuation

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length lat and ablation threshold Fth are given by (10): lat = B and (11): Fth = exp ( − A B ) S foc .

4 Results and discussion Quantitative results of our initial experiments carried out at the FLASH facility in Oct/Nov 2005 are plotted in Figs. 1 and 2. An AFM image of a typical ablation crater can be seen in Fig. 3. Ablation characteristics determined from the experimental results using Liu’s method described above are summarized in Tab. 1.

2

ablated area S[μm ]

2500 2000

crater area (AFM) - no atenuation crater area (Nomarski) - no attenuation crater area (Nomarski) - attenuated linear regression of (Nomarski) crater area (AFM) - attenuated linear regression of (AFM)

1500 1000 500 0 -5

-4

-3

-2

-1

0

1

2

ln(Epulse[μJ])

Fig. 1. Dependence of ablated area on FLASH pulse energy. Only results obtained with the attenuated beam were taken for the regression.

It can be seen in Fig. 3 that the FLASH-induced ablation area is very clean. The PMMA surface roughness as determined by the AFM before irradiation was (0.45±0.01)nm, whereas the roughness increased to only (3.72±0.06)nm inside a typical crater. The roughness change is almost independent of fluence. Together with the very low ablation threshold obtained from the results shown in Figs. 1 and 2, it can be explained by efficient PMMA chain scissions induced by FLASH photons carrying enough energy (38.7eV each photon) to break any chemical covalent bond. Simultaneously, a thermalized portion of radiation energy absorbed in the sam-

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ple could participate in the process directly and/or influencing the rate and mechanisms of polymer radiolysis. However, the direct thermal action does not seem to play a key role in this case because, as mentioned above, the ablated surface is very smooth, without any thermal damage, such as those registered for PMMA ablation induced by UV laser, both nanosecond as well as femtosecond, pulses [15]. Both processes may benefit from a short attenuation length of 32-nm radiation in PMMA, which is about 55nm (see [16] and Tab. 1), leading to a high energy density achieved in the near surface layer of the material irradiated.

maximum crater depth d[nm]

800 ( ( 600

) d=f(ln[Epulse]) ... attenuated ) d=f(ln[Epulse]) ... no atenuation linear regression of ( )

400

200

0 -5

-4

-3

-2

-1

0

1

ln(Epulse[μJ]) Fig. 2. Dependence of ablation (etch) depth on FLASH pulse energy. Only results obtained with the attenuated radiation were taken for the regression because the ablation rates are bigger than the PMMA layer thickness (=500nm) when the full power beam is applied.

The absorption coefficient and high-photon energy play important roles because the ablation threshold of PMMA lies at a much higher fluence for optical pulses (λ=800nm) of comparable duration (150fs), i.e., around 2.3J·cm-2 [17], than that found with 25-fs pulses of 32-nm radiation. Our finding confirms the trend observed in the VUV region, where the threshold falls to ~ (1-10)mJ·cm-2 with decreasing laser wavelengths, even for longer pulses [18,19].

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5 Conclusion The lowest fluence required for single-shot PMMA ablation induced by 32-nm FEL radiation lies at around 2mJ·cm-2. The attenuation length lat = (56.9±7.5)nm agrees well with the value of ~55nm measured in PMMA using synchrotron radiation [16]. The diameter of the FEL beam in focus is 2ρ=(23.8±0.6)μm. The full width at half maximum (FWHM) is 1/2 FWHM=2ρ(ln2) =(19.9±0.5)μm. Both values are in a good agreement with the expected spot diameter according to the focusing system parameters and the beam characteristics. The PMMA ablation is under the given irradiation conditions extremely clean. There are no bubbles and/or micron sized surface imperfections attributed to PMMA thermal modification. Non-thermal processes are expected to play a key role in this case.

Fig. 3. AFM image of a typical crater ablated in PMMA by the focused FLASH beam. Tab. 1 Characteristics of FLASH-induced PMMA ablation ablation feature evaluated crater area crater depth

microscope DIC AFM AFM

ablation threshold

Fth ⎡⎣ mJ ⋅ cm −2 ⎤⎦ (2.6±1.2) (2.1±1.1) (1.8±1.4)

attenuation length

lat [ nm ] -----

(56.9±7.5)

focal spot diameter

2 ρ [ μ m]

(23.0±0.5) (24.6±0.6) ---

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Acknowledgements This work was partially funded by the Czech Ministry of Education within the framework of programs INGO (Grant 1P2004LA235), 1K (Grant 1K05026) and National Research Centers (Grants LC510 and LC528), State Committee for Scientific Research of the Republic of Poland (Grant No72/E-67/SPB/5.PR UE/DZ 27/2003-2005), the Swedish Research Foundation and the European Commission (Grants G1MA-CI-2002-4017; CEPHEUS and II-02-049 FEL). This work was performed under the auspices of the US Department of Energy by the University of California, Lawrence Livermore National Laboratory under Contract No. W-7405Eng-48.

References 1. B. R. Benware, A. Ozols, J. J. Rocca, I. A. Artioukov, V. V. Kondratenko, A. V. Vinogradov: Focusing of a tabletop soft-X-ray laser beam and laser ablation, Opt. Lett. 24, 1714-1716 (1999). 2. L. Juha, J. Krása, A..Cejnarová, D. Chvostová, V. Vorlíček, J. Krzywinski, R. Sobierajski, A. Andrejczuk, M. Jurek, D. Klinger, H. Fiedorowicz, A. Bartnik, M. Pfeifer, P. Kubát, L. Pína, J. Kravárik, P. Kubeš, Yu. L. Bakshaev, A. S. Chernenko, V. D. Korolev, M. I. Ivanov, M. Scholz, L. Ryc, J. Feldhaus, J. Ullschmied, F. P. Boody: Ablation of various materials with intense XUV radiation, Nucl. Instrum. Meth. Phys. Res. A507, 577-581 (2003). 3. P. E. Dyer: Excimer laser polymer ablation: twenty years on, Appl. Phys. A77, 167-173 (2003), and references cited therein. 4. T. Lippert, J. T. Dickinson: Chemical and spectroscopic aspects of polymer ablation: special features and novel directions, Chem. Rev. 103, 453-485 (2003), and references cited therein. 5. Zhang, Y.: Synchrotron radiation direct photo-etching of polymers, Adv. Polym. Sci. 168, 291-340 (2004), and references cited therein. 6. M. C. K. Tinone, K. Tanaka, N. Ueno: Photodecomposition of poly(methyl methacrylate) thin films by monochromatic soft x-ray radiation, J. Vac. Sci. Technol. A13, 1885-1892 (1995), and references cited therein. 7. L. Juha, J. Krása, A. Präg, A. Cejnarová, D. Chvostová, K. Rohlena, K. Jungwirth, J. Kravárik, P. Kubeš, Yu. L. Bakshaev, A. S. Chernenko, V. D. Korolev, V. I. Tumanov, M. I. Ivanov, A. Bernardinello, J. Ullschmied, F. P. Boody: Ablation of poly(methyl methacrylate) by a single pulse of soft X-rays emitted from Z-pinch and laser-produced plasmas, Surf. Rev. Lett. 9, 347-352 (2002). 8. H. Fiedorowics, A. Bartnik, M. Bittner, L. Juha, J. Krasa, P. Kubat, J. Mikolajczyk, R. Rakowski, Micromachining of organic polymers by direct photo-

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etching using a laser plasma X-ray source, Microelectronic Eng. 73-74, 336339 (2004). 9. L. Juha, M. Bittner, D. Chvostova, J. Krasa, Z. Otcenasek, A. R. Präg, J. Ullschmied, Z. Pientka, J. Krzywinski, J. B. Pelka, A. Wawro, M. E. Grisham, G. Vaschenko, C. S. Menoni, and J. J. Rocca: Ablation of organic polymers by 46.9-nm laser radiation, Appl. Phys. Lett. 86, 034109 (2005). 10. L. Juha, M. Bittner, D. Chvostova, J. Krasa, M. Kozlova, M. Pfeifer, J. Polan, A. R. Präg, B. Rus, M. Stupka, J. Feldhaus, V. Letal, Z. Otcenasek, J. Krzywinski, R. Nietubyc, J. B. Pelka, A. Andrejczuk, R. Sobierajski, L. Ryc, F. P. Boody, H. Fiedorowicz, A. Bartnik, J. Mikolajczyk, R. Rakowski, P. Kubat, L. Pina, M. Horvath, M. E. Grisham, G. O. Vaschenko, C. S. Menoni, J. J. Rocca: Short-wavelength ablation of molecular solids: pulse duration and wavelength effects, J. Microlith. Microfab. Microsyst. 4, 033007 (2005). 11. T. Mocek, B. Rus, M. Kozlová, M. Stupka, A. R. Präg, J. Polan, M. Bittner, R. Sobierajski, L. Juha: Focusing a multimillijoule soft x-ray laser at 21 nm, Appl. Phys. Lett. 89, 051501 (2006). 12. V. Ayvazyan et al.: First operation of a free-electron laser generating GW power radiation at 32 nm wavelength, Eur. J. Phys. D37, 297-303 (2006). 13. M. Richter, A. Gottwald, U. Kroth, A. A. Sorokin, S. V. Bobashev, L. A. Shmaenok, J. Feldhaus, C. Gerth, B. Steeg, K. Tiedtke, R. Treusch: Measurement of gigawatt radiation pulses from a vacuum and extreme ultraviolet freeelectron laser, Appl. Phys. Lett. 83, 2970-2972 (2003). 14. J. M. Liu: Simple technique for measurements of pulsed Gaussian-beam spot sizes, Opt. Lett. 7, 196-198 (1982). 15. S. Küper, M. Stuke: Ablation of UV-transparent materials with femtosecond UV excimer laser pulses, Mat. Res. Soc. Symp. Proc. 129, 375-384 (1989). 16. P. W. Bohn, J. W. Taylor, H. Guckel: Vacuum ultraviolet photochemistry of thin resist films, Anal. Chem. 53, 1082-1087 (1981). 17. S. Baudach, J. Bonse, J. Krüger, W. Kautek: Ultrashort pulse laser ablation of polycarbonate and polymethylmethacrylate, Appl. Surf. Sci. 154-5, 555-560 (2000). 18. A. Costela, I. Garciamoreno, F. Florido, J. M. Figuera, R. Sastre, S. M. Hooker, J. S. Cashmore, C. E. Webb: Laser ablation of polymeric materials at 157 nm, J. Appl. Phys. 77, 2343-2350 (1995). 19. D. Riedel, M.C. Castex: Effective absorption coefficient measurements in PMMA and PTFE by clean ablation process with a coherent VUV source at 125 nm, Appl. Phys. A 69, 375-380 (1999).

Inner-Shell Ionization in Xe Clusters Irradiated with X-Ray Laser Pulse S. Namba1, N. Hasegawa, M. Nishikino, T. Kawachi, M. Kishimoto, M. Tanaka, Y. Ochi, K. Nagashima and K. Takiyama1 1

Graduate school of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima, Hiroshima, 739-8527, JAPAN Advanced Photon Research Center, Japan Atomic Energy Agency, 8-1 Umemidai, Kizu-cyo, Souraku-gun, Kyoto, 619-0215, JAPAN

Summary. The interaction of large xenon clusters with an x-ray laser pulse having a wavelength of 13.9 nm and intensity of up to 2x1010 W/cm2 was investigated using a time-of-flight ion mass spectrometer. The photon energy is high enough to photoionize the inner-shell electron of the Xe atom. In contrast to the experiment at synchrotron radiation, the enhancement of double Auger decay probability with increasing cluster size and x-ray laser intensity was observed for the first time.

1 Introduction The interaction of rare gas clusters with ultrashort, high-intensity laser pulses from IR to UV wavelength regime has attracted a great deal of interest for fundamental condensed matter physics and various applications.1 However, little was known about the ionization process and expansion dynamics of the cluster irradiated with an intense x-ray laser pulse. In the recent vacuum ultraviolet free electron laser (VUV-FEL) experiment at DESY, Wabnitz et al. found that each atom in large Xe cluster subjected to VUV laser pulse with a 98 nm, 100 fs and 2x1013 W/cm2 absorbed 30 photons (~400 eV).2 This result was very surprising, since for short wavelength laser pulses the collisional heating is suppressed significantly due to its small ponderomotive energy and quiver amplitude,3 which are the most decisive differences between the conventional optical lasers and x-ray laser. In order to identify the photoabsorption mechanism in clusters, various numerical approaches have been also attempted so far. We have tried to clarify the ionization dynamics in Xe clusters irradiated with much shorter wavelength laser (λ=13.9 nm) than that of VUVFEL. In contrast to the optical laser regime, where the ionization is initi-

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ated from the outermost valence electrons, the electrons illuminated with x-ray laser should be stripped from inside, i.e., inner-shell ionization. The photon energy of the x-ray laser (89.2 eV) is high enough to photoionize the inner-shell 4d electron (threshold energy: ~70eV) and its cross section is by ten times larger than that of the valence electron. Subsequently, this inner-hole is instantaneously refilled by the valence electron, resulting in the productions of a photo- and an Auger electron and a Xe2+ ion. Similar experiments have been extensively performed at synchrotron radiation facilities.4 It should be noted that, compared with these light sources, the x-ray laser pulse has considerably higher intensity, so that the nonlinear process and collective effect in the clusters could be expected.

2 Experimental setup The experiment was carried out with the x-ray laser facility at JAEA Kansai. The detailed description of the x-ray laser system is given in Ref. 5. The x-ray laser with a wavelength of 13.9 nm, duration ~7 ps and energy ~500 nJ was generated by transient collisional excitation (TCE) scheme for nickel-like silver. The maximum laser intensity focused with a Mo/Si multilayer spherical mirror was ~2x1010 W/cm2 on target. Xe and Kr cluster targets were prepared by injecting the high stagnation pressure gas into vacuum with a pulsed supersonic nozzle.6 The average cluster size was estimated by Hagena scaling law.7 In order to examine the size effect of Xe clusters subjected to x-ray laser pulse, various average sizes of clusters from 103 up to 106 atoms/cluster were generated by changing the stagnation pressure. Moreover, a seeding technique (Xe 30%-He 70%) was also applied to promote the formation of larger clusters.6 The Xeq+ ion emitted from Xe clusters was measured using a time-offlight mass spectrometer (TOF-MS). The observation was achieved along to the parallel direction to the laser polarization plane. To measure the xray laser intensity, a soft x-ray CCD camera was also installed 50 cm from the intersection of the laser and cluster beam.

3 Results and Discussion TOF spectra for the Kr clusters irradiated with the x-ray laser pulse are shown in Fig. 1 for various backing pressures. Ion count rate of Kr+ increased monotonically with the backing pressure, while Kr2+ ion spectrum was not observed. Considering that the threshold energies for the inner-

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Fig. 1. TOF ion mass spectra for various Kr stagnation pressure

shell ionizations of Kr 3d electrons are 93.8 and 95.0 eV for 3d5/2 and 3d3/2, respectively,8 the core-hole arising from the absorption of single photon cannot be generated. Therefore, it is reasonable that only singly-charged ion was observed for the Kr gas jet. The ion mass spectra obtained also suggest that the photoelectron with kinetic energy of ~75 eV did not contribute to a further ionization of Kr+, creating Kr2+ ion, due to the collisional ionization process. In contrast to the results for Kr cluster targets, the highly-charged ion mass spectra up to Xe3+ were observed for Xe clusters as shown in Fig. 2 for various Xe-He stagnation pressures. The cross section for the innershell ionization of 4d electron is ~16 Mb at photon energy of ~90 eV.8 According to the similar results with synchrotron radiations, the dominant decay process following the inner vacancy is the normal Auger process denoted by N4,5O2,3O2,3, and the ratio of Xe2+ to Xe3+ ion yield was estimated to be ~4, which is independent upon incidence photon energy in 4d shape resonance region.9 Nevertheless, the Xe3+ ions generated in the present study became dominant ionic fragment for the higher backing pressure (Xe2+/Xe3+ ratio: ~0.55). A similar trend in the laser intensity was also obtained. The results, therefore, implies that the double Auger decay, which emits two electrons simultaneously or stepwise, should be preferable for larger Xe clusters exposed to brighter x-ray laser pulse. For pure Xe gas jet without being diluted by helium, the higher stagnation pressure and laser intensity were required to obtain the similar spectra with in Xe-He gas jets. Given that the average cluster size in Xe gas jet

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1.5 15atm 1.0 0.5 0.0 1.5 10atm 1.0 0.5 0.0 1.5 5atm 1.0 0.5 0.0 1.5 1atm 1.0 0.5 0.0

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Fig. 2.. TOF ion spectra for various Xe-He stagnation pressures.

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Fig. 3.. Intensity dependence of Xeq+ and He+ ions on the laser intensity.

was probably smaller than that in Xe-He gas injection, this result strongly suggests that the appearance of larger clusters in Xe-He gas jet should significantly influence the photoabsorption and subsequent cluster dynamics. Figure 3 shows the dependence of ionic products on the x-ray laser intensity at the Xe-He stagnation pressure of 15 atm. The fact that in contrast to

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the Xeq+ ion yield behaviors the He+ ion yield increased almost linearly with the laser intensity probably indicates that He+ ion did not suffer from the nonlinear process. Although the mechanism underlying the enhancement of double Auger probability with the cluster size and x-ray laser intensity has not been clarified, the collective effect in the clusters, such as lowering of ionization potential due to polarization screening,10 is likely to play an important role in the efficient production of Xe3+ ions. The further investigation using electron TOF spectrometer will make it possible to identify the ionization and decay processes of inner-hole in the clusters.

4 Summary The interaction of large Xe clusters with intense x-ray laser pulse with a wavelength of 13.9 nm and intensity 2x1010 W/cm2 was investigated using TOF mass spectrometer. In contrast to the experiment at synchrotron radiation, the enhancement of double Auger decay probability with the cluster size and x-ray laser intensity was observed for first time. Although the mechanism underlying the enhancement of double Auger probability with the cluster size and x-ray laser intensity has not been clarified, the further investigation using electron TOF spectrometer will make it possible to identify the ionization and decay processes of inner-hole in the clusters.

References 1. V.P. Krainov and M.B. Smirnov, Phys. Rep. 370 237 (2002), and references therein. 2. H. Wabnitz, et al., Nature 420 482 (2002). 3. U. Saalmann and J. M Rost, Phys. Rev. Lett. 89 143401 (2002). 4. U. Becker, et al., Phys. Rev. A 39 3902 (1989). 5. T. Kawachi, et al., Phys. Rev. A 66 033815 (2002). 6. M.D. Morse, Atomic, Molecular, and Optical Physics: Atoms and Molecules, ed. F. B. Dunning and R.G. Hulet, Academic Press (1996). 7. O.F. Hagena and W. Obert, J. Chem. Phys. 56 1739 (1972). 8. D.M. Holland, et al., J. Phys. B: Atom. Molec. Phys. 12 2465 (1979). 9. T. Luhmann, et al., Phys. Rev. A 57 282 (1998). 10. O. Björneholm, et al., Phys. Rev. Lett. 74 3017 (1995).

VUV and Soft X-Ray Spectroscopy Using a Toroidal Grating Spectrograph E. Jourdain1, W. Biel2, D. Lepère1, J. Serre1, A. Liard1, A. Greiche2 and R. Burhenn3 1

HORIBA Jobin Yvon SAS, 16-18 rue du Canal, 91165 Longjumeau, France 2 Institut für Plasmaphysik, Forschungszentrum Jülich Gmbh, D-52425 Jülich, Germany 3 Max-Planck-Institut für Plasmaphysik, D-17491 Greifswald, Germany

Summary. Optical spectroscopy is a key tool to monitor and therefore analyse properties of laser emission light sources such as X-Ray lasers. A spectrograph instrument that produces flat field detection over relative wide spectral range enables quick and reliable analysis of X-Ray laser emitted spectra thanks to the easy coupling with CCD camera or MCP detector. We present a compact spectrograph design based on aberration corrected toroidal diffraction gratings dedicated to optical spectroscopy in the VUV and Soft X-Ray wavelength range. The toroidal aberration corrected grating acts as a diffractive and focusing element allowing compact design with only one optical element. Such compact design provides high throughput, good wavelength purity as well as great stability and reproducibility. After a review of the flat field toroidal grating parameters design, we present the performances of several toroidal gratings optimised for operation in the 2.5 to 170 nm wavelength range. Measured spectra of pinch discharge sources are presented to illustrate the performance of toroidal spectrograph instruments

1 Introduction Spectrograph instruments that produce flat field detection over relative wide spectral range enables quick and reliable analysis of X-Ray laser emitted spectra thanks to the easy coupling with CCD camera or MCP detector. We present a compact spectrograph design based on aberration corrected toroidal diffraction gratings dedicated to optical spectroscopy in the VUV and Soft X-Ray wavelength range. The toroidal aberration corrected grating acts as a diffractive and focusing element allowing compact design with only one optical element. Such compact design provides high

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throughput, good wavelength purity as well as great stability and reproducibility.

2 Optical Layout Definition and Optimisation

2.1 Optical principle The toroidal grating spectrograph is based on an optical design that includes a single optical piece in order to maximise instrument throughput while maintaining good spectral purity. This optical piece is a diffraction grating engraved on a toroidal substrate which therefore acts as focusing (toroidal surface) and dispersive optic (grating)1. In addition to the required focusing effect in the dispersive direction the toroidal surface focus the beam in the sagittal direction operating thus as a stigmatic system. The dispersive property of the system is provided by the groove pattern (diffraction grating) holographically recorded on the toroidal surface. Using the interference of two spherical wavefronts to generate the groove distribution over the grating surface it is possible to obtain non constant groove variation of the grating surface which permit to correct partially optical aberrations of the optical system. 2.2 Geometry The spectrograph optical geometry is defined by a set of a few parameters that are the incidence angle (α), the central groove distribution (N), the entrance arm length (La), the exit arm length (LH ), the detection angle (βH), the wavelength range (λmin, λmax) and the flat field length. The incidence angle is mainly fixed by the reflectivity of the coating at αmin, the flat field length is defined according to detector length (40 or 25.4 mm), the arm length and groove density are defined according to grating law and dispersion in order to minimise the overall instrument length while keeping good spectral resolution. The detection angle is fixed according to detector efficiency2 and alignment issues. When the optical geometry of the system is defined, we can optimise the grating parameters (radii of curvature, holographic recording wavefronts). This optimisation is performed numerically through minimisation of optical path difference at different wavelengths while taking into account manufacturing constraints3.

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Fig. 1. Optical layout of a Toroidal Grating Spectrograph.

3 Performances Simulation and Mechanical Design

3.1 Ray Tracing Ray tracing simulation is performed using dedicated software to predict the line width of the instrument. Source geometry (size, divergence), entrance slit size, grating active area and detector configuration (pixel equivalent size) are key parameters that are used to determine the image size and therefore determine the spectral line width. As shown in Figure 2 the toroidal aberration diffraction grating provides images with low astigmatism, geometrical throughput (TH) close to 100%, which is not the case for spherical grating based instrument such as Rowland circle designs. 3.2 Mechanical Design The designed TGS instrument is a robust and stable vacuum compatible setup that has some adjustment possibilities such as entrance slit width, detection plane position in order to accommodate different detector type

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Fig. 2. Ray Tracing Simulation of TGS image.

(MCP, CCD). These two adjustments can be locked providing stable long term operation of the instrument. The detection flange is a standard DN100CF enabling operation with any type of vacuum compatible detector. Pressure in the range of 1x10-6 mbar is achievable ensuring safe operation of MCP detector.

Fig. 3. TGS Mechanical Setup.

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4 Toroidal Spectrograph Performances

800 N VI N2 750 O2 700 Ne 650 Ar ArI X 600 Ne V II 550 500 450 O VI 400 350 Ne VIII 300 250 ArIX 200 O VI N VI(2nd) 150 N VI Ne V II 100 50 0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 / nm

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si gnal/cts

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A set of 7 different diffraction gratings has been developed and tested to monitor VUV and Soft X-Ray radiation in the range 2.5 to 170 nm. The TGS300 series includes three gratings which work with the same optical layout, i.e. these gratings are interchangeable and can therefore be included in the same mechanical setup. The HEXOS diffraction gratings series has been initially developed to monitor the emission spectra of the Wendelstein 7-X Stellarator Experiment4 in the range of 2.5 to 160 nm. These four gratings exhibit high etendue with good spectral resolution5.

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In the Table 1 we present the measured spectral resolution (FWHM) of the different gratings developed. The table 1 present also the source used to test the grating. Table 1 Main parameters of the different developped TGS gratings including spectral range detectable over 40 mm and measured spectral resolution Spectrometer

Spectral Range (nm)

Resolution FWHM (nm)

Focal (mm)

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20 – 66

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350

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60 – 160

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10 – 32

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5 Conclusion A compact spectrograph design has been developed and tested to characterise VUV and Soft X-ray sources using a single optical element concept. Up to seven aberrations corrected toroidal gratings have been developed to monitor and analyse Vacuum Ultra Violet and Soft X-Ray source emission spectra. Spectral as well as temporal studies of laser X sources can be easily done combining such diffraction gratings with a robust and stable TGS mechanical design.

References 1. D Lepère, Nouvelle Revue d’Optique 6, 173, 1975 2. A. Kenter et al, HRC Quantum Efficiency Versus Angle of Incidence (internal memorandum) (Center of Astrophysics, 1998). http://cxc.harvard.edu/cal/Hrc/Documents/pore_ang.ps 3. Biel W., Bertschinger G., Burhenn R., König R. and Jourdain E., Rev. Sci. Instrum. 75, 3268, 2004 4. Wanner M. and the W7-X team, Plasma Phys. Controlled Fusion 42, 1179, 2000 5. Biel W., Greiche A., Burhenn R., Jourdain E. and Lepère D., Rev. Sci. Instrum. 77, 2006 6. K. Bergmann et al., Appl Opt 38, 5413, 1999

Development and Application of a Compact Broadband Laser-Plasma EUV Source L. Koch and B. Wellegehausen Institut für Quantenoptik, Leibniz Universität Hannover

Summary. An incoherent compact broadband (ca. 10 nm to 50 nm) laser-plasma EUV source was developed, witch consists of a small-sized 20 mJ diode-pumped Nd:YAG laser and a cylindrical target with galvanic gold coating.

1 Introduction For the measurement and control of EUV optical components, easy to use sources and complete spectrometers are needed. For this, an incoherent compact EUV source based on a laser-induced plasma was developed, consisting of a small-sized diode-pumped Nd:YAG laser (1064 nm) with

Fig.1. Photo of the complete apparatus and look into the target chamber

20 Hz repetition rate, 20 mJ pulse energy and 8.5 ns pulse duration. Fig. 1 shows two photos of the source, Fig. 3 presents a schematic setup.

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The targets consist of a steel cylinder (100 mm height, 50 mm diameter) with a galvanic gold coating and are rotated and translated to offer a fresh surface for each laser pulse, allowing an operating time of 80 hours with one cylinder. Jenoptik Spektrograph Jobin Yvon Monochromator calibration with Jenoptik E-Mon

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With the gold target a broadband spectrum extending from about 10 nm to 50 nm is generated with a photon flux of 1.5x1014 photons/sec/(2π sr 2%BW) at 13.5 nm and a source size of 0.01 mm². This corresponds to a brilliance of 2.4x1015 ph/sec/(sr mm² 2%BW). At a wavelength of 18 nm, photon flux and brilliance are about six times larger (Fig.2).

2 The debris problem For laser induced plasmas with a solid state target, handling of the debris emission (particles emitted from the target by laser-ablation), which may disable surrounding optics, is of crucial importance.

The emission of debris depends on the angle with respect to the target surface. For the cylindrical target surface used here, measurements yield a near Gaussian distribution (Fig. 2). The emission of bigger particles is even more directed to the target normal. Consequently, radiation emitted at 90° to the target normal is used for the spectrometer. At this angle the radiation flux is for example still about 40 % of the flux which is emitted at an angle of about 60°. A further advantage of this geometry is the use of an alignment laser directed along the tangent.

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Fig. 3. Debris flux distribution and schematic setup

For further reduction of the debris emission, a background gas in combination with a conic capillary structure as a pressure stage, as indicated in Fig. 4, was tested. For different target materials like copper, silver, gold and aluminium it turns out that the amount of debris can be reduced by more than two orders of magnitude at a loss of radiation of only about 75% at 20 nm (Fig.4).

Fig. 4. Reducing debris with a capillary structure and a gas jet: schematic setup and transmission of the capillary structure with a gas jet with different resulting background pressures in the vacuum chamber

3 Gold debris on gold coated mirrors Measurements of the effect of the gold debris particles still hitting the gold coated grazing incidence collector mirror (Fig.3) show, that under the given geometric conditions this debris does not deteriorate the reflectivity and focussing conditions of this mirror in a measurable degree after hundreds of operating hours. When placing uncoated test mirrors at the posi-

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tion of the grazing incidence mirror or even closer or at other position to the target (to enhance the debris flux), these mirrors are coated more or less fast, and it was found that the generated surfaces and measured reflectivities were almost as good as those of commercial mirrors. Thus the usual debris problem of plasmas and especially solid state plasmas doesn’t exist with this developed EUV source, at least for so far more than several hundreds of operation hours.

4 EUV signal deviations The EUV radiation flux of laser induced plasma generally shows shot-toshot fluctuations of at least 5 %. In addition there can be flux variations for longer time durations depending on thermal and mechanical instabilities, for example on a decrease of the laser pulse energy through a temperature increase or degradation of the diode pump power. To compensate such variations, a reference diode (Fig. 3) is used together with an aluminium filter to avoid visible and UV light. 1,08

signal behind monochromator, 30 nm reference diode with aluminium filter quotient

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Fig. 5. Reduction of the signal deviation with a reference diode

Figure 5 shows the effect of the reference diode. The filter in front of the reference diode should be such that it is transparent near to the wavelength at which the measurements are done and that strong signals are obtained, to better suppress radiation-independent deviations of the measuring devices, which doesn’t correlate for the two detectors. It turned out, that the aluminium filter is the best compromise (although examined were a zirconium filter and a 13.5 nm multilayer mirror), even

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for measurements at 13.5 nm. With the reference diode the fluctuations can be reduced by a wavelength-depending factor of 3.6 at 13.5 nm and 7.7 at 30 nm. For example, averaging over 400 pulses (that takes 20 seconds) results in a standard error of < 0.1% at measurements of the reflectivity.

5 Applications This EUV source, based on a laser-induced gold plasma and a gold coated collector mirror, is an easy to use compact device for all purpose measurement applications and has been used for the characterization of multilayer mirrors at different wavelengths. As an example of the specific possibilities of this source due to the broadband spectrum, Fig. 6 shows transmission measurements of gaseous samples. The transmission measurement in argon (left diagram) is compared with theoretical values [1]. The right diagram shows in detail a structure due to innershell excitation (Ar → Ar+ : (3s)²(3p)6 → (3s)²(3p)54p), which is not included in the theory. 0,45

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Fig. 6. Transmission in argon. Left: measured and literature values Right: inner shell excitation in Argon (for different pressures)

In conclusion, an easy to handle EUV plasma source has been developed, which is well applicable in the spectral range of 10 nm to 50 nm. By using a more powerful pump laser system of 100 mJ, the wavelength range can easily be expanded to the “water window”.

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Acknowledgements This project was supported by the BMWi under grant VDI Innonet 16IN0211. The authors thank IfG – Institute for Scientific Instruments GmbH for supply and help in using the capillary structure.

References 1. http://www-cxro.lbl.gov/optical_constants/

Generation of the Submicron Soft X-Ray Beam Using a Fresnel Zone Plate M. Nishikino, H. Kawazome, M. Tanaka, M. Kishimoto, N. Hasegawa, Y. Ochi, T. Kawachi, K. Sukegawa, H. Yamatani, K. Nagashima and Y. Kato Advanced Photon Research Center, Quantum Beam Science Directorate, Japan Atomic Energy Agency

Summary. We have developed a fully coherent x-ray laser at 13.9 nm and the application research has been started. The generation of submicron x-ray beam is important for the application of high intensity x-ray beam, such as the non-linear optics, the material science, and the biology. The submicron x-ray bee am is generated by the soft x-ray laser with using a Fresnel zone plate. The spot diameter is estimated about 680 nm (290 nm at FWHM) by the theoretical calculation. In this experiment, the diameter of the x-ray beam is measured by the knife-edge scan. The diameter and the intensity are estimated 730 nm (310 nm at FWHM) and 3×1011 W/cm2, respectively.

1 Introduction We have demonstrated a fully coherent x-ray laser (XRL) at a wavelength of 13.9 nm by the double-target configuration1-3). The application researches, such as microscopy4), interferometry5), and speckle measurement6) have also progressed. An intense micro-focus x-ray beam is expected to open various fields, such as the non-linear phenomena and the local irradiation of the material and the cell tissue. Many types of x-ray focusing device have been developed to generate micro-focus x-ray beam713) , and sub-µm spot size has already been achieved in hard x-ray region913) .In this paper, we present the results of x-ray focusing test using the Fresnel zone plate (FZP) in x-ray wavelength of 13.9 nm.

2 Experiment setup and results A schematic view of the experimental setup is shown in Fig.1(a). The experiment has been performed at JAEA Plasma X-ray Laser (JAEA-XRL) beamline. Figure 1(b) shows a far-field pattern (FFP) of the double-target

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XRL beam. The XRL beam divergences along the vertical and horizontal directions are 0.4 and 1.0 mrad at full width half maximum (FWHM), respectively. The output energy of the XRL beam is about 0.2 µJ. The distance between the first target and the FZP is 2820 mm, and the distance between the FZP and the CCD camera is 240 mm. The image of the diffracted x-ray beams was measured with the CCD camera. In this experimental arrangement, the efficiency of the incident XRL energy to the FZP is about 10 %, wihich is evaluated from the XRL beam divergence and the diameter of the FZP of 500 µm.

(a)

(b)

1950 mm

1.0mrad

1st target

Laser

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2nd target

W-target XRL CCD camera

FZP

Mo/Si Mirror Knife edge 870 mm

240 mm

Fig. 1. (a) Schematic view of the experimental setup. (b) The FFP of the doubletarget XRL.

The FZP consist of the polymethyl methacrylate (PMMA) zone on a 1×1 mm silicon nitride (SiN) membrane. The diameter of the FZP is 500 µm, and the total zone number and outermost zone width are 450 and 280 nm, respectively. The focal length at 13.9 nm is 10 mm. The expected spot diameter at the focal position is 680 nm (290 nm at FWHM) theoretically. The first order diffraction efficiency of Generic FZPs with alternately opaque and transparent circular annuli is given by 1/π2 ≈ 0.10. In contrast, the diffraction efficiency can be increased by replacing the opaque zones

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with phase shift of π. Then, the first order diffraction efficiency increases by a factor of four compared to the generic FZP. Since, the refractive index n = 1-δ+iβ is not negligible for x-ray region, the factor of four is not possible. The optimum zone plate thickness of the phase zone plate (PZP) has been calculated by a function of the parameter β/δ14,15). Then, the thickness of PMMA zone is determined as 250 nm, and the phase sift of the PMMA zones is 2.9 rad ≈ 0.92 π. The efficiency of the first order diffraction is about 0.23. The focusing efficiency of the PZP is about 2 times better than the FZP (~1/π2).

(b)

(a)

1.0 Ratio of diameter

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0.8 0.6 0.4 0.2

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Z=0µm Z=+14.6µm

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2 310 nm

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Fig. 2. (a) The diffraction pattern of the PZP. (b) The measured ratio of the diameter of the submicron x-ray beam. The white dot line is the 1st diffracted x-ray. (c) The estimated intensity profiles in the case of the focal plane (Z = 0 µm) and Z = 14.6 µm.

Figure 2(a) shows the 1st order diffracted x-ray, the -1st order diffracted x-ray, and the transmitted 0th order x-ray. The diameter of an x-ray beam

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has been measured by using the knife-edge scan. The knife-edge cuts the diffracted x-ray beams and the transmitted x-ray by using a 10 nm control stage. It is better to put in the order-selecting aperture for selecting the 1st order diffracted x-ray beam. Figure 2(b) shows the ratio of the diameter of the submicron x-ray beam. The diameter of an x-ray beam is estimated to be 730 nm (310 nm at FWHM) or less by the measured distribution of the 1st order diffracted beam. The spatial sift of the optical axis (Z-axis) from the focal plane is estimated to be 14.6 µm, and the peak intensity of measurement position is estimated to be about 70 % of the ideal peak intensity of the focal plane. Figure 2(c) shows the intensity profiles in the case of the focal plane and Z = 14. 6µm. The peak intensity is estimated to be about 3×1011 W/cm2 at the measurement position. The focal intensity is influenced by the beam divergence, and the experimental setup. When the distance between the light source of the XRL and the FZP is long, the efficiency of the incident XRL energy to the FZP is low. In the case of the optimum position of the FZP alignment, the peak intensity can increase 10 times.

3 Conclusion We have performed the generation of submicron x-ray beam by using the FZP. In the experiment of the submicron x-ray beam, the spot diameter and the peak intensity of the focused beam are estimated to be 730 nm (310 nm at FWHM) and 3×1011 W/cm2, respectively. In order to increase focal intensity, we need further improvement of the output of the XRL and the arrangement of the FZP. On the other hand, the focal intensity can be increased by using the FZP with the small outermost zone width. The submicron x-ray beam can also be used as the x-ray source of the Fourier transform holography as one of the application of submicron x-ray beam generation. A Fourier transform hologram records the interference between the object wave diffracted from the object and the spherical reference wave. The FZP generates a point reference source and works as a beam splitter. The transmitted 0th order beam illuminates the object directly.

Acknowledgements The authors would like to acknowledge the support and encouragement of Dr. Y. Kato, Dr. T. Kimura, Dr. T. Tajima, and Dr. K. Namikawa. This re-

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search was partially supported by the Ministry of Education, culture, sports, science and technology, Grant-in-Aid for Young Scientists (A), 17684030, 2006.

References 1. M. Tanaka et al., Opt. Lett., 28, 1680-1682, 2003. 2. M. Nishikino et al., Phys. Rev. A68, 061802(R), 2003. 3. M. Nishikino et al., IEEE Journal of Selected topics in quantum electronics, 10, November/December 2004, 1382-1387. 4. M. Kishimoto et al., J. Phys. IV France, 104, 141-143, 2003. 5. H. Tang et al., Appl. Phys. B 78, 975-977, 2004. 6. R. Z. Tai et al., Phys. Rev. Lett., 93, 087601, 2004. 7. B. R. Benware et al., Opt. Lett, 24, 1714-1716, 1999. 8. H. Mashiko et al., Opt Lett., 29, 1927-1929, 2004. 9. A. Snigirev, Rev. Sci. Instrum. 66, 2053-2058, 1995. 10. W. Yun et al., Rev. Sci. Instrum. 70, 2238- 2241, 1999. 11. B. Lengeler et al., Appl. Phys. Lett.74, 3924-3926 ,1999. 12. M. Awaji et al., Rev. Sci. Instrum 74 4948-4949, 2003. 13. H. Yumoto et al., Rev. Sci. Instrum 78, 063708,2005. 14. D. Atwood, Soft X-rays and Extreme Ultraviolet Radiation, Cambridge University Press, 1999. 15. J. Kirz, J. Opt Soc. Amer. 64, 301-309, 1974.

Hydrodynamic Simulations and Soft X-Ray Laser Interferometric Studies of Energy Transport in Tightly Focused Laser-Heated Aluminum Plasmas J. Dunn, S. J. Moon, R. F. Smith, R. Keenan, J. Nilsen and J. R. Hunter Lawrence Livermore National Laboratory, Livermore, CA 94551, USA J. Filevich, J. J. Rocca and M. C. Marconi NSF ERC for Extreme Ultraviolet Science and Technology and Dept. of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO 80523, USA V. N. Shlyaptsev University of California Davis-Livermore, Livermore, CA 94551, USA

Summary. A plasma generated by a tightly focused ~14 µm (FWHM), 600 ps duration laser beam at an irradiance of 1013 W cm-2 on a flat aluminum target is investigated. We report new findings that give a better understanding of the energy transport mechanisms in the measured plasma. The formation of a small, on-axis dip or concave electron density profile is observed. Detailed modeling of the spatial and temporal profile of a laser-produced plasma with the 2-D LASNEX hydrodynamics code gives good agreement with the observed features. The observed cold plasma formation along the target surface hundreds of microns away from the small focal spot is generated by heated material outside of the laser focus. Plasma generated by low intensity wings in the laser spatial profile is augmented by soft x-ray radiation from the hot coronal plasma heated by the laser. The simulations show that the x-ray heating will produce a plasma outside the focal spot without the low intensity wings. Strong thermal electron conductive heating due to large thermal gradients continues to generate ablation outside the laser spot and formation of lobes on each side of the focal spot.

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1 Introduction Soft x-ray laser interferometry is an important diagnostic for measuring 2dimensional (2-D) density profiles of laser-produced plasmas [1, 2]. When combined with a short temporal pulse it allows dense plasma features to be studied close to the target surface with micron and picosecond resolution [3, 4]. For example, several recent experiments using ~ 14 nm wavelength interferometry have shown fringe reversal close to the target surface at late times during the recombination stage for cool aluminum plasmas [5, 6]. This was interpreted as the effect of low charge state bound electron contribution to the plasma index of refraction [6]. Our efforts over the years have been to refine and direct the technique to study dense plasma regimes that cannot be accessed by other techniques. In particular, x-ray laser interferometry can give new insight and better understanding of the energy transport mechanisms in high-density plasmas. In this paper, we have investigated the plasma evolution at various times for a tight laser line focus on a flat aluminum target. Preliminary results were reported at the 9th International Conference on X-ray Lasers held in Beijing, China in 2004 [7]. We have observed the formation of a small plasma dip on-axis during the rising edge of the laser pulse where there is a change from a convex to a concave density spatial profile. The latter is observed to persist well after the laser has ended. There is also the formation of denser side lobes on the periphery of the laser focus. These evolve progressively at farther distances from the laser spot. We discuss the experimental data and compare with 2-D LASNEX simulations.

2 Experimental Description The experiments were conducted on the Compact Multipulse Terawatt (COMET) laser at the Lawrence Livermore National Laboratory. Several papers have described the technique in detail for generating the Ni-like Pd 4d – 4p transition at 14.7 nm: The skewed Mach-Zehnder interferometer uses 900 lines per mm gratings as beam splitters with 0th and 1st order reflections for the two arms [3, 4]. The main features of high reflectivity, established technology and robustness of the diffraction grating interferometer (DGI) are well suited to the microjoule level output of this tabletop xray laser. The x-ray laser pulse duration of ~5 ps gives the time-resolution for the interferometry. The x-ray laser and the plasma-forming beam were generated by the same laser oscillator and were synchronized. The relative timing was adjusted with a delay line on the plasma-forming beam.

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The laser-produced plasma conditions were generated with a 600 ps (FWHM), 1054 nm wavelength laser containing 3.1 J of energy. A line focus of dimension 14 µm (FWHM) by 0.32 cm was generated with a combination of a spherical and cylindrical lens. This was incident on a 0.1 cm wide flat aluminium target. The x-ray laser probed the axis of the 0.1 cm plasma longitudinally. The end of the plasma was imaged by a Mo:Si multilayer-coated spherical mirror with a focal length of 25 cm. The image was magnified 22 times onto a back-thinned charge-coupled device (CCD) with 1024 × 1024 pixels (pixel size 13 × 13 µm2).

Fig. 1. (a) 14.7 nm x-ray laser interferogram measured at 0.3 ns after the peak of the laser pulse of aluminum plasma heated at 1013 W cm-2 in 14 µm (FWHM) focus. Note that the laser is incident from right side and the vertical axis has a different scale. (b) Density profile extracted from interferogram. (c) 2-D LASNEX simulation at same time.

Figure 1 shows experimental and simulation results at 0.3 ns after the peak of the plasma-heating beam. The interferogram of Fig. 1(a) indicates that the plasma has an expected convex density profile from an approximately cylindrically expanding plasma at distances further than 50 µm from the target surface. However closer to the surface, typically within 25 µm, there is a pronounced on-axis density dip centered at the peak intensity of the laser. This feature is well established at this time and is observed to form during the rising edge of the laser pulse. Side lobes adjacent to the dip are observed to expand laterally in time.

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3 Hydrodynamic Simulations The hydrodynamic simulations of the experimental laser plasma conditions were performed using the 2-D LASNEX code [8]. The experimental spatial and temporal profiles were used in the simulations for comparison with the measured density profiles at various times. Arbitrary Lagrange Eulerian (ALE) hydrodynamics was adopted. A 3-D laser ray-tracing and deposition packages were included with inverse bremsstrahlung as the main absorption mechanism. Radiation transport utilized flux limited multigroup diffusion with a flux limiter f = 0.1. The flat aluminium target was zoned with 1-µm steps laterally with finer steps inside the target. Thermal conductivity and electron-ion coupling were from the Lee-More model [9] and the Quotidian Equation of State (QEOS) was used [10]. Figure 1(b) shows the 2-D density profile extracted from the interferogram as well as a 2-D simulation from LASNEX, Fig. 1(c). There is excellent agreement showing the formation of the main features at various times.

Fig. 2. 2-D LASNEX simulations of an Al target heated by a 600 ps pulse at 1013 W cm-2 in a 10 µm square spatial focus. The laser is incident from left. The 1021 cm-3 and 1020 cm-3 contours indicated by black and gray filled circles, respectively. (a) Taken at -0.5 ns before the laser peak. (b) Taken at 0.3 ns after peak of laser.

Additional hydrodynamic simulations were performed to study a square spatial beam profile with a 10 µm wide focus irradiated at 1013 W

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cm-2. The experimental temporal pulse shape was used. The square spatial profile was used to remove the effect of plasma formation outside of the focal spot from direct laser heating and therefore study the basic energy transport mechanisms. Figure 2(a) and (b) show the density profile at -0.5 ns and 0.3 ns, respectively, to the laser peak before and after the formation of the on-axis density dip. The early time has the classic convex 2-D density profile expected from a small laser focus. Approximately 200 ps later as the plasma corona is rapidly heated by the laser, mass is ablated outside the laser spot from a combination of x-rays and thermal electron conduction. The critical surface becomes concave due to the rapid expansion of the directly heated material while the cooler surrounding material beside the corona experiences thermal pressure from the hotter material. The result is the formation of denser side lobes that remain part of the density profile late in time, Fig. 2 (b). Low temperature ionized material outside the laser spot continues to be generated by x-rays and is further heated by thermal electron conduction. This plasma moves perpendicular to the target surface in a larger area surrounding the central region.

4 Discussion The observation of an on-axis, density depression using 46.9 nm interferometry was reported three years ago [11]. While the underlying energy transport mechanisms are similar, there are differences between these two experiments. The 600 ps pulse duration here is twenty times shorter and two orders of magnitude higher irradiance than the earlier line focus work. Although the non-local radiative heating is shorter the higher coronal temperatures (Te ~ 200 eV versus ~30 eV) produce strong ablation outside of the laser focal spot. In the earlier work the peripheral region is clearly heated by softer energy photons and for longer times that establishes a more steady-state condition. This may explain the reason for the observation of the lobes extending further away and beyond 100 µm from the target surface. The lobes in this work, shown by Fig.1, are visible only up to 40 µm from the target.

5 Conclusions We have reported the use of picosecond duration, 14.7 nm x-ray laser interferometry to study the energy transport in narrow line focus laserproduced plasmas. The main features of the on-axis density dip and forma-

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tion of the side lobes have been observed and are explained by the nonlocal soft x-ray heating generating cool plasma outside of the laser focus. This is then further heated by thermal electron conduction. The detailed 2D hydrodynamic simulations from LASNEX allow the study and physics of this effect.

Acknowledgments Work performed under the auspices of the US Department of Energy by the University of California Lawrence Livermore National Laboratory under Contract No. W-7405-Eng-48 and in part by US Department of Energy grant No. #DE-FG52-06NA26152.

References 1. L. B. Da Silva, T. W. Barbee Jr, R. Cauble, P. Celliers, D. Ciarlo, S. Libby, R. A. London, D. Matthews, S. Mrowka, J. C. Moreno, D. Ress, J. E. Trebes, A. S. Wan, and F. Weber, Phys. Rev. Lett. 74, 3991 - 3994 (1995). 2. J. Filevich, K. Kanizay, M. C. Marconi, J. L. A. Chilla, and J. J. Rocca, Opt. Lett. 25, 356-357 (2000). 3. R. F. Smith, J. Dunn, J. Nilsen, V. N. Shlyaptsev, S. Moon, J. Filevich, J.J. Rocca, M. C. Marconi, J. R. Hunter, and T. W. Barbee, Jr., Phys. Rev. Lett. 89(6), 065004-1 (2002). 4. J. Filevich, J. J. Rocca, M. C. Marconi, R. F. Smith, J. Dunn, R. Keenan, J. R. Hunter, S. J. Moon, J. Nilsen, A. Ng, and V.N. Shlyaptsev, Appl. Opt. 43(19), 3938 - 46 (2004). 5. H. Tang, O. Guilbaud, G. Jamelot, D. Ros, A. Klisnick, D. Joyeux, D. Phalippou, M. Kado, M. Nishikino, M. Kishimoto, K. Sukegawa, M. Ishino, K. Nagashima, and H. Daido, Appl. Phys. B 78, 975 (2004). 6. J. Filevich, J. J. Rocca, M. C. Marconi, S. J. Moon, J. Nilsen, J. H. Scofield, J. Dunn, R. F. Smith, R. Keenan, J. R. Hunter, and V. N. Shlyaptsev, Phys. Rev. Lett. 94, 035005 (2005). 7. S. Moon et al., Inst. Phys. Conf. Ser. No. 186, ed. J. Zhang, (Institute of Physics Publishing, Bristol and Philadelphia), 551 – 554 (2005). 8. G. B Zimmerman and W. L. Kruer, Comments Plasma Phys. Control. Fusion 2, 51 - 61 (1975). 9. Y. T. Lee and R. M. More, Phys. Fluids 27, 1273 (1984). 10. R. M. More, K. H. Warren, D. A. Young, and G. B. Zimmerman, Phys. Fluids 31, 3059 (1988). 11. J. Filevich, J. J. Rocca, E. Jankowska, E. C. Hammarsten, K. Kanizay, M. C. Marconi, S. J. Moon, and V. N. Shlyaptsev. Phys. Rev. E, 67(5), 56409-1-6 (2003).

Combination of Surface Characterization Techniques for Analyzing the Roughness of the Substrate S. Zhang, Z. Wang, Z. Shen, W. Wu and L. Chen Institute of Precision Optical Engineering (IPOE), Tongji University, Shanghai 200092, China

Summary. The extreme ultraviolet (EUV) molybdenum/silicon (Mo/Si) multilayers were fabricated using the direct current magnetron sputtering method on different preparation substrate: (a) wiped method, (b) untreated and (c) ultrasonic cleaning method. To meet the requirement of comprehensive characterization of morphology of substrates for EUV multilayer, a suitable combination of different measuring techniques, such as atomic force microscopy (AFM), x-ray diffractometer (XRD) rocking curve and synchrotron radiation (SR) reflectance, were chosen. It is shown that the reflectance of x-ray multilayers is sensitive to the roughness and cleanness of the substrate from the SR measurement results, and the maximum reflectance of 68.6% at 13.5nm was obtained using the ultrasonic cleaning method. It is demonstrated on the analysis according to the experimental results that the combination of surface characterization techniques using the AFM, x-ray scattering technique and SR characterization can be used for investigating the detail topography information of the substrate.

1 Introduction Multilayer mirror coatings are a key enabling technology for x-ray laser plasma diagnosis. [1] High reflectance is achieved with careful control of layer thicknesses, multilayer materials, interface quality, surface termination and substrate quality. [2] In particular, the surface topographies of substrates play a key role in achieving high-quality coating. [3] To achieve this aim, numerous surface-cleaning methods devoted to production of clean and smooth substrate surfaces have been developed. [4-7] Meanwhile, these cleaning methods are available depending on the sizes of the parts, and purpose of the cleaning. To investigate the surface morphology of thin films and substrates, numerous direct (such as the Alpha-Step, WYKO TOPO and AFM, etc.) and indirect (scattering measurements) techniques

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are available. [8] However, each of these instruments is sensitive to a specific, finite range of spatial frequencies. Therefore, some of these methods should be combined in order to provide the exact information of the surface. [9]

2 Experiments The substrate is the super-polished single-crystal Si (100) wafer. Three different surface treatment procedures were performed before coating the Mo/Si multilayer. The sample (a) is wiped using the absorbent cotton dipped with acetone and ethanol sequentially; the sample (b) is untreated and sample (c) is treated using supersonic cleaning with organic solvents (acetone, ethanol) followed drying by the canned pure N2 gas. The AFM was used to investigate the substrates surface and the topography images of three kinds substrate surfaces are shown in Fig.1. The Root-meansquare roughnesses of three samples with 5μm×5μm scanning range are (a) σ=0.143nm (b) σ=0.12nm (c) σ=0.108nm, respectively. From Fig.1 we can also see that some small scratches appear on the surface of sample (a), and some contamination exist on the surface of sample (b). The roughness of the sample (c) is smallest among these samples. Although such instrument can investigate the surface roughness directly, the samples are likely to be contaminated during the measurement process.

Fig. 1. AFM topography images of uncoated substrate: (a) wiping: σ=0.143nm (b) untreated: σ=0.12nm (c) ultrasonic cleaning: σ=0.108nm

After the pre-treatment of the substrates, the Mo/Si multilayers designed for the wavelength of 13.5nm were deposited onto these three silicon substrates by using an ultrahigh vacuum magnetron sputtering deposition system. The rocking curves of these deposited multilayers were measured by a small angle X-ray diffractometer. The reflectivities of these multilayers

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were measured by the reflectometer on beam line U27 at the National Synchrotron Radiation Facility (NSRL).

3 Results and discussion To investigate the roughness and scattering of the substrate of these multilayers, we characterized the surface smooth of substrates directly by measuring the rocking scanning curves using XRD. As shown in Fig. 2.1, the second-order Bragg peaks of these samples were measured by rotating the multilayer with fixed incident beam and detector. We observe a scattering intensity is about a factor 2000 lower than the specular intensity, and the scattering intensity of sample (c) is lower than (b) and (a). From Fig.2.1, we can find that the ultrasonic cleaning method can decrease the roughness and scattering of the substrate. While the wiped method destroy the surface of substrate and increase the roughness, which can be duplicated by the multilayer and decrease the EUV reflectance.

Fig. 2 (1) Second- order rocking curves and (2) EUV reflectance of samples a, b, and c., which were treated using different methods

In order to verify the results of the rocking curves, the performances of the Mo/Si multilayers have been evaluated using the reflectometer at NSRL, and the measurement results are shown Figure 2.2. The reflectance of sample (c) is achieved up to 68.6% at 13.5nm and higher than that of sample (a) (60.9%) and (b) (65.3%). Optical performances of multilayers depend substantially on the structure of the interfaces, especially on their

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roughness. Since the same deposition parameters were used, and the difference of reflectance of these samples is affected directly by the substrates. Therefore, the surface of the substrate will greatly influence the interface and reflectance of the multilayer in the soft x-ray and EUV range.

4 Summary The Mo/Si multilayers were fabricated with the same deposition parameters on the different substrates, and the high reflectance of 68.6% at 13.5nm was achieved using the ultrasonic cleaning method. The difference of the reflectance demonstrates that the roughness of each boundary in this range is a replication of the roughness of the substrate. Different methods were performed to investigate the roughness of the substrate, and the results indicate that the combination of the direct and indirect techniques can totally reflect the surface information.

Acknowledgements This work was supported by the National Natural Science Foundation of China (contract numbers 60378021 and 10435050).

References 1. Back C. A., Kauffman, R. L., Bell, P. M. et al.: 'Characterization of Nova plasmas using an x-ray spectrometer with temporal and spatial resolution' Rev Sci. Instrum., 66, 764~766. 1995 2. Taylor, J. S., Sommargren,G. E. Sweeney, D. W. R. et al.: 'The fabrication and testing of Optics for EUV Projection Lithography', SPIE, 3331, 580 – 583, 1998 3. Ruppe, C. Duparre, A.: 'Roughness analysis of optical films and substrates by atomic force microscopy', Thin Solid Films, 255, 8-13, 1996 4. Bennett, J. M. 'how to clean surfaces', SPIE, 5273 195-206, 2004 5. Stock, H. J. Hamelmann, F. Kleineberg, U. et al: 'Carbon buffer layers for smoothing superpolished glass surfaces as substrates for molybdenum silicon multilayer soft-x-ray mirrors', Appl. Opt., 36, 1650-1654 (1997) 6. Chemal, M. Durand-Vidal, D. Zanna, S. et al: 'Silicon surface wet cleaning and chemical oxide growth by a novel treatment in aqueous chlorine solutions', Elec. Acta, 49, 3545-3553, 2004

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7. Busnaina, A. A. Gale, G. W. and Kashkoush, I. I.: 'Ultrasonic and Megasonic Theory and Experimentation', Prec. Cle., II, 13-19, 1994 8. Windt, D. L. Waskiewicz, W. K. and Griffith, J. E.: 'Surface finish requirements for soft x-ray mirrors', Appl. Opt, 33, 2025-2031, 1996 9. Duparre, A and Jakobs, S.: 'Combination of surface characterization techniques for investigating optical thin-film components', Appl. Opt, 35, 50525058, 1996 10. Spiller, E. Stearns, D. and Krumrey, M.: 'Multilayer x-ray mirrors: Interfacial roughness, scattering, and image quality', J. Appl. Phys. 74,107-118, 1993

Fabrication of Multilayer Reflective Mirrors for Soft X-Ray Laser Working at the Wavelength of 4.48 nm J. T. Zhu1, B. Wang1, Z. Zhang1, H. C. Wang1, Y. Xu1, F. L. Wang1, Z. S. Wang* , L. Y. Chen1 and M. Q. Cui2 1. Institute of Precision Optical Engineering (IPOE), Tongji University, Shanghai 200092, China 2. Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China

Summary. Near normal incident high reflective and polarized multilayer mirrors were designed and fabricated for Ni-like Ta X-ray laser working at the wavelength of 4.48 nm. The influence of the imperfect interface on the reflectivity of the multilayer was simulated. Using the direct current magnetron sputtering technique, the Cr/C and Cr/Sc multilayers were deposited. Then, the layer thickness and structure of the multilayer were measured and fitted by an X-ray diffractometer. The reflectivities of these multilayers were measured on the beam line UE56/1-PGM at BESSY-II. At grazing incident angle of 85˚, the measured peak reflectivities were 7.50% and 6.12% for Cr/C and Cr/Sc multilayer mirrors, respectively. At the grazing angle of 44˚, the s-reflectivity is 13.61% for Cr/C multilayer polarizer. The measurement and simulation results suggest that the interface roughness strongly reduces the reflectivity of the multilayers. Thus, there is still a potential for improvement by introducing diffusion barriers and using more perfect substrate.

1. Introduction Nickel- (Ni)-like soft X-ray lasers from various materials have been obtained successfully [1-6]. In China, Ni-like tantalum (Ta) soft X-ray laser has been demonstrated working at the wavelength of 4.48 nm [7]. The preparation and study of small d-spacing multilayer mirrors are required for Nilike Ta soft X-ray laser. Carbon-based multilayer mirrors are expected to show a high reflectivity nearby carbon K-edge at 4.38 nm. Cr/C, Co/C, Ni/C and W/C multilayers have been studied well for X-rays near 5 nm. Meanwhile, Cr/Sc multilayer can also work well near “water window”. In the present work, we report the design, fabrication and evaluation of multi*

Corresponding author: Tel/fax: 86-21-65984652, [email protected].

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layers working at 4.48 nm. The thickness of each layer is only 1~2 nm, and the number of bi-layer needs more than 100. Thus, it is necessary to control the layer thickness more precisely and to reduce the interfacial roughness to fabricate such small d-spacing structure multilayers.

2. Design and fabrication The material combinations of multilayer were selected by determining their complex refractive indices. Typically, low absorbing materials (small imaginary part k) with maximum contrast in the real part n are combined. At the wavelength of 4.48 nm, carbon-based material combinations were expected to show a high reflectivity nearby carbon K-edge at 4.38 nm. Cobalt (Co), chromium (Cr), Ni and tungsten (W) have low absorption and fairly large difference of n from that of carbon, and were selected as multilayer material combinations. Figure 1 shows the peak reflectivities of Co/C, Cr/C, Ni/C, and W/C multilayers for optimally designed structures versus bi-layer number at the wavelength of 4.48 nm. As shown in Fig. 1, the peak reflectivities of Co/C and Cr/C multilayers are higher than those of Ni/C and W/C multilayers. Here, Cr/Sc multilayer was also calculated at λ=4.48 nm for its advantages working in the “water window” region.

Fig. 1. Theoretical reflectivities for carbon-based multilayers vs. bi-layer number at λ=4.48 nm and grazing incident angle 85˚. Cr/Sc multilayer was also shown here.

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For the small d-spacing multilayer, interface roughness and diffusion strongly reduce the optical performance of multilayer mirrors. As shown in Fig. 2(a), the interface roughness not only reduces the peak reflectivities, but also shifts the peak positions significantly. Because of the narrow bandwidth of these multilayers working at 4.48 nm, the multilayer structures must be modified according to different interface roughnesses in the design of multilayer (Fig. 2(b)).

Fig. 2. Calculated peak reflectivities under different interface roughness (a). The peak position fixed at λ=4.48 nm after modifying multilayer structures according to different interface roughnesses (b).

Besides the theoretical calculation, we have fabricated and evaluated a few samples of Cr/C, Cr/Sc and Co/C multilayers as a preliminary experiment. All multilayer were deposited by an ultra high vacuum direct current magnetron sputtering (JGP560C6, made in China) with circular targets with the size of 100 mm in diameter. The base pressure is less than 5×10-5 Pa, and the working gas is argon (Ar) at the pressure of 0.1 Pa. The sputtering power keeps constant during coating, and the multilayers were deposited onto 20 mm×30 mm silicon substrates at room temperature. Then, the deposited multilayers were measured, for quality control and depositing rate control, using a small angle X-ray diffractometer (XRD) (D1 system, made by Bede Ltd., UK). The optical performances multilayers were evaluated using the ultra-high vacuum polarimeter on beamline UE56/1PGM-1 at BESSY-II, which enabled measurements in s-, or p-polarization geometries. The detector was a GaAsP-diode and the absolute reflectivities were obtained by the sample in/out measurement using this same detector.

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3. Preliminary experimental results The layer thickness and structure of these multilayers were measured by the small angle X-ray diffractometer (XRD), and the reflectivities of these multilayers were measured by synchrotron radiation (SR) at BESSY-II. Figure 3 shows the measurement results of Cr/C multilayer. At the grazing angle of 85˚, up to 7.50% peak reflectivity has been obtained at λ=4.49 nm with bi-layer number of 200.

Fig. 3. Experimental results of Cr/C multilayer structure measured by XRD (a), and normal incident reflectivity measured by synchrotron radiation (b).

Fig. 4. XRD (a) and SR (b) measurement results of Cr/Sc multilayer for Ni-like Ta laser.

These curves measured by XRD and synchrotron radiation were fitted to evaluate the layer thickness and interface roughness, and the measurement and fitting results were listed in table 1. The SR fitting results suggest that the interface roughness of Cr/C multilayer is about 0.5 nm. We also found a large discrepancy in layer thicknesses and interface roughness fitted by XRD versus synchrotron radiation (SR) measured data. The discrepancy

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may be explained by the different incident angle and optical constants for XRD and SR measurement. The XRD works at Cu Kα-line (0.154 nm), and the small angle scan was performed in structure measurement. The roughness and interlayer diffuseness is the main reason why the measured reflectivity is lower than the theoretical one. Thus, there is still a potential for improvement by introducing diffusion barriers and using more perfect substrate. This work is ongoing in our laboratory.

Fig. 5. Measurement results of synchrotron radiation for Cr/C multilayer polarizer.

Figure 4 shows the measurement results of Cr/Sc multilayer. At the grazing angle of 85˚, the reflectivity is 6.12% at λ=4.49 nm with bi-layer number of 350. The fitting results suggest the interface roughness (~0.4 nm) is lower than that of Cr/C multilayer. Table 1. The measurement and fitting results of XRD and SR for Cr/C and Cr/C multilayers shown in Figs. 3 and 4. Multilayer XRD_fitting SR_fitting XRD_fitting SR_fitting

Cr/C Cr/C Cr/Sc Cr/Sc

N

D d_C(Sc) d_Cr /nm /nm /nm 200 2.264 1.136 1.118 200 2.270 1.210 1.060 350 2.269 1.305 0.964 350 2.270 1.233 1.037

Roughness Roughness /nm /nm 0.216(Cr-C) 0.439(C-Cr) 0.460(Cr-C) 0.540(C-Cr) 0.385(Cr-Sc) 0.161(Sc-Cr) 0.418(Cr-Sc) 0.422(Sc-Cr)

Besides the multilayer reflective mirrors, the Cr/C multilayer polarizer was also fabricated and measured. This Cr/C multilayer was designed as polarizer for 4.48 nm, and the bi-layer number is 80. At the grazing angle of 44 degree, the measured s-reflectivity is 13.61%, and the polarization

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degree is more than 98% at wavelength of 4.52 nm (Fig. 5). Further work is required to control the layer thickness more precisely.

4. Conclusion Near normal incident high reflective and polarized multilayer mirrors have been fabricated for Ni-like Ta X-ray laser working at wavelength of 4.48 nm. At grazing incident angle of 85˚, the measured peak reflectivities were 7.50% and 6.12% for Cr/C and Cr/Sc multilayer mirrors, respectively. The Cr/C multilayer polarizer was also fabricated. And at the grazing angle of 44˚, the s-reflectivity is 13.61%, where the polarization is more than 98%. The measured and simulated results suggest that the interface roughness strongly reduces the reflectivity of the multilayer. Thus, more perfect substrate and interface engineering were required to improve the optical performance of such small d-spacing multilayers for Ni-like Ta laser. Furthermore, it is necessary to control the layer thickness more precisely.

Acknowledgement The authors are indebted to Prof. Alan G Michette and Dr. A Keith Powell of King’s College London, Dr. Franz Schäfers, and Dr. Andreas Gaupp of BESSY-II for their kindly help in synchrotron radiation measurement. This work is supported by 863-804 Sustentation Fund, and NCET-04-0376.

Reference 1.

2.

3. 4.

B. J. MacGowan, S. Maxon, P. L. hagelstein, C. J. Kean, R. A. London, D, L. Matthews, M. D. Rosen, J. H. Scofield, and D. A. Whelan, “ Demonstration of soft X-ray amplification in Nickel-like ions”, Phys. Rev. Lett. 59, 2157-2160, (1987) H. Daido, Y. Kato, K. Murai, S. Ninomiya, R. Kodama, G. Yuan, Y. Oshikane, M. Takagi, H. Takabe, and F, Koike, “Efficient soft X-ray lasing at 6 to 8 nm with nickel-like lanthanide ions”, Phys. Rev. Lett. 75, 1074-1077, (1995) J. Nilsen and J. C. Moreno, “Lasing at 7.9 nm in nickel- like neodymium,” Opt. Lett. 20, 1386-1388, (1995) H. Daido, S. Ninomiya, T. Imani, R. Kodama, M. Takagi, Y. Kata, K. Murai, J. Zhang, and Y. Gu, “Ni-like soft X-ray lasing at the wavelengths between 14 nm and 7.9 nm,” Opt. Lett. 21, 958-960, (1996)

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7.

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J. Zhang, A. G. MacPhee, J. Nilsen, J. Lin, T. W. Barbee, Jr., C. Danson, M. H. Key, C. L. S. Lewis, K. Neely, R. M. N. Orourke, G. J. Pert, R. Smith, G. J. Tallents, J. S. Wark, and E. Wolfrum, “Demonstration of saturation in a Ni-like Ag X-ray laser at 14 nm,” Phys. Rev. Lett. 78, 3856-3859 (1997) J. Zhang, A. G. MacPhee, J. Lin, E, Wolfrum, R. Smith, C. Danson, M. H. Key, C. L. S. Lewis, D. Neely, J. Nilsen, G. J. Pert, G. J. Tallents, and J. S. Wark, “ A saturated X-ray laser beam at 7 nm,“ Science 276, 1097-1100 (1997) C. Wang, W. Wang, J. Wu, J.Q. Dong, J. R. Sun, R. R. Wang, S. Z. Fu, Y. Gu, S. J. Wang, G. L. Huang, Z. Q. Lin, G. P. Zhang, T. X. Zhang, W. D. Zheng, “Experimental studies of Ni-like Ta X-ray laser“, Acta Physica Sinica 53, 3752-3755 (2004). (In Chinese)

Imaging Research With Non-Periodic Multilayers for Inertial Confinement Fusion Diagnostic Experiments F. L.Wang, B. Z. Mu, Z. S. Wang, C. S. Gu, Z. Zhang, S. J. Qin and L. Y. Chen Institute of Precision Optical Engineering, Department of Physics, Tongji University, Shanghai 200092, China

Summary. A grazing Kirkpatrick-Baez (K-B) microscope was designed for hard x-ray (8keV; Cu Ka radiation) imaging in Inertial Confinement Fusion (ICF) diagnostic experiments. Ray tracing software was used to simulate optical system performance. The optimized theoretical resolution of K-B microscope was about 2 micron and better than 10 micron in 200 micron field of view. Tungsten and boron carbide were chosen as multilayer materials and the multilayer was deposited onto the silicon wafer substrate and the reflectivity was measured by x-ray diffraction (XRD). The reflectivity of supermirror was about 20 % in 0.3 % of bandwidth. 8keV Cu target x-ray tube source was used in x-ray imaging experiments and the magnification of 1× and 2× x-ray images were obtained.

1 Introduction X-ray imaging is often an essential component of diagnostics used in Inertial Confinement Fusion (ICF) experiments. One of the important goals in the diagnostics of laser-target implosions is measurement of the conditions in highly compressed cores where high areal densities and small-scale sizes indicate the need for good spatial resolution (≤ 5 µm). Current methods used for imaging x-rays emitted by laser plasmas include pinhole imaging, synthetic aperture imaging and imaging by reflective optics. Pinhole imaging suffers from a lack of sensitivity at high energy and so is often impractical. In the x-ray domain, normal reflective optics are not suitable for their small reflectivity, and only grazing reflective optics is optimal, such as a Kirkpatrick-Baez (K-B) microscope which was first proposed by Paul Kirkpatrick and A.V Baez in 1948 [1] and a Wolter microscope proposed by H Wolter [2]. A Wolter microscope is made with two off-axis aspherical mirrors (elliptical and/or parabolic) [3,4], the accuracy need for both the shape and the smoothness of the optics is one of the main difficul-

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ties in manufacturing. Compared with other grazing incidence optics system, the K-B system is only made of spherical mirrors, which are easier to manufacture with both the required shape and roughness. It has been widely used in synchrotron radiation and ICF experiments [4-7]. Typically, in ICF experiments the resolution of K-B microscope can reach a few microns in hundreds microns object field [7]. In this paper, a K-B system was describled which used non-periodic multilyer as reflective element to image x-ray at 8keV in ICF experiments.

2 Design of the x-ray KB microscope To design an imaging system, analyzing the tolerance of the system is very important. In KB microscope system, the main tolerance is spherical aberration, which is determined according to the equation of (1) s/M=3d2/(8R)

(1)

where, s is spherical aberration, d is length of the mirror, M is mean magnification, and R is curvature radius of the mirror. It can be concluded that to decrease spherical aberration is to decrease mean magnification, length of the mirror, and increase the curvature radius of the mirror.

Fig. 1. The schematic diagram of the K-B microscope

According to the requirements of the ICF experiments, some original optical characteristics of the K-B microscope were determined based on the theory of optical imaging, such as M, object distance (u), imaging distance (v), grazing incidence angle (i) and so on. Here M is 8, u is 100mm, v is 800mm, E is 8keV, the curvature radius (R1=R2) of both mirrors are 9700mm, d is 10mm, grazing angles are 1.052° and 1.143°, respectively. The resolution of this system is better than 10μm on object plane within a

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view of field of 200μm, The maximal spherical aberration (smax) is 30μm. Fig.1 shows the schematic diagram of the KB microscope.

a)

b)

Fig. 2. Characteriaztion of k-b system a is Spot diagram of different fields of view and b is modulate transfer function of different fields of view

The optical characterization was simulated using the ray-tracing software of ZEMAX, the results show in Fig.2. It can be concluded that the spatial resolution is less than 2 μm in the central field of view and in the whole field of view of 200 μm, the spatial resolution is less than 10μm. It meets with the requirement of the ICF experiments.

3 Design and manufacture of the reflective elements The K-B microscope would be used in x-ray region, where x-ray is strongly absorbed by almost materials, and the refractive indices of almost materials are lower than unit, and almost equal unit. When x-ray beam irradiates on the surface of mirror from air or vacuum, the external total reflective will happen. The angle of the total reflective on the surface of single high-Z mental layer is very small at this region, such as Tungsten (W), the angle is about 0.5° at 8keV, which is too small to have enough the angular object aperture. The periodic multilayer has enough reflectivity at high grazing incidence angle, but the bandwidth is too narrow to assemble easily. To overcome the above shortcomings, a new type multilayer mirror - X-ray supermirrors from the depth-graded multilayer was proposed by Joensen et al [8] based on neutron supermirrors [9] ,which was chosen as reflective element, and has enough bandwidth at fixed angle or energy, can meet with the requirement of the K-B microscope [10]. Tungsten and Bo-

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ron carbide (W/B4C) were chosen as coating materials according to the criterion proposed by Yamamoto [11] and used the Simplex method [12] to optimize the multilayers which work in the grazing angle range of 0.902°~1.202° and 0.993°~1.293° at fixed energy of 8.0 keV.respectively. The calculated reflectivity curves of the both multiayers are shown in Fig.4 compared with two periodic multiayers. All of the mutilayers have 40 layers. The reflective bandwidth is 0.3 % for both non-periodic multilayers and about 0.06 % for both periodic multilayers.

a

b

c

Fig. 3 The designed, measured and fitting reflectivity curves of multilayers

The multilayers were fabricated on to silicon substrates at first and then on spherical glass surfaces using DC magnetron sputtering. An X-ray diffractometer (XRD) (D1 system, Bede Inc., UK, working at 8.0 keV, the Kα line of Cu) was used to provide the optical performances of the multilayers. Fig.3b and Fig.3c show the measured and fitting results of the supermirrors on silicon substrates, which coincides with the designed one, respectively. The reflective bandwidth is about 0.3° and the mean reflectivity in this angle range is above 20 %.

4 X-ray imaging experiments The x-ray imaging experiments were made using the x-ray tube (working at 8.0 keV, the Kα line of Cu) as source, the object is 100 µm grid of Cu, the detector is the general x-ray film. To avoid the exposed time too long for the detector’s insensitive and convenience operation, only one spherical mirror(the mirror with the center angle of 1.052°) was used to do experiment. The configuration of one dimension x-ray imaging system is shown in Fig.4. The K-B microscope imaging experiments are undergoing. Using the focal length equation:

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F=R sin(i)/2

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(2)

It can be calculated that f is 89.05 mm. When M is 1, u and v are equal, 178.09 mm, when M is 2, u is 133.57 mm, v=267.13 mm. Fig. 5 shows the above relevant imaging results. The imaging on the left side of the both figures was x-ray directed imaging without being reflected by the

Fig. 4 Configuration of one dimension x-ray imaging system

spherical mirror. And imaging on the right side was formed using the light reflected by the spherical mirror. There are only two blasts because the incidence light was limited using the slit diaphragm. From these experiments, it can be concluded that the supermirrors made in our lab has been successfully used in x-ray imaging system at high grazing angle.

M=1

M=2

Fig. 5 X-ray images of the100 μm grid with spherical mirror.

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5 Conclusion The K-B microscope system was designed, whose spatial resolution on axis is less than 2 µm, and the spatial resolution in 200 µm field of view is less than 10 µm. Imaing experiments at 8 keV using one spherical mirror have been done, and the supermirror was successfully used in China.and obtained the x-ray image of M=1 and M=2.

6 Acknowledgment This work was supported by National Natural Science Foundation of China under Grant No.10435050, 60378021, National High Technology Research and Development (863) Program of China No. 2005AA843031, by Program for New Century Excellent Talents in University and the Science Foundation of Tongji University.

References 1. 2. 3. 4. 5. 6. 7. 8. 9.

Kirkpatrick P., Baez A.V. Formation of Optical Images by X-Rays. J. Opt. Soc. Am. 1948, 38, 766. Wolter, H. Mirror Systems with Grazing Incidence as Image-Forming Optics for X-Rays Ann. Phys. 1952, 39 Ice G. E, Chung J. C, Tischler J. Z, Lunt A, and Assoufid L, Elliptical x-ray microprobe mirrors by differential deposition. Rev. Sci. Instrum, 2000, 71(7): 2635-2639 Dhez P, Chevallier P, Lucatorto T. B, Tarrio C, Instrumental aspects of x-ray microbeams in the range above 1 keV. Rev. Sci. Instrum, 1999, 70(4): 19071920 Jiashen H, Xu W, Manufacturing and testing of X-ray imaging components with high precision. Optics and Precision Engineering, 2005,13(5): 620-625 Marshall F. J, Oertel J. A, A framed monochromatic x-ray microscope for ICF (invited). Rev. Sci. Instrum, 1997, 68(1): 735-739 Sauneuf R, Dalmasso J. M. Jalinaud T, Le Breton J.P, Large-field highresolution x-ray microscope for studying laser plasmas. Rev. Sci. Instrum1997, 68(9), 3412-3420 Joensen K.D, Christensen F.E, Schnopper H,W, Gorenstein P, Susini J, Hoghoj P, Hustache R,Wood J, Parker K, Proc. SPIE, 1992,1736, 239. Mezei F. Novel polarized neutron devices: supermirror and spin component amplifier. Communications on Physics, 1976, 1(3), 81-5

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10. Bridou F, Mercier R, Raynal A, Clotaire J. Y, Colas C, Fournet P. Large field double Kirkpatrick–Baez microscope with nonperiodic multilayers for laser plasma imaging. Rev. Sci. Instrum. 2002, 73(11), 3789-3795 11. Yamamoto M, Namioka, T, Layer-by-layer design method for soft-X-ray multilayers, Applied Optics, 1992, 31(10),1622-30 12. Tang J F, Zheng Q, Applied Thin Film Optics, Shanghai, Publish of Shanghai Science Technology[M], 1984, 383-384

Analysis of 46.9-nm Pulsed Laser Radiation Aftereffects in Sc/Si Multilayer X-Ray Mirrors Yu. P. Pershyn, D. L. Voronov, E. N. Zubarev, V. A. Sevryukova, V. V. Kondratenko; G. Vaschenko, M. Grisham, C. S. Menoni, J. J. Rocca; A.V. Vinogradov, I. A. Artyukov and Yu. A. Uspenskii National Technical University “KhPI”, Kharkiv, Ukraine; Colorado State University, Fort Collins, CO 80523; P.N. Lebedev Physical Institute, Moscow, Russian Federation

Summary. Specific structural changes in Sc/Si multilayers (MLs) irradiated by nanosecond 46.9-nm single laser pulses with fluences of 0.04-5.00 J/cm2 were studied by methods of SEM and cross-sectional TEM. The threshold damage was found to be 0.08 J/cm2. The ML melts down under the fluence F >0.08 J/cm2, and the exothermic reaction of silicide formation starts. Main degradation mechanisms of MLs are discussed. The results of this study can be used for development of advanced multilayer mirrors capable handling the intense radiation conditions of new generation coherent X-ray sources.

1 Introduction Multilayer (ML) X-ray mirrors are widely used as optical components in the regions of UV and soft X-rays (1-50 nm) due to their high efficiency and flexibility in the parameters and forms. Under aggressive environment (heating, ion irradiation and exposure to high-power laser radiation) they can degrade as a result of the structural nonequilibrium conditions [1-4]. Growing power of new generation coherent X-ray sources (tabletop laser [5], FEL [6] and others) makes the stability of ML optical properties even more critical. The Sc/Si MLs developed for the wavelength range 35-50 nm have been successfully used in many applications with the capillary-discharge laser generating at the wavelength λ=46.9 nm [7]. Knowledge of radiationinduced degradation mechanisms in the Sc/Si structures will help finding high-end edges of the application and the ways to enhance their stability.

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On the other hand, the very laser radiation represents a specific interest for the surface processing [8]. Diffusion mixing of the layers and formation of the chemical compounds at moderate temperatures indicate the excessive free energy of the MLs. Moreover, the energy released in the mixing process can trigger self-sustained reaction observed in multilayer nanofoils [9]. In this work we discuss features of a single-shot laser influence onto Sc/Si ML degradation process related to the nonequilibrium of the layered structure.

2 Experimental Sc/Si MLs with the period of ~27 nm were deposited onto silicon and float glass substrates by the method of DC magnetron sputtering. Part of Sccontaining layer in the period was ~0.5. Number of the periods was 10 (Sc/Si/10) on glass substrate and 33 (Sc/Si/33) on Si. MLs deposited onto both type of substrates were exposed to the focused laser radiation operating at λ=46.9 nm. The energy of the pulsed (1.2 ns) laser beam was ~ 0.13 mJ. To vary the fluence value (F) we translated ML sample with respect to the beam focus. Each laser shot stroke the sample surface in a new ML region at normal incidence. Scanning electron microscope JSM-820 was used to get the information on surface morphology and chemical composition of Sc/Si MLs. Crosssectional images were produced with the help of transmission electron microscope PEM-U (SELMI, Ukraine) at accelerating voltage of 100 kV.

3 Results and discussions

3.1 Scanning electron microscopy study We investigated different laser imprints (LIs) obtained with the change of irradiated area on the Sc/Si ML surface, which corresponded to a set of the fluences in the range of 0.04-5.00 J/cm2. We observed traces of a ML melting at the fluence values starting from F~0.08 J/cm2. This fluence corresponds to the melting threshold predicted using the thermal diffusion model [10] for the MLs with average thermal characteristics being between Sc and Si.

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An incidental change in the morphology of the molten surface was observed at the fluences up to F~0.3 J/cm2 (fig. 1a) in the irradiated areas of Sc/Si/33 ML deposited on Si substrate. Note that the rectangular undamaged area in the center of LI is a shadow of the ML sample inherited from the irradiation scheme [11]. Further growth of the fluence resulted in the melt cracking structures. Cracks advent is an evidence of deep ML melting; better contrast SEM images obtained with the reflected electrons (penetration depth up to ~1 μm) have denoted this fact. First signs of evaporation were revealed at F~0.9 J/cm2 (fig. 1b) in the form of small micron-sized pits (visible in fig. 1b as black dots inside the LI center) indicating a melt boiling. Simultaneously a “crown” was formed as a result of pressing out the melt to the LI rim by excessive vapor pressure. The thermal diffusion model gives the lower threshold fluence for evaporation to be F~0.2 J/cm2. Perhaps, the evaporation process would start before the cracks appearing at the surface, but to define the threshold value more precisely one need to use more accurate and sensitive instruments (for example, probe beam deflection technique [12]). At F~2.2 J/cm2 the active evaporation or ablation of Sc/Si/33 ML becomes visible. The specific features of this stage are a crater formation in the LI center (fig. 1c) and appearing solidified drops around the LI. According to electron microanalysis there is no Sc within the crater of evaporated region, i.e. ML is completely absent in this region. The crater as a rule occupies less than a half the LI area. Presence of the drops means the ML being removed from the center in liquid phase as well. So, the mechanism of a combined ablation is characteristic for the Sc/Si ML: an ejection of the melt and vaporization; it is similar to that for metals [13].

0.3 J/cm2

0.9 J/cm2

10 μm

10 μm

a

b

2.2 J/cm2

10 μm

c

Fig. 1. SEM images of Sc/Si/33 ML on Si substrate irradiated with 46.9-nm laser pulses of different fluences.

Despite the fact that ~97% of absorbed energy is concentrated in top 10 periods, melting and ablation in Sc/Si/10 ML deposited on the glass goes

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in completely different way as compared to Sc/Si/33 ML. Melting as a rule is accompanied by cracking and flaking the ML practically up to F~0.5 J/cm2 (fig. 2a). An ablation processes in some LI areas begins at F~0.6 J/cm2 (fig. 2b) that is considerably less than that for Sc/Si/33 (2.2 J/cm2). Fig. 2c shows SEM picture for LI at 1.4 J/cm2 with ML removed from the most LIs. Judging from the presence of the drops the ablation mechanism here didn’t change. The rest of laser energy (~3%) is concentrated within the substrate surface because of high absorption [14] and low heat conductivity of the glass [15] compared to Si and Sc [16]. However this energy is insufficient to reduce the observed threshold of the ablation for Sc/Si/10 ML at least to one-third. Taking into account the strong absorption of practically all incident energy in the ML material we expected the similar behavior of MLs with 10 and 33 periods under the irradiation. We believe the difference of heat conductivity in glass and the ML material is the reason of observed distinction.

0.3-0.5 J/cm2

0.6 J/cm2

10 μm

10 μm

a

b

1.4 J/cm2

10 μm

c

Fig. 2. SEM images of Sc/Si/10 ML on float glass substrate irradiated with 46.9nm laser pulses of different fluences.

According to our calculation, at F~0.4 J/cm2 the laser radiation can ablate the Sc/Si/10 ML material completely. However, it looks like it doesn’t take place (see fig. 2a). Our estimations show that even at F~0.6 J/cm2 (fig. 2b) the bottom two periods cannot be melted by the absorbed laser energy directly. Complete ablation can occur at F≥1.4 J/cm2, with all the layers being melted under the laser irradiation. 3.2 Transmission electron microscopy study Fig. 2 shows cross-sectional image of the Sc/Si/33 ML after irradiation by the laser beam at F~0.13 J/cm2 (laser source is on the left). The most of

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ML has been molten, and according to electron diffraction analysis the alloy composition corresponds to Sc3Si5 silicide. Only 7 periods of 33 survived at the substrate (on the right). This ratio of molten and survived volumes indicates the fluence approaching the full structure melting threshold for the Sc/Si/33 ML. The estimations, however, show that only 4 periods can be molten at that fluency, i.e. only one-sixth of the value observed in the experiment. Such a discrepancy can be explained by the suggestion that the formation of the Sc3Si5 silicide results in a release of up to 570 kJ/mol [17]. This energy is enough to heat and melt the material. For the short laser pulse duration (~1.2 ns) no efficient diffusion process can occur, therefore that melting is believed to be the main mechanism of ML degradation.

F~0.13 J/cm2

Sc3Si5

ML

Si

Fig. 3. Cross-sectional TEM image of Sc/Si/33 ML after irradiation at fluence of 0.13 J/cm2. Laser beam falls from the left. Substrate (S) is on the right.

So, we see that melting of the Sc/Si ML by the laser beam initiates the exothermic reaction, which, from one hand, facilitates the ML ablation (for F≥1.4 J/cm2) and, from the other hand, enlarges the molten region at low fluences (F<0.6 J/cm2). The smallest fluence capable melting the surface layers and activating the reaction of silicide formation is calculated to be about 0.08-0.10 J/cm2 that is rather close to the observed experimental value of 0.08 J/cm2. Note that the presented experimental data are a solid ground for the use of the special barrier layers in Sc-Si and Si-Sc interfaces for increasing radiation resistivity of Sc/Si MLs near the laser-radiation induced melting thresholds.

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4 Conclusions We have studied the specific features of Sc/Si ML degradation under the influence of nanosecond 46.9-nm laser pulses. The layer melting at the minimum fluence of 0.08 J/cm2 was shown to be the main mechanism of ML degradation. The melting initiates the silicide formation and the liberation of considerable amount of heat. In the case of high fluences (F≥1.4 J/cm2) this heat facilitates early ML ablation and at low fluences (F<0.6 J/cm2) it increases the material’s molten volume in several times.

References 1. Stearns, D.G.: ‘Thermally induced structural modification of Mo-Si multilayers’, J. Appl. Phys., 67, 2415-2427, 1990. 2. Penkov, A.V.: ‘Thermal dependence of ion-beam mixing in Mo/Si multilayer periodic coatings’, Metallofiz. Noveysh. Tekhnol., 28, #2, 183-192, 2006 (in Russian). 3. MacGowan, B.J.: ‘Investigation of damage to multilayer optics in X-ray laser cavity: W/C, Wre/C, WC/C, stainless-steel/C, and Cr3C2/C mirrors’, J. X-ray Sci. Technol., 3, 231-282, 1993. 4. Leguern, F.: ‘Experimental study of simulation of the damage induce to various multilayer interferential mirrors by soft X-ray plasma-laser sources’, J. X-ray Sci. Technol., 7, 271-283, 1997. 5. Grisham, M.: ‘Damage to extreme-ultraviolet Sc/Si multilayer mirrors exposed to intense 46.9-nm laser pulses’, Opt. Lett., 29, 620-622, 2004. 6. Yu, L.H.: ‘First Ultraviolet High-Gain Harmonic-Generation Free-Electron Laser’, Phys. Rev. Lett., 91, 074801, 2003. 7. Benware, B.R.: ‘Generation and application of a high-average-power polarized soft-x-ray laser beam’, J. Opt. Soc. Am. B, 18, 1041-1045, 2001. 8. Rosenfeld, A.: ‘Picosecond UV-ablation of Au and Ni films’, Appl. Surf. Sci., 96-98, 339-442, 1996. 9. Mann, A.B.: ‘Predicting the characteristics of self-propagating exothermic reactions in multilayer foils’, J. Appl. Phys., 82, 1178-1188, 1997. 10. Siegel, J.: ‘UV-laser ablation of ductile and brittle metal films’, Appl. Phys. A, 64, 213-218, 1997. 11. Benware B.R.: ‘Focusing of a tabletop soft x-ray laser beam and laser ablation’, Opt. Lett., 24, 1714-1716, 1999. 12. Matthias, E.: ‘In-situ investigation of laser ablation of thin films’, Thin Solid Films, 254, 139-146, 1995. 13. Veiko, V.P.: ‘Two-phase mechanism of laser-induced removal of thin absorbing films. II. Experiment’, J. Phys. D: Appl. Phys., 13, 1571-1575, 1980. 14. Henke, B.L.: ‘At. Data Nuclear Data Tables’, 54, 181-342, 1993.

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15. Samsonov G.V. (ed.): Handbook on physical and chemical properties of oxides, Metallurgiya, 1978 (in Russian). 16. Samsonov G.V. (ed.): Handbook on properties of elements. Ch. 1. Physical properties, Metallurgiya, 1976 (in Russian). 17. Golutvin, Yu.M.: ‘Enthalpy of silicide formation in Sc-Si system’, Izv. AN SSSR. Metals, #6, 47-54, 1984 (in Russian).

X-Ray Laser Interference Microscopy for Advanced Studies of Laser-Induced Damages G. Jamelot1,2, D. Ros1,2, B. Rus3, M. Kozlová3, K. Cassou1,2, S. Kazamias1,2, A. Klisnick1,2, T. Mocek3, P. Homer3, J. Polan3 and M. Stupka3 1

Univ. Paris-Sud, LIXAM, UMR n° 8624, Bâtiment 350, Orsay, F-91405 CNRS, LIXAM, Orsay, F-91405 3 Department of X-ray Lasers, Institute of Physics, PALS Centre, 18221 Prague 8, Czech Republic 2

Summary. We show results obtained using XUV interference microscopy to observe in situ nanometer-scale modifications of optical surfaces exposed to intense sub-ns laser pulses. The surface was irradiated by a blue “damaging” laser (438 nm) and diagnosed by a soft X-ray laser based on neon-like zinc, emitting at 21.2 nm. Investigated objects were thin plane beam-splitters made of fused silica (SiO2). This technique could be used to reveal effects involved in formation of laser-induced damages in optical surfaces exposed to intense laser pulses.

1 Introduction Laser-induced damage (LID) of transmission optics is one of the main limitations of the next generation of large-energy lasers. As a result, pellicles and beam-splitters are usually the weakest elements, with LID threshold of fused silica typically well below 30 Jcm-2. A particular case of interest is LID occurring at the rear surface of pellicles when acting as a beam-splitter at the blue (3ω) frequency, the physical nature of which being currently not well understood. Soft X-ray lasers offer a very suitable probing tool for high-resolution, in situ investigation of phenomena occurring in a thin surface layer in situations relevant to LID studies [1]. The soft X-ray beam incident at the surface at e.g. 12 degrees (probing angle of incidence used throughout this work) will be totally reflected with efficiency of 0.48. Due to the penetration depth (1/e) of only 5.8 nm, the soft X-rays will thus ensure genuine surface probing. In contrast, visible

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light with n~1.5 will be refracted into the optical material, and, as a consequence, the reflected fraction will carry information both from the surface as well as from the bulk material (see Figure 1-a and 1-b). The second major advantage of soft X-rays is illustrated in Figure 1-c and consists in the imaging with only very small numerical aperture.

Fig. 1. Mechanisms of reflection of soft X-ray radiation and of VIS radiation: whereas the soft X-rays undergo total reflection VIS light is refracted into the material (a) and the reflected light carries information from the bulk material (b), preventing net surface sensing. (c) Illustration of small numerical aperture issues when imaging surface at oblique incidence in LID studies.

2. Experimental set-up and results The arrangement of the presented experiment [1], conducted at the PALS facility, is shown in Figure 2. The probing soft X-ray radiation at the wavelength of 21.2 nm is supplied by a double-pass Ne-like zinc laser [6, 7], operated in configuration with a low-energy prepulse applied 10 ns before the main pumping pulse. The X-ray laser provides ~100-ps pulses and is driven by the fundamental wavelength of 1.3 μm of the PALS iodine laser; the X-ray laser shot may be fired every 20 minutes. The studied sample is located at the distance of 2.5 m from the X-ray laser exit and is illuminated/damaged by ~300-ps long pulses, delivered by the third harmonics of the PALS laser, at the wavelength of 438 nm. Energy of the damaging pulses was varied in order to produce well-defined energy density in the impact area between 5 and 50 Jcm-2; the diagnostics included calorimeters to monitor the incident, transmitted, and reflected energy. The size of the laser impact was typically 1 mm in diameter, in a geometry where the pellicle was placed behind the lens focus. High-quality digital cameras moni-

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tored the intensity patterns of the incident beam on the damage site as well as that transmitted through the pellicle. The X-ray beam probes the sample under an angle of 12º. Upon reflection, it is relayed by an imaging concave mirror (operated at a fairly small off-axis angle, of less than 2 degrees) towards the detection plane. The double Lloyd’s mirror, aligned to reflect by its individual arms respectively the portion of the beam reflected by the damaged surface and the portion reflected by the unperturbed surface, produces interference fringes on the detector and ensures the topography mapping of the imaged impact site.

Fig. 2. Schematic of experimental (not to scale) configuration showing both the elements of X-ray interference microscopy and adjacent optical in-situ and postshot diagnostics. The rear surface of the pellicle under investigation is imaged onto the CCD detector (27.6×6.9 mm, 2048×512 pixels) by a f=300 mm concave mirror with Mo:Si multilayer coating; the relay mirrors M1 andM2 in the XRL beamline are employed only for geometrical reasons. Post-shot inspection of the impact site on the rear surface of the pellicle is carried out by a high-resolution microscope, by accurately turning the sample clockwise to bring the site of interest face to the microscope objective.

The damage studies employing the full array of diagnostics deployed were carried out with the X-ray pulse probing the impact site 1 ns and 5 ns after the arrival of the damaging 438-nm optical pulse. Below we show an example of the obtained raw data, corresponding to the probing time of 5 ns. Figure 3 shows a sequence of snapshots of a damage site on the rear side of a 10-mm thick fused silica pellicle, produced by laser impact with energy density of 10 Jcm-2, i.e., lower than the damage threshold. Figure 3(a) is an interference image of the unperturbed surface, obtained when

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only the X-ray laser probe arrives. When the damaging optical pulse is fired, reflected X-ray laser strongly decreases and interference field practically disappears over the entire impact site, as seen in Fig. 3(b). This implies that the corresponding surface is not merely distorted, but rather suggests that the X-ray emission is either absorbed or that the surface scatters the X-rays significantly, resulting in a local loss of signal. In the subsequent shot, Fig.4, in which the irradiated surface is probed (after about 20 minutes) without firing the damaging optical beam, the fringes are fully restored and only rather minor “post-mortem” damage is revealed, as summarised in the plot of the Figure 4.

Fig. 3. X-ray laser interference microscopy of the rear surface of a fused silica pellicle: Upper part: interference pattern of the non-irradiated surface. Lower part: interference pattern 5 ns after the damaging laser beam passed through the surface.

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Fig. 4. Upper part : Interference pattern of the same surface as in Fig. 3, but 20 minutes after the previous shot, without damaging laser beam. Lower part : Lineouts showing the three interference patterns

4 Summary and perspectives Fused silica pellicles, both with clean surface and with microgrooves as a seed to initiate the laser-induced damage, were probed by the X-ray laser 1 ns and 5 ns after the arrival of the damaging pulse. Under the given experimental conditions, the impact sites at the rear pellicle surface were observed to exhibit very strong perturbation within the 5-ns time after the impact of the damaging pulse, while only moderate permanent perturbation is seen subsequently. The “post-mortem” interference images of the

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damage sites correlate well with the site appearance seen by the visual inspection camera. The reasons of the observed strong transient perturbation are not understood at present time, however detailed analysis of the extensive experimental data is expected to provide more insights into this matter. Besides, the possibility to use very soon the French laser facility “LASERIX” (see Ros et al., this proceedings) will be very useful to extend these surface investigations.

5 Acknowledgments This work benefited from support of the Czech Science Foundation grant No. 202/05/2316. Financial support by the Access to Research Infrastructures activity in the 6th Framework Programme of the EU, Contract RII3CT-2003-506350, LASERLAB Europe, as well as by the Centres of Fundamental Research project LC528 of the Czech Ministry of Education, is also gratefully acknowledged. One of the authors (K.C.) benefited from the Marie Curie Fellowship Contract HPMT-CT-2001-00263. Valuable discussions with Hervé Bercegol (CEA-CESTA) and Guillaume Petite (SESI) are warmly acknowledged.

References 1. 2. 3. 4. 5. 6. 7.

B. Rus et al., Proc. SPIE 5919, pp.146-154, 2005 S.G. Demos et al., Proc. SPIE 4347, pp. 277-284, 2001 H. Bercegol et al., Proc. SPIE 4932, pp. 276-285, 2003 M.R. Kozlowski et al., Proc. SPIE 3902, pp. 138-144, 2000 G. Razé et al., Proc. SPIE 4932, pp. 127-135, 2003 B. Rus et al., Phys. Rev. A 66, 063806-12, 2002 T. Mocek et al., J. Opt. Soc. Am. B 20, 1386-1391, 2003

X-Ray Laser Thomson Scattering at 21 nm of Laser-Heated High-Density Foil Plasmas B. Rus1, J. Dunn2, T. Mocek1, A. J. Nelson2, M. E. Foord2, R. Shepherd2, W. Rozmus3, H. A. Baldis4, M. Kozlová1, J. Polan1, P. Homer1 and M. Stupka1 1

Institute of Physics / PALS Centre, 18221 Prague 8, Czech Republic Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 94551, USA 3 University of Alberta, Edmonton, T6G 2J1, Canada 4 Department of Applied Science, University of California, Davis, CA 95616, USA 2

Summary. Results of our preliminary studies for a demonstration of soft X-ray laser Thomson scattering in laser-produced dense plasma are presented. The investigated plasmas are produced by single-side heated foil targets using a 300-ps pulse of 438-nm wavelength at irradiances between 1013 and 1014 Wcm-2. The Nelike zinc X-ray laser, delivering ~1 mJ of focused energy at 21.2 nm, is injected to the plasma as the Thomson probe. The X-ray laser pulse is timed to arrive to the plasma 0.5 or 1 ns after the peak of the optical pulse, encountering electron densities in the range of 1020–1022 cm-3. The spectrum near 21 nm, emitted at ~30° with respect to the incident X-ray laser, is analyzed by a flat-field spectrometer viewing through the back of the target. The results show that the choice of appropriate target material and thickness are essential to the success of this experiment. From the spectroscopic measurements using Al and polypropylene (C3H6) foils, the latter appears as a suitable candidate for Thomson scattering experiments near 21 nm. A weak spectral feature near 21.2 nm potentially indicating Thomson scattering was observed using a 1.2 µm polypropylene foil. Further data analysis is required to support this conclusion.

1 Introduction Thomson scattering (TS) has been demonstrated over the last several decades as tool for probing laser-produced plasmas in order to determine the plasma electron temperature, for example [1]. The underdense plasma corona ne < 1021 cm-3 has been studied by ultra-violet (UV) wavelength

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probes and compared with the results from hydrodynamic code simulations [1]. More recently, keV x-rays from laser plasmas [2, 3] have been utilized in order to extend the technique to near-solid density plasmas. These require an energetic laser pulse to deliver sufficient x-ray photon flux for the TS probe [3]. A study to employ a soft X-ray laser probe for Thomson scattering was reported where high resolution spectroscopy was required to study and resolve the TS ion features [4]. One of the conclusions from this work was the need for a millijoule X-ray laser to measure the Thomson scattered feature above the thermal emission spectrum of the laser plasma. In this work, we used the Ne-like zinc X-ray laser, routinely operated as a user beamline at PALS [5], delivering multimillijoule output at 21.2 nm. The goal of this study was assessing the feasibility of the X-ray laser Thomson scattering, employing well-defined experimental conditions, and to identify suitable target parameters and plasma probing regimes.

2 Numerical simulations of Thomson scattering near 21 nm

Fig. 1 Calculated differential Thomson scattering cross-sections for 21.2 nm radiation, for plasma Te of 400 eV and electron density (a) of 1021 cm-3 (left) and (b) 1022 cm-3 (right). θ is the angle between the incident and scattered waves.

Figure 1 shows Thomson scattering cross-sections in LTE plasmas with two values of electron density, ne=1021 cm-3 and ne=1022 cm-3, at the electron temperature, Te, of 400 eV. The simulations (for classical theory of Thomson scattering see [6]) show that besides the central narrow ion scattering feature the spectrum contains, for a specific range of scattering angles, well-defined electron satellite peaks. These peaks, due to collective (incoherent) Thomson scattering, are shifted from the frequency of the scattered radiation approximately by the electron plasma frequency ±ωpe and scale as ne1/2. The electron feature is well-defined in the forward

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scattered direction and can be measured with an instrument with moderate spectral resolution. Te

Te (a)

(b) ne

Te

ne

Te (d)

(c)

ne ne

Fig. 2. Hydrodynamic HYDRA 1D simulations showing the electron density and electron temperature profiles of single-side illuminated 2-µm thick Al foil at (a) t=-0.2 ns, (b) t=0 ns, (c) t=0.5 ns and (d) t=1.0 ns with respect to the peak of the ~300-ps driving pulse. The peak laser irradiance is 3 × 1014 Wcm-2. Laser is incident from the right and original target position is between 0 and 2 µm.

Figure 2 shows results of hydrodynamic simulations of the time evolution of the electron density and temperature of a plasma produced from a 2-µm Al foil irradiated at 3 × 1014 W cm-2. The measured laser pulse shape of 300 ps (FWHM) at 438 nm wavelength was used in the calculation. These were run on the HYDRA code as a 1D simulation [7] to guide the preliminary target design. It is seen that the heated foil does not burn through during the laser pulse and behaves like a flyer plate leaving behind a relatively uniform plasma with ne ~ 1021 - 1022 cm-3.

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3 Experimental arrangement The experimental setup is shown in Fig. 3 and the method of superposition of the x-ray and optical laser is indicated in Fig. 4. The investigated plasmas are generated by irradiating either thin Al or polypropylene (C3H6) foils by ~300-ps pulses at the wavelength 438 nm (3ω of the iodine laser), producing 1013 to 1014 Wcm-2 over ~150 µm diameter spot focus. The 21.2-nm X-ray laser pulse is injected to this plasma near collinearly with the optical laser, in a narrow ~20-µm spot, delivering ~1 mJ of net energy.

Fig. 3. Experimental setup: the X-ray laser pulse is focused down to the surface of a thin foil, to a spot with diameter ~20 µm, by f=125 mm 13° off-axis parabola coated with a Mo:Si multilayer. The investigated plasma is produced in the ~150µm focus of the 438-nm laser, largely overfilling the X-ray laser focus (see inset). The soft-x-ray emission at θ~30 degrees with respect to the direction of the incident X-ray beam is analyzed by a flat-field 1200 line/ mm grating spectrometer.

4 Results and Discussion A 0.8-µm Al foil plasma produced intense line emission near 21.2 nm, making a possible Thomson scattered X-ray laser signal difficult to detect. In contrast, the polypropylene spectrum, Fig. 5, has a strong H-like oxygen Balmer-α line at 18.2 nm but is free of thermal line emission near 21.2 nm.

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Fig. 4. Superposition of the optical and X-ray laser foci at the 1.2-µm polypropylene target. The optical and the X-ray laser bore holes in the foil in two consecutive shots while the foil is displaced vertically by 450µm (post-shot image taken by the telemicroscope camera shown in Fig. 3).

Fig. 5. Spectrum of polypropylene (C3H6) plasma produced from a 1.2-µm foil heated at 1014 Wcm-2. X-ray laser is injected 1 ns after the peak of the optical laser.

Fig. 6. Lineouts of C3H6 plasmas produced at 1014 Wcm-2 (X-ray laser injected 1 ns after the optical pulse, top trace) and 6×1013 Wcm-2 (with and without X-ray laser injected).

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The polypropylene plasma thus constitutes a good candidate for this preliminary Thomson scattering study using the zinc laser. However, the downside is that cold, unablated solid C3H6 strongly absorbs the 21.2 nm emission (transmission 4×10-4 for thickness 1.2 µm). It would be necessary to employ a thickness that would be heated through at the time of the arrival of the X-ray laser pulse. Figure 6 shows the spectra from the plastic for a number of different irradiances. The spectrometer is viewing from behind the target in order to measure the forward scattered spectrum, see Fig. 3. We observe some indication of a very weak scattered signal in the vicinity of 21 nm at the highest laser irradiance (top trace Fig. 6) but this requires further detailed analysis to confirm on a series of shots. At the lower irradiances the emission spectrum was reduced indicating that part of the target may not be heated leaving cold absorbing material. In conclusion we have described the first preliminary study to measure the Thomson scattered signal from a dense plasma using a 1 mJ, 21.2 nm X-ray laser probe. The analysis is ongoing and we will report more details at a later date.

Acknowledgments We thank M. Purvis of Colorado State University and S.J. Moon of LLNL for the HYDRA simulations. We thank C. Fortmann of Rostock University for assistance in the Thomson scattering cross-sections. The work was performed in part under the auspices of the US Department of Energy by the University of California Lawrence Livermore National Laboratory under Contract No. W-7405-Eng-48, and supported by LASERLAB Europe Access to Research Infrastructures activity Contract RII3-CT-2003506350. Support of the Czech Grant Agency Contract No. 202/05/2316 and of the Centres of Fundamental Research Project LC528 of the Czech Ministry of Education is also acknowledged.

References 1. La Fontaine, B. et al: Characterization of laser-produced plasmas by ultraviolet Thomson scattering, Phys. Plasmas 1, 2329, 1994. 2. Riley, D. et al: X-Ray Diffraction from a Dense Plasma, Phys. Rev. Lett. 84, 1704, 2000. 3. Glenzer, S.H., et al: Demonstration of Spectrally Resolved X-Ray Scattering in Dense Plasmas, Phys. Rev. Lett. 90, 175002, 2003.

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4. Baldis, H.A., Dunn, J., Foord, M.E., Rozmus, W.: Thomson scattering diagnostic of solid density plasmas using x-ray lasers, Rev. Sci. Instr. 73, 4223, 2002. 5. Rus, B. et al: Multimillijoule, highly coherent x-ray laser at 21 nm operating in deep saturation through double-pass amplification, Phys. Rev. A 66, 063806, 2002. 6. Salpeter, E.E., Electron Density Fluctuations in a Plasma, Phys. Rev. 120, 1528, 1960. 7. Marinak, M. M. et al.: Three-dimensional HYDRA simulations of National Ignition Facility targets, Phys. Plasmas 8, 2275, 2001.

One Year of User Operation of FLASH, the FreeElectron Laser in Hamburg J. Feldhaus Deutsches Elektronen-Synchrotron DESY, D-22603 Hamburg, Germany

Summary. The Free-electron LASer at DESY in Hamburg (FLASH) is the first free-electron laser (FEL) built for the vacuum-ultraviolet (VUV) and soft X-ray region. In the present configuration the FEL can be tuned to any wavelength between ~50 nm and ~13 nm by changing the electron beam energy from ~ 350 MeV to ~ 700 MeV. The FEL has been operated at various wavelengths, the radiation pulses were characterised in terms of pulse energy, statistical properties, spectral distribution and coherence, and they have been used for a variety of experiments. Saturated intensities in the 10 – 100 µJ range have been reached with pulse durations between 10 fs and 50 fs. At these intensities strong harmonic radiation up to 7th order has been observed. FLASH has started regular user operation in summer 2005. Currently 16 science projects involving approximately 200 scientists are sharing approximately 20 weeks of beamtime per year. In order to make efficient use of the single FEL beam, it can be switched between four experimental stations by movable mirrors. A synchronised optical laser system is available for pump-probe experiments. Diagnostics has been implemented to monitor the pulse energy and its timing with respect to the optical laser.

1 Introduction In a free-electron laser (FEL) the lasing medium is a high-density bunch of electrons flying with relativistic speed through the periodic magnetic field of a very long undulator. The interaction between the undulator radiation that is produced and the electrons in the bunch induces a periodic density modulation of the electrons, known as FEL instability, causing many electrons (of the order 109) to radiate in phase and thereby increasing the intensity of the radiation by this factor compared to the spontaneous radiation which is used at synchrotron radiation facilities. The FEL concept can be adapted to produce radiation wavelengths from millimeters to Ångstroms, and can, in principle, produce hard x-ray beams with unprecedented peak

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brightness, exceeding that of the brightest synchrotron sources by ten orders of magnitude. The technical challenge associated with a short-wavelength FEL is the preparation and accurate steering of a high-quality electron beam through a very long undulator with typically 1000 magnet periods or more in order to achieve optimum interaction of the undulator radiation field with the electron beam. Typical electron beam parameters required for the FEL are a normalized emittance of ~1 µm rad, an energy spread of <0.1% and a peak current of >1kA. Since the FEL instability is initiated by the spontaneous undulator radiation, the process is called self-amplified spontaneous emission (SASE). A large part of the undulator is needed to build up a strong spontaneousradiation field which first modulates the electron energy. When this energy modulation transforms into a charge density modulation, exponential gain sets in saturating typically within a few hundred to a thousand undulator periods. Accordingly, the coherence length (time) ranges from ~20 µm (~60 fs) at 100 nm wavelength to ~0.1 µm (~0.3 fs) at 1 Å wavelength. It determines the minimum possible pulse duration of a FEL which can be much shorter than a vibration period of a molecule. The coherence length also determines the spectral width of the radiation pulse. Usually an electron bunch is longer than the coherence length such that several or even tens to hundreds of longitudinal modes are amplified. The phases of these modes are randomly distributed due to the start-up from noise, and the intensity distribution along the radiation pulse as well as the phases of the modes is different from pulse to pulse. This is reflected in the spectral distribution which contains a similar number of modes and differs from shot to shot [1, 2]. In contrast, the degree of spatial coherence is much higher; values of 80-90% have been measured at 100 nm wavelength [3]. In principle, an external coherent radiation source can be used to seed the FEL process and to improve the radiation properties. Various schemes are currently investigated, including the use of high-gain harmonic generation cascades. However, at this time there are still many open questions and technical challenges associated with seeding, and it is not clear down to which wavelengths and for which applications such schemes will be useful. The SASE principle has recently been tested very successfully in the vacuum ultraviolet (VUV) near 100 nm wavelength [2] at the previous TESLA Test Facility at DESY. Subsequently this facility has been extended to the first free-electron laser for soft X-rays which is now called FLASH (for Free-electron LASer in Hamburg). After first lasing at 32 nm wavelength in January 2005 [4], it has started user operation in summer 2005.

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2 Overview of the FLASH facility The layout of the FEL facility at DESY is schematically shown in Fig. 1. It has been described in more detail in Reference [4]. Briefly, the electron bunches are generated by a laser driven photocathode radio frequency gun; the bunch charge is typically 1 nC. They are accelerated by a superconducting linear accelerator consisting of currently five cryo-modules, each containing eight superconducting niobium cavities which operate at a resonant frequency of 1.3 GHz. A sixth cryo-module will be installed in summer 2007 in order to reach the design energy of 1 GeV and the corresponding minimum wavelength of ~6.5 nm. Two bunch compressor units compress the electron bunches longitudinally in order to generate the kiloAmpere peak current at low emittance required for the FEL process. Presently the injector is still missing a short accelerator section in front of the first bunch compressor which will be used to linearize the energy chirp along the electron bunches and thus to optimize the bunch compression. Without this section the energy chirp has a curvature leading to a very high peak current at the head of each electron bunch followed by a long tail with much smaller charge density. Only the high-density head of the bunch supports the FEL process leading to radiation pulses of only 10-50 fs duration. RF gun

Accelerating Structures

Collimator Undulator

Bunch Laser Compressor 5 MeV 127 MeV

Bunch Compressor 370 MeV

445 MeV

bypass

FEL diagnostics

Fig. 1. Schematic layout of FLASH. The total length of the facility is ~300 m.

The full energy electron beam is then cleaned by a set of collimators before it enters the undulator. The magnetic period is 27.3 mm with a peak field of 0.47 T. It has a fixed gap of 12 mm; the FEL wavelength is tuned by changing the electron beam energy. The undulator consists of six modules, each 4.5 m long, with 0.6 m long sections in between which contain two quadrupoles for focusing the electron beam, wirescanners for measuring the beam profile, and beam position monitors. The quadrupole magnets can be moved in order to adjust their magnetic axes accurately on a straight line, a necessary condition for maximizing the interaction between the electron beam and the radiation field. The electron beam is then deflected into a water-cooled absorber. The FEL radiation passes a diagnostics section at the end of the accelerator tunnel before it travels in ultra-high vacuum to the experimental

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area. The diagnostics section in the tunnel is essential for commissioning and tuning the FEL. It includes in particular different detectors and view screens which allow finding the radiation beam and measuring its intensity on a pulse to pulse basis. In addition, the beam can be steered by a plane mirror into a grating spectrometer which is equipped with a gated CCD camera to measure the spectral distribution of single radiation pulses [5].

Fig. 2. Photograph of the experimental area. The FEL beam can be switched to four experimental stations (in the background close to the window) by moving plane mirrors. Similarly, a synchronised optical laser beam can be transported in vacuum to each of the stations by switching plane mirrors which are mounted in the four cylindrical vacuum vessels in the foreground. The optical laser is located in a hutch on the right just outside the picture.

A photograph of the experimental area is shown in Fig. 2. The FEL radiation enters the experimental building at a distance of approximately 40 m from the undulator. At this point the peak fluence of the radiation pulses is sufficiently reduced such that conventional X-ray optics at grazing angles of incidence can be used. The section of the experimental hall where the photon beam enters the building includes beam collimation and radiation shielding, online, non-destructive photon diagnostics and four mirrors, two on either side, to switch the photon beam either to the right into a

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high-resolution plane-grating monochromator, or to the left where it can be further deflected into three experimental stations. A calibrated gas ionisation detector is used to monitor the intensity of each radiation pulse [6] before it is deflected by the first plane mirror. The second plane mirror in the left-hand branch will be replaced by a plane grating with varied line spacing (VLS) to monitor the spectral distribution of individual pulses. This spectrometer is currently under construction. The experimental floor has a size of 20 m x 30 m. Currently there are four beamlines in operation, including a beamline with a ~100 µm focus behind a toroidal mirror, a beamline with a ~25 µm spot produced by an ellipsoidal mirror, and a high-resolution plane-grating monochromator beamline with a 100 µm focus. Another station has no focusing optics yet but can be used for experiments which do not need high photon density or which have their own optics. A fifth beamline is under construction behind the monochromator. It will be used for inelastic scattering experiments employing a high-resolution, two-stage spectrometer which will be permanently installed at this station. In order to use the FEL beam most efficiently, at least two experiments are set up at a time at different stations between which the FEL beam is switched by plane mirrors. Usually one experiment is online for 12 hours and then the beam is switched to another station. An optical laser system fully synchronized with the FEL beam has been developed and installed in a separate, air-conditioned hutch [7]. Evacuated beamlines guide the laser beam to the experimental stations (see Fig. 2). The laser beam can be switched by moving plane mirrors in or out, just like the FEL beam. Suitable delay lines in the laser hutch are used to adjust the timing between the FEL and the optical laser pulses. The relative timing can be measured by two systems: (i) by a streak camera in the laser hutch on the entrance slit of which some of the optical laser light and visible synchrotron radiation from the same electron bunch are simultaneously focused; (ii) by an electro-optic sampling system with sub-100fs resolution where part of the laser light is transported via optical fibre to the accelerator and sent through an electro-optical crystal near the electron beam [8].

3 Current performance of the free-electron laser The commissioning of the linear accelerator started in September 2004. In December 2004 the first electron beam was sent through the undulator, and first lasing at 32 nm wavelength was observed in January 2005 [4]. The first experimental stations were commissioned with beam in June 2005,

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accompanied by a steady improvement of the FEL with intensities close to the saturation level, i.e. average pulse energies around 30 µJ and peak values around 100 µJ. At this time also strong second and third harmonic radiation was observed with the spectrometer, indicative of saturation. Photo-ionisation experiments on Xenon were used to estimate the relative intensity of the second and third harmonic to be around 0.5 % of the fundamental line [9]. Pulse durations between 20 fs and 50 fs were inferred from the characteristic features in the single-shot spectra.

Fig. 3. FEL performance at 13.7 nm wavelength: The picture on the left is a falsecolour CCD image of the beam profile on a Ce:YAG crystal some 20 m behind the undulator. The graph on the right hand side shows the radiation pulse energy of the FEL at 13.7 nm wavelength increasing with the active length of the undulator. The gain is maximum in the fourth undulator module and saturates towards the end of the undulator where an average pulse energy of ~60 µJ is reached.

The performance of the FEL has been steadily improved during the first year of operation. After the first round of user experiments the FEL has also been tuned to a number of other wavelengths with similar performance. Typically it takes now a few hours to change from one wavelength to any other in the range between ~13 nm and ~50 nm. Fig. 3 shows recent measurements of the beam profile and the intensity variation along the undulator at 13.7 nm wavelength. Maximum gain is reached in the fourth undulator segment, then it decreases and the intensity approaches saturation with an average pulse energy of ~60 µJ. Under these conditions strong harmonic radiation up to 7th order has been observed, and the beam divergence (~60 µrad FWHM) is almost diffraction limited. The major milestones reached until August 2006 are briefly summarized in Table 1 below.

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Table 1: Major milestones achieved in 2005-2006

14th January, 2005 30th June, 2005 June-August, 2005 end of July, 2005 26th April, 2006 4th May, 2006 July - August 2006

first lasing at 32 nm wavelength, single bunches at 2 Hz ~30 µJ pulse energy at 32 nm, observation of intense second and third harmonic radiation commissioning of photon beamlines first experiments, start of user operation lasing at 13.1 nm wavelength (~µJ pulse energy) lasing at 25.5 nm, >10 µJ pulse energy, intense second and third harmonic radiation - saturation at 13.8 nm (up to 70 µJ av., 170 µJ peak) - saturation at 32 nm (up to 100 µJ av., 200 µJ peak) - demonstration of long pulse trains (up to 600 pulses, up to 100 mW average FEL power)

4 The current science program The first user experiments started in the last week of July 2005. Currently, there are 16 active projects, out of 18 which were evaluated by a Project Review Panel in 2002. Approximately 200 scientists from 11 countries are involved in these projects. Most projects are collaborations of several teams who have built new instrumentation especially for the experiments at FLASH. The beamtime for the 16 projects has been organised in blocks of typically four weeks, preceded by two or three weeks of FEL studies to improve the beam characteristics. Some of the user projects as well as additional projects conducted by the DESY photon diagnostics group with partner institutes are also concerned with the development of critical diagnostics such as an online intensity monitor, a wavefront sensor or a singleshot cross-correlator for measuring the time difference between the FEL pulse and the optical laser on a shot-to-shot basis. The science projects may be grouped into four categories, although this classification is somewhat arbitrary and not always unique: 1.) Interaction of ultra-intense XUV pulses with matter. This group includes several projects dealing with multi-photon excitation of atoms, molecules and clusters; a large collaboration working on different aspects of creating and characterizing warm, dense matter; and teams interested in imaging biological samples with the vision of determining the structure of

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large molecules at Ångstrom wavelengths when the first X-ray FELs become available. 2.) Femtosecond time-resolved experiments. There are currently three projects dealing both with technical developments and first pump-probe experiments on atoms and molecules. 3.) Investigation of extremely dilute samples. Three projects are dealing with photodissociation of molecular ions, spectroscopy of highly charged ions, and mass selected clusters. 4.) Investigation of surfaces and solids. This group includes projects on XUV laser desorption, surface dynamics, luminescence under FEL radiation, and meV-resolution photon and photoelectron spectroscopy of surfaces and solids with nm spatial resolution Although first results have already been published or submitted to scientific journals, many of the first experiments have been feasibility studies or demonstration experiments, and much of the data is still being evaluated. Therefore, only a few examples can be given at this time. The first example deals with Coulomb explosion and diffraction imaging of biological samples. Fig. 4 shows schematically the diffraction experiment. The object is illuminated by a single FEL pulse focused tightly on the sample. The diffracted radiation is reflected by a specially designed multilayer mirror onto a CCD camera, effectively suppressing background from the direct FEL beam. The first experiments have been very successful demonstrating the feasibility of ultra-fast, single-shot diffraction imaging and reconstruction of an object with diffraction-limited resolution.

Fig 4. Schematics of a single-shot diffraction imaging experiment (courtesy of H. Chapman).

Photoelectron yield in a.u.

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The second example is photoionisation of rare gases and first demonstration of femtosecond time-resolved experiments combining the focused FEL beam with a femtosecond optical laser pulse [10]. When an atom is ionised in the presence of a strong optical laser field, sidebands appear in the photoelectron spectra arising from additional excitation by or absorption of optical photons. This effect has been used to demonstrate, for the first time, full spatial and temporal overlap of FEL and optical laser pulses focused on a Xe gas target. Fig. 5 shows a sequence of photoelectron spectra of Xe gas for different delay times between the FEL and the optical laser pulses. When the two pulses overlap, sidebands appear on the highkinetic energy (shorter time of flight) side of the 5p photoelectron lines, showing additional absorption of one or more optical photons. The FEL was very stable during the experiments such that the delay of the optical laser beam could be scanned and the range of temporal overlap could be measured. A value of ~500 fs FWHM was measured reproducibly at different times, with ~50 fs duration of the FEL pulse and ~120 fs of the optical laser pulse. The value of 500 fs is in good agreement with the present phase stability of the accelerator leading to path length variations through

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the bunch compressors. Nonetheless, it should be possible to increase the temporal resolution of pump-probe experiments down to the level of the radiation pulse duration by measuring the accurate time difference e.g. by electro-optical sampling methods [8].

References 1. J. Feldhaus, J. Arthur and J.B. Hastings: 'X-ray free-electron lasers', J. Phys. B 38, S799-S819, 2005. 2. V. Ayvazyan et al.: 'A New Powerful Source for Coherent VUV Radiation: Demonstration of Exponential Growth and Saturation at the TTF FreeElectron Laser', Eur. Phys. J. D 20, 149-56, 2002. 3. R. Ischebeck et al.: 'Measurement of the Transverse Coherence of the TTF Free Electron Laser', Proceedings of EPAC 2004, Lucerne, Switzerland, 25772579, 2004. 4. V. Ayvazyan et al.: 'First operation of a free-electron laser generating GW power radiation at 32 nm wavelength', Eur. Phys. J. D 37, 297-303, 2006. 5. P. Nicolosi et al.: 'Grazing-incidence spectrometer for the monitoring of the VUVFEL beam at DESY', J. Electron Spectr. Rel. Phenomena 144, 10551058, 2005. 6. M. Richter et al.: 'Measurement of gigawatt radiation pulses from a VUV/EUV free-electron laser', Appl. Phys. Lett. 83, 2970-2972, 2003. 7. I. Will, H. Redlin, S. Düsterer, J. Feldhaus and E. Plönjes: 'Optical laser synchronized to the DESY VUV-FEL for two-color pump-probe experiments', Proceedings of FEL 2005, Stanford, California, USA, 689-693, 2005. 8. F. Van den Berghe et al.: 'Proposal for a Sub-100 fs Electron Bunch Arrivaltime Monitor for the VUV-FEL at DESY', Proceedings of EPAC 2004, Lucerne, Switzerland, 345-347, 2005. 9. S. Düsterer et al.: 'Spectroscopic characterization of vacuum ultraviolet free electron laser pulses', Optics Lett. 31, 1750-1752, 2006; 10. M. Meyer et al.: 'Two-color photoionization in xuv free-electron and visible laser fields', Phys. Rev. A 74, 011401, 2006; P. Radcliffe et al.: 'Crosscorrelation of independent femtosecond XUV free electron and infrared lasers', submitted to Appl. Phys. Lett.

Intense Femto-Second Laser-Driven X-Ray Source Coupled With Multiple Directional Quantum Beams for Applications H. Daido1 , A. Sagisaka1, K. Ogura1, S. Orimo1, M. Nishiuchi1, A. Yogo1, M. Mori1, Z. Li1, H. Kiriyama1, S. Kanazawa1, A. Akutsu1, Y. Nakai1, A. Pirozhkov1, S. Bulanov1, T. Esirkepov1, T. Kimura1, T. Tajima1, K. Nemoto2, Y. Oishi2, T. Nayuki2,T. Fujii2, A. Zhidkov2, A. Noda3, S. Nakamura 3, I. W. Choi4, T. J. Yu4, J. H.Sung4, H. T. Kim4, T. M. Jeong4, K.H. Hong4, J.-H. Kim4, Y.-C. Noh4, D.-K. Ko4, J. Lee4, S. Nashima5, K. Shimizu5 and M. Hosoda5 1

Advanced Photon Research Center, Japan Atomic Energy Agency, Japan Central Research Institute of Electric Power Industry, Japan 3 Institute for Chemical Research, Kyoto University, Japan 4 Femto Science Laboratory, Advanced Photonics Research Institute, Gwangju Institute of Science and Technology, Korea 5 Department of Applied Physics, Osaka City University, Japan 2

Summary. An ultra-high laser pulse creates the relativistic collective phenomena such as high energy proton generation induced by high energy electrons, high order harmonic generation with a relativistic collective electron motion, intense MeV x-ray generation via Bremstrahlung as well as ultra-short mono-energetic electron bunch generation, an intense THz radiation with the thin foil or gas target techniques. These beams interact with matter with quantum effects. We call them quantum beams. Here we describe the high intensity laser driven multiple quantum beams for applications such as various pump-probe techniques.

1 Introduction Recently, an ultra-high intensity short-pulse laser based on the chirped pulse amplification technique is commonly used for high-intensity physics applications. A thin foil target irradiated by a clean femto-second pulse exhibits collective relativistic plasma phenomena such as generation of collimated ions[1], hard x-rays[2], coherent high order harmonics[3], high intensity THz radiation[4] and so on.

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The feature of the laser-driven relativistic plasmas is that the ultra-short laser field interacts collectively with significant amount of mass. This means that the laser produced plasma motion is governed directly by the laser field. From this point of view, the mass limited target such as gas, cluster, low density foam and thin foil targets are the important candidate for the source of collective relativistic phenomena. Advantages and disadvantages are listed as follows; the gas target is attractive source for creating a uniform under-dense plasma especially for the laser driven wake-field accelerator [5] and possibly ion acceleration in the under-dense plasma [6]. A cluster target provides locally high density region [7] however it does not have regular structure against laser field. The latter two sometimes have disadvantage because nonlinear laser propagation should be taken into account. Based on the concept described above, we describe the high intensity femto-second laser driven quantum beams such as x-ray, electron, proton, THz radiation and their combinations for fruitful applications such as various pump-probe techniques. S i B o lo m eter T e ra h e rtz ra dia tio n

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We have performed high intensity laser-matter interaction experiments using a thin-foil target irradiated by Titanium Sapphire lasers of APRC[8],

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CRIEP[9] and GIST[10] with a peak irradiance between 1017 to 1019 W/cm2. A tape target driver provides a fresh surface of a metal foil such as Ta, Ti as well as Cu with the thickness of 3 to 5 μm during the experiments. To obtain the plasma parameters shot by shot, we have developed several on-line real time monitors such as x-ray pinhole camera which could measure x-ray emission size and reproducibility of the place of the emission as well as x-ray spectrum with a single photon counting technique, laser pre-pulse monitors, electron spectrometers, a time of flight proton spectrometer which is placed along the target normal direction in the rear side.

3 X-ray simultaneously with a proton beam Ultra short high intensity laser driven sources have been investigated for long time. The hard x-ray is generated via Bremstralung[2,11]. The quasimonochromatic ultra-short duration of less than pico-second keV x-ray has been obtained via K-α scheme [12, 13].

Fig. 2. X-ray contact image of a cutter knife (central white region) with 18 mm width and 0.5 mm thickness. The distance between the x-ray source and the knife is 528 mm and the image is obtained with 80 shots accumulated.

Another x-ray generation with novel mechanisms has also been proposed and been tested [14, 15]. Figure 2 shows the contact x-ray image of a knife with 18 mm width and 0.5 mm thickness placed outside the target chamber. The distance between the source and the knife is mm. The 15 mm thick glass frange is placed between the two to keep the vacuum. Therefore the dominant x-ray spectrum is beyond 10 keV. The 400mJ in 100fs laser is irradiated a target with 80 shots accumulated. Based on this number if we reduces the distance between the source and the sample to be

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60 mm, similar quality x-ray image is obtained with a few laser shots accumulated. On the other hand, we succeeded in performing the ion acceleration experiment and obtained a few MeV protons with the laser intensity of 3×1018W/cm2. Firstly, the stability of the focus position as well as the reproducibility of the plasma on the target were monitored by the x-ray pinhole camera in real time. The reproducibility of the plasma was high enough and the stability of the shooting point was also well within the Rayleigh length of our focusing system. It is important technique for the repetitive and reproducible ion production. Secondly, the density distribution of the preformed plasma was monitored at both front and back sides of the target with the two-color interferometer at every shot [16], which provides us the important information for the proton acceleration. We have also proposed the physical mechanism of the ion acceleration in our experimental condition [17]. The simple one-dimensional model, described in above section, successfully explains our experimental data. 0

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For demonstration of useful application of the laser driven proton source, we have performed proton imaging experiment firstly done by British group using single shot based machine [18]. Figure 3 shows the projection image of the test pattern for an electron microscope with a resolution of 10 μm [19]. Based on the successful test of the proton imaging experiment at GIST in Korea, we have tested simultaneous generation of x-ray and protons from a thin Cu tape target resulting in a demonstration of projection images of the test pattern for an electron microscope. We have also tested x-ray emission together with protons having energy of several

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hundred keV and with an intense THz radiation [20] at APRC, JAEA. Both experimental results show the future prospects of simultaneous or synchronized generation of high brightness ultra-short duration multiple quantum beams which originate from a laser driven thin tape target. For this purpose, we have to use x-ray optics for collecting x-ray and controlling the direction of it and adjusting their time delay properly for pumpprobe techniques.

4 Monoenergetic electron bunch and short keV x-ray source We have tested experimentally the laser driven wake-field acceleration [5] with a few TW laser JLITE-X [8]. By varying the plasma density in the laser irradiated gas-target, the regimes of quasi-mono-energetic electron beam generation are found in the sub-relativistic vacuum intensity, 9 x 1017 W/cm2 [21]. Electron beams with multi-peaked energy spectra having energy maxima each of which is well separated and an each electron bunch is well collimated are observed. A typical energy spectrum of quasi-monoenergetic electron beam is shown in Fig. 4. Figure 5 shows the corresponding beam divergence (transverse beam profile) of such a quasi-monoenergetic electrons with a divergence of 2~3 mrad (full width at half maximum) These results are well reproduced by a two-dimensional-particle-incell computer simulation of laser-wake field acceleration in the selfmodulation regime in which the electron injection occurs via wake-wave breaking, and the accelerated electrons are wiggling under the action of the transversally inhomogeneous component of the wake field. By slightly changing the target density, the peak energy of the quasi-mono-energetic electron beam can be shifted, which suggests how to tune the peak energy obtained by this technique. Using this technique, all laser driven femto-second keV x-ray source can be made. A femto-second intense laser beam irradiates the gas-target to produce a mono-energetic electron beam having femto-second width. Then a next laser is focused to hit a bunch of electrons. A copious kiloVolt x-ray is generated at the interaction region [22]. This is one of the most attractive applications of the technique for pump-probe experiment.

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Fig. 5. Spatially collimated electron beam with a divergence angle of a few mrad.

5 Attosecond pulse generation with a thin foil technique High-order harmonics can be generated during the relativistic-irradiance laser – solid-density target interactions [23-26]. In this case, the intensity and the energy of the driving pulses are much higher than in the case of gas-generated harmonics. The conversion efficiency is expected to be significantly high such as >10-4.Thus, it is very attractive to use relativistic harmonics for the attosecond pulse generation. The theory of the attosecond pulse generation [3,27] in the framework of the sliding mirror model

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[24] has been developed. As was demonstrated by the PIC simulations [23,24], when a few-cycle relativistic-irradiance laser pulse interacts with a thin foil target as shown in Fig. 6, the ions remain at rest, while the electrons move as a whole. We consider the case when the electron motion in the direction perpendicular to the foil is negligible, so they move ("slide") mainly along the foil. Perpendicular electron motion can be neglected in two cases. First, when it is suppressed by the strong electric charge separation field Ech = 2πenl, which is of the order of the laser field amplitude E0 or more in this case; here e is the electron charge, n and l are the foil density and thickness. Second, when the thin foil target is irradiated by two identical laser pulses from both sides. We consider a p-polarized incident pulse obliquely incident on the thin foil. The problem was solved using the plane wave approximation in the boosted reference frame moving along the foil with the velocity V = c sinθ, where c is the velocity of light and θ is the incidence angle; in this reference frame, the incidence is normal [26]. Under the above assumptions, calculation has been performed. Both reflected and transmitted pulses contain harmonics of the incident laser radiation as shown in Fig. 7; furthermore, the spectral phase varies little at high harmonic orders. After spectral filtering, these harmonics form isolated attosecond pulses, like in the case of harmonics generated in gases for few-cycle driver pulses. Using spectral filtering, it is possible to obtain extreme ultraviolet pulses with the duration of few hundred attoseconds and the conversion efficiency of 10-8 – 10-5 [3, 27]. In order to obtain high conversion efficiency, we should not use spectral filtering technique. We found new regime of attosecond pulse generation in transmission, where the conversion efficiency can be as high as several percent. Example of the transmitted attosecond pulse is shown in Fig. 9 (a). Driver laser pulse has the duration of 6.3 fs and the dimensionless amplitude a0 = eE0/(mcω0) = 16 (I0 = 5.5×1020 W/cm2 for λ0 = 800 nm). Normalized aerial foil density is ε0 = 13.6, which corresponds, for example, to a fully-ionized 10-nm carbon foil. Duration of the transmitted attosecond pulse is τFWHM = 0.44/ω0 (190 as for λ0 = 800 nm), the energy conversion efficiency into the main pulse is 0.033. For the 5-µm focal spot this corresponds to 12 mJ, 60 TW attosecond pulse, which is at least six orders of magnitude larger than can be generated in gases. We take advantage of the analytic theory to establish the optimum parameters for the attosecond pulse generation in this regime. We obtain that the dimensionless pulse amplitude should be approximately equal to the normalized aerial foil density: a0 ≈ ε0, which can be cast into the form I0 ≈ 1.1×1019 W/cm2× (n/1024cm-3)2(l/nm)2. If a0 << ε0, the foil is too heavy for the laser; the electrons are driven at relatively small velocity v << c, which results in a simple linear reflection of the laser pulse like from a metal mir-

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ror. If a0 >> ε0, the pulse is transmitted through the foil almost without change; thus, only small part of the laser energy is transformed to higher frequencies, so the interaction is not efficient, and the transmitted pulse remains femtosecond. Dependencies of attosecond pulse duration and conversion efficiency on a0 under the optimum conditions are shown in Fig. 8 (b). The established relation a0 ≈ ε0 is rather general. It represents the condition of strongest coupling between a laser and a thin foil, so it holds not only for the attosecond pulse generation, but also for harmonic generation [3], ion acceleration [28-30] and so on. Experimental implementation of the sliding mirror technique requires clean femtosecond pulses with extremely low ASE(amplified spontaneous emission) level so the thin foil is not destroyed before the arrival of the main pulse. We will employ techniques to dramatically reduce the ASE level.

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6 Summary The high intensity femtosecond laser driven quantum beams such as x-ray, electron, proton, THz radiation and their combinations for fruitful applications such as various pump-probe technique are described. A well defined thin plasma layer in a thin foil target created by a clean femtosecond pulse opens collective relativistic phenomena which may bring a lot of fruitful applications.

References [1] M. Borghesi et al., Fusion Science and Technol. 49 April (2006). [2] K. W. Ledingham et al., Phys. Rev. Lett.84, 899(2000). [3] A. Pirozhkov et al., Phys. Plasmas 13, 13107(2006) [4] Hamster et al., Phys. Rev. Lett.71, 2725(1993). [5] T. Tajima and J. M. Dawson, Phys. Rev. Lett.43, 267(1979). [6] L. Willingale et al., Phys. Rev. Lett.96, 245002(2006). [7] T. Detmire et al., Phys. Rev. Lett. 78, 3121(1997). [8] M. Mori et al., Laser Physics 16, 1092(2006). [9] T. Fujii et al., Appl. Phys. Lett. 83, 1524(2003). [10] D-K Ko and J. Lee, Abstracts of ICUIL 2006 Ref:ICUIL067-Session1 “Recent progress on APRI PW Project and related high field physics researches”, pp. 49-50. [11] H. Shwoerer et al., Phys. Rev. Lett. 86, 2317(2001). [12] A. Rousse et al., Rev. Mod. Phys. 73, 17(2001). [13] C. Reich et al., Phys. Rev. Lett. 84, 4846 (2000). [14] K. Ta Phuoc et al., Phys. Rev. Lett. 91, 195001(2003). [15] A. Rousse et al., Phys. Rev. Lett.93, 135005(2004). [16] A. Sagisaka et al., Appl. Phys. B84, 415(2006) [17] M. Nishiuchi et al., Phys. Lett. A357, 339(2006). [18] Borghesi et al., Phys. Rev. Lett. 92,55003(2004). [19] M. Nishiuchi et al., Repetitive highly collimated intense proton beam with sub-MeV energy range driven by a compact few tera-watt femto-second laser, submitted for publication. [20] S. Nashima et al., IEEE Proc. 2004 Conf. Optelectronics and Microelectronics materials and Devices(COMMAD 2004), Brisbane, Australia, 8-10 December 2004, (2004) p.303 [21] M. Mori et al., Phys. Lett. A356, 146(2006) [22] Kando, Proc. APRC symposium 2006 ; H. Schwoerer et al., Phys. Rev. Lett. 96, 014802 (2006). [23] S. V. Bulanov et al., Phys. Plasmas 1, 745 (1994). [24] V. A. Vshivkov et al., Phys. Plasmas 5, 2727 (1998).

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[25] M. Zepf et al., Phys. Rev. E 58, R5253 (1998); A. Tarasevitch et al., Phys. Rev. A 62, 023816 (2000); I. Watts et al., Phys. Rev. Lett. 88, 155001 (2002); I. Watts et al., Phys. Rev. E 66, 036409 (2002); U. Teubner et al., Phys. Rev. A 67, 013816 (2003). [26] U. Teubner et al., Phys. Rev. Lett. 92, 185001 (2004). [27] A. Pirozhkov et al., Phys. Lett. A.349, 256(2006) [28] K. Matsukado et al., Phys. Rev. Lett. 91, 215001 (2003). [29] T. Esirkepov et al. Phys. Rev. Lett. 89,175003(2002) [30] T. Esirkepov et al. Phys. Rev. Lett. 92, 175003(2004)

Radiative Properties and Hydrodynamics of LaserProduced Tin Plasma for Efficient Extreme Ultraviolet Light Source S. Fujioka1, H. Nishimura1, K. Nishihara1, Y. Tao1, T. Aota1, T. Ando1, K. Nagai1, T. Norimatsu1, N. Miyanaga1, Y. Izawa1, K. Mima1, H. Tanuma2, H. Ohnishi2, A. Sunahara3, Y. Shimada3 and A. Sasaki4 1) Institute of Laser Engineering, Osaka University, 2) Department of Physics Tokyo Metropolitan University, 3) Institute for Laser Technology, 4) Japan Atomic Energy Agency.

Summary. A laser-produced tin (Sn) plasma is an attractive extreme-ultraviolet (EUV) light source for the next generation lithography in terms of its brightness and compactness. Radiative properties and hydrodynamics of the laser-produced Sn plasmas are quite important for investigating the optimum conditions for EUV generation. Several experiments have been performed to clarify the above issues; (i) EUV spectra emitted from isolated Snq+ (5 < q < 15) ions and opacity spectrum of a 30-eV Sn plasma have been measured as fundamental data for accurate modeling radiation energy transport in plasmas, (ii) electron density profile in 13.5 nm emission dominant region of a laser-produced Sn plasma was measured with a laser interferometer for understanding hydrodynamics of an EUV source plasma. (iii) benchmarking one-dimensional (1D) radiation-hydrodynamic simulation code with multiple laser beam irradiated spherical 1D Sn plasma. Based on the experimental results and calculations, it was found that optically thinner plasma emits 13.5 nm light more efficiently. Optical depth of Sn plasma is actively controlled with changing laser pulse duration and the use of low-density porous target.

1. Introduction Laser-produced high-Z plasma is a typical example of radiationhydrodynamics, in which the radiative properties of a plasma are tightly coupled with hydrodynamic motion via energy transport. A clear understanding of radiation-hydrodynamics is important for the fields of inertial fusion energy, astro- and planetary physics, and x-ray source applications.Extreme ultraviolet (EUV) light sources for microlithography are receiving much attention as an application of laser-produced high-Z plasma. EUV lithography (EUVL) is a promising technology for volume produc-

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tion of next-generation microprocessors whose node size is less than 40 nm [1]. A commercial EUVL system requires > 300 W of output EUV power into a solid angle of 2π sr. from a plasma source of 13.5 nm wavelength within a 2% bandwidth (BW). Laser produced tin (Sn) plasma has a highly intense emission peak at 13.5 nm of wavelength, thus much effort is devoted to the development of the Sn-based EUV light source [2].

2. Radiation properties of laser-produced Sn plasma

2.1 Absolute opacity of 30-eV Sn plasma The opacity, as well as the emissivity, of laser-produced Sn plasma is so high for 13.5-nm light that the light emitted from deep within the Sn plasma is absorbed strongly during propagation through surrounding plasma as it expands. To obtain high conversion efficiency (CE) from incident laser energy to output EUV energy, the plasma size should be controlled to attain an appropriate optical depth, i.e., the product of the mass absorption coefficient and area density of the plasma for 13.5-nm light. The opacity of Sn plasma in the dominant EUV emission region is a critical parameter for investigating the optimum conditions for EUV generation, however no reliable experimental data has been available. The electron temperature and ion density of the dominant EUV emission region are in the ranges from 20 to 80 eV and from 1017 to 1020 cm-3, respectively [3]. Opacity measurements of Sn plasma were performed on the Gekko-XII laser facility [4]. Figure1 (a) shows the experimental set up for opacity measurement. A radiation-confining gold cavity, called the "dog-bone (DB)" [5], was used to uniformly heat an opacity sample. The opacity sample consisted of a thin Sn layer sandwiched between two 100-nm-thick CH tampers mounted on an observation window (200 μm x 200 μm) of the DB. The CH tamper was used to minimize the density gradient of the Sn plasma. The area density of the Sn layer in the sample was 2.04 +/- 0.18 x 10-5 g/cm2, which was analyzed with an inductively coupled plasma (ICP) device. Six beams of the Gekko-XII laser [6] (1.053 μm wavelength, 500 ps pulse duration) were focused through two inlet holes of 500 μm diameter onto the inner surface of x-ray generation sections set at both end of the DB. X-ray radiation from the sections propagated diffusively toward the central cavity for thermal radiation confinement.

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The radiatively heated sample was backlit with broadband EUV light from another Sn plasma generated with a laser pulse of 1.053 mm wavelength and 500 ps duration at 1 x 1013 W/cm2. The backlight source was set 2 mm away from the DB and backlight x-rays were shone at 1.0 ns after the peak of the heating x-ray. The transmitted EUV spectrum through the sample was measured by a grazing incidence spectrograph (GIS) coupled with an x-ray streak camera (XSC). The Sn sample was heated by a TR = 50 eV thermal radiation pulse with a Gaussian shape (500-ps FWHM). Radiation hydrodynamic simulation (ILESTA-1D) [7] predicts an averaged temperature and density of the heated Sn sample of 30 eV and 0.01 g/cm3 at 1 ns after the peak of the heating x-ray pulse. Since the spectrum inevitably includes self-emission from the Sn and CH plasmas, we separately measured the self-emission spectra from the sandwiched Sn sample and from the CH tamper alone.

Fig.1 (a) Schematic of opacity measurement, (b) transmission of 30 eV Sn plasma for EUV light.

The dots in Fig. 1 (b) represent the raw measured spectrum of the transmission, while the solid line in Fig. 1 (b) is the smoothed measured spectrum in consideration of the spectral resolution of the GIS-XSC. The dash-dotted, dashed, and dotted lines represent the spectra calculated by an atomic code HULLAC [8] with electron temperatures of 20.9, 31.0, and 40.3 eV, respectively. The configuration interaction between the 4dn, 4dn1 4f, 4dn-15p, 4dn-15f, and 4p54dn configurations were taken into account, since the configuration interaction changes the wavelength and strength of emission lines considerably [9]. The population of the ionization state was calculated under the collisional radiative equilibrium condition. Strong absorption is seen around 13.5 nm, arising mainly due to the 4p-4d and 4d-4f transitions of Sn8+ to Sn13+

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The transmission at 13.5 nm, the most interesting wavelength, shows quite good agreement between the measurement and calculation, demonstrating that the HULLAC calculation is useful for calculating 13.5 nm light generation. The measured mass absorption coefficient of the Sn plasma at 13.5 nm is 0.96 +/- 0.18 x 105 cm2/g. 2.2 Identification of transition energies of multiply charged ions For accurate modeling of atomic process in plasma, spectroscopic data of Sn ions is necessary. However, the available spectroscopic information on multiply charged Sn ions is fairly limited at present. Even though much spectroscopic data has been reported, the energy levels of multiply charged Sn ions have not been established yet, because of the complexity of their electric structures attributed to the strong electron correlation among the large number of active electron. Photon-emission spectroscopy, in which the line intensities of the photon emissions are measured following the charge-transfer reaction in collisions of multiply charged ions with neutral target gases, is a very powerful experimental technique to investigate the transition energies and energy levels of multiply charged ions [10]. The multiply charged Sn ions were produced in a 14.25 GHz ECR (electron cyclotron resonance) ion source at Tokyo Metropolitan University. The Snq+ (5 < q < 15) ions were extracted with an electric potential of 20 kV and select by a double-focusing dipole magnet according to their massto-charge ratio. The ion beam was directed into a collision chamber, where the ion beam interacts a target gas jet ejected from a capillary plate. The background pressure in the collision chamber was 6 x 10-6 Pa and the target gas pressure in the chamber was held at about 1 x 10-3 Pa during the measurement. The target gas pressure was low enough to maintain the single-collision conditions. The EUV emission from the collision center was observed at 90 deg. to the ion beam direction with a GIS spectrometer equipped with a toroidaltype conversing mirror. As a photon detector, a liquid nitrogen cooled CCD camera was attached to the EUV spectrometer and an emission spectrum in the wavelength range of 6 – 24 nm was accumulated simultaneously. Spectral resolution of the spectrometer is about 0.1 nm. Wavelength calibration was performed using the established EUV emission lines of oxygen ions. From comparison between the measured spectrum and calculation, photon wavelength calculated by the HULLAC code is systematically different by 0.5 nm from the measured one for 4d-4f transitions. Therefore calculated wavelength of 4d-4f transition is manually adjusted to match the

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experimental results for coupling with radiation-hydrodynamic simulation. Furthermore, the measurement reveals transitions corresponding to the dip observed in the opacity spectrum, i.e. the characteristic absorption peaks at 11, 12, 16 and 18 nm are caused by 4d-5f of Sn9+, 4d-5f of Sn8+ 4d-5p of Sn10+ and 4d-5p of Sn9+, respectively.

3. Hydrodynamics of 13.5 nm emission dominant region in laser-produced Sn plasma

3.1 Dynamic imaging of 13.5 nm emission from laser-produced Sn plasmas EUV emission from a laser-produced Sn plasma was imaged on an XSC using a monochromatic EUV Schwarzschild microscope. The microscope employed two concentric spherical mirrors with Mo/Si multilayer coating, operating at 13.5 nm in 4% BW [11]. A 0.4 µm Zr filter over coated on a 0.5 µm CH foil was placed in front of the mirrors to block visible light and particles from the plasma. In the present experiment, spatial and temporal resolutions of the microscope were checked to be better than 15 m and 1.5 ns, respectively. The microscope was installed in the plane of laser incidence and parallel with the target. A 10 ns laser pulse at 1064 nm with energy up to 2 J was illuminated onto the target. The laser beam was focused by an F/4 lens onto the target surface at normal incidence. The focal spot size was measured with both an optical imaging system and a monochromatic EUV pinhole camera. The diameter defined by FWHM was 220 μm and the width defined at 10% of the peak intensity was 450 μm. Targets used in the experiment consists of a strip Sn foil with a width of 200 μm and a thickness of 15 μm. It was placed on a 1 μm-thick CH film. Since CH plasma has much less average mass, CH plasma expands faster than Sn plasma, and CH plasma acts as a tamper to prevent lateral expansion of Sn plasma. Figure 2 shows temporal evolution of the EUV emission profiles at laser intensity of 1 x 1011 W/cm2, which is appropriate for efficient EUV generation [12]. Zero time represents the peak of the laser pulse. The EUV emission region expands with time and the peak of the EUV emission moves away from the target surface. At the peak of the laser pulse, the peak of the EUV emission locates 200 μm away from the target surface.

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Fig. 2 Temporal evolution of EUV emission observed from the side direction.

3.2 Density profile of 13.5-nm dominant emission region in laserproduced Sn plasma The electron density profile of laser-produced Sn plasma was investigated using two interferometers: a Mach-Zehnder interferometer using a probing beam of 266 nm UV light and a Michelson interferometer using 532 nm green light [13]. A small amount of laser energy, split from the heating beam, was used as a probe beam. The wavelength of the probe beam was converted to 532 and 266 nm. High temporal resolution was achieved by using a visible framing camera (HAMAMATSU C7400), which was synchronized with the laser pulse with a jitter less than 1 ns. The gate interval was set to 1 ns. The temporal resolution was less than 1.5 ns. The spatial resolution limited by the camera was 15 µm. For the both the green and UV interferometers, an interferometer data evaluation algorithm was used to calculate the Abel inversion to extract the density map from the phase shift map. Density profiles along the center of the plasma are plotted in Fig. 3. The circles an triangles represent the data from the green and UV interferometers, respectively. The error bars arise from the Abel inversion process, due to the irregular phase profiles. The solid line is an exponential decay fit to the experimental points with two typical scale length of 70 and 120 μm. Electron density of the EUV emission dominant region (EDR) is in range from 1019 to 1020 cm-3, those are much lower than the critical density for 1.064 μm light.

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The measured density profile was compared with that predicted by onedimensional (1D) code (STAR-1D) [15]. It can be seen in Fig. 3 that there is a considerable discrepancy in their absolute values. A possible reason for this discrepancy arises from three dimensional plasma expansion. Because of the finite size of the focal spot, a lateral plasma expansion occurs as well as a longitude expansion. It is noted that the plasma scale length and the diameter of the focal spot are comparable, so multi-dimensional expansion becomes to have significant effects on plasma structure. As is expected, two-dimensional radiation hydrodynamic code reproduces the density reduction caused by the multi-dimensional expansion.

Fig. 3 Comparison of electron density profile between measurement and simulation. Dashed and solid lines are calculated by 1D and 2D code.

4. Benchmarking radiation-hydrodynamic simulation code with one-dimensional spherical plasmas Radiation-hydrodynamic simulation code is a powerful tool to investigate the optimum conditions for the EUV generation. Its reliability is proven only by experimental data, however a plasma produced from a planar target irradiated by single laser beam shows the multi-dimensional effects. The multi-dimensional plasma expansion make it difficult to compare the experimental results with 1D simulation. For eliminating these problems, spherical targets were irradiated uniformly with a multiple laser beam [14] on Gekko-XII laser facility [6]. Spherical plastic targets coated with a 1 μm-thick tin layer, were used in the experiment. The target diameter was varied from 300 to 750 μm. A 1.2 ns Gaussian pulse of 1.05 μm wavelength and 0.5 – 15 J in total energy

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was focused with an F/3 lens and the focal point was displaced based on the target diameter such that the target was illuminated uniformly. The laser intensity on the target was varied from 2 x 1010 to 1 x 1012 W/cm2 by adjusting the laser energy and the target diameter. The radiation-hydrodynamic code (STAR-1D) [15] describes radiation transport with a multi-group diffusion approximation, in which photon from 0.5 to 1500 eV is divided into 1500 groups. Electron thermal conduction is treated with a flux-limited Spitzer-Harm model, and laser absorption is calculated using a ray-tracing method. Tabulated emissivities and opacities calculated by the HULLAC code under the collisional radiative equilibrium condition are coupled with the radiation-hydrodynamic code.

Fig. 4 EUV spectra emitted from multiple laser beams irradiated spherical target. (a) experiment, (b) calculated by 1D code.

Figure 4 shows the comparison of spectra between experiment [14] and calculation at the laser intensity of 9 x 1011 W/cm2. The EUV spectrum was measured with a transmission-grating spectrometer coupled with a CCD camera. Its spectral resolution is better than 0.42 nm. The simulation spectrum is smoothed with taking into account of the instrument spectral resolution. The calculated spectrum shows quite good agreement with the experimental results. The agreement is observed in the wide range of the laser intensity from 1010 to 1012 W/cm2. The atomic process and energy transport included in the simulation code are proven to be appropriate for the EUV source modeling. The conversion efficiencies (CEs) from incident laser energy to output 13.5 nm 2 % BW energy were measured with a calibrated energy-meter called E-mon. Figure shows the CE dependence as a function of laser intensity. The highest CE of 3% was attained at an intensity of 0.5 – 1 x 1011 W/cm2. The calculated CEs are almost consistent with, but somehow higher than, the experimental values, because 20 % of intensity non-

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uniformity still remains on a spherical target irradiated by finite (twelve) laser beams.

5. Active control of the laser produced Sn plasma for efficient EUV generation

5.1

Dependence of EUV-CEs on laser pulse duration

Optical depth of a produced Sn plasma is a key parameter to obtain efficient EUV light [4]. The optical depth can be controlled by changing the laser pulse duration. We investigated dependence of optical depth on the laser pulse duration. Pulse duration, which makes the optical depth unity, is calculated to be 3.7 ns at 1 x 1011 W/cm2 of 1.064 µm laser [16]. Experiments were carried out using a Q-switched Nd:YAG laser of 1.064 μm in wavelength. Pulse duration was changed from 2 to 9 ns using a pockels cell pulse slicer, and from 1 to 2 ns using a stimulated-Brillouinscattering pulse compressor. The laser was focused onto Sn plates with an F/30 lens from the target normal direction. Spot size was changed from 300 to 900 μm to obtain laser intensity in the range from 1 x 1010 to 1 x 1012 W/cm2. A 100-nm thick Sn layer coated on a plastic plate was used as a target to minimize influence of oxidation layer formed at the target surface on EUV conversion. Absolute 13.5 nm light energy was measured with the E-mon installed at 45 deg. with respect to the target normal. The spectral response of the E-MON, the measured spectral shape and measured angular distribution of the EUV emission were taken into account for the CE evaluation. Figure 5 shows dependence of EUV CEs on the incident laser intensities for various pulse durations. The optimum laser intensities are in the range from 5.0 x 1010 W/cm2 to 1.0 x 1011 W/cm2 for all the pulse durations. The maximum CE of 2.2 % was attained with the pulse duration of 2.3 ns at 5.0 x 1010 W/cm2. The CEs increase with shortening laser pulse duration for longer than 2.3 ns, however, the peak CE which obtained with 1.2 ns pulse is lower than that with 2.3 ns pulse. This result implies that the optimum pulse duration is determined not only by the optical depth but also by a fraction of laser energy absorbed in the EUV-EDR. The fraction of laser energy absorbed in the EDR were calculated to be, respectively, 25, 42, 73 and 85 % in 1.2, 2.3, 5.6 and 8.5 ns pulse produced plasmas. Therefore , for shorter pulse produced plasma, incident laser energy is not directly ab-

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sorbed in the EDR, but in higher dense region. Optimum laser pulse should have enough duration to absorb sufficient laser energy in the EDR.

Fig. 5 Dependence of EUV-CEs on laser pulse duration.

5.2

Low-density porous target for efficient EUV generation

The other method to change plasma properties is the use of low density porous target [17]. Experiments were carried out using a Q-switched Nd:YAG laser (1.064 m in wavelength and 10 ns in pulse duration) focused with an F/30 lens at the target normal. The focal spot size was optically measured to be 500 µm, and was unchanged within this experiment. Three kinds of planar targets were used. The first target is a solid-density Sn foil, whose initial density is 7.28 g/cm3. The second and third ones are low-density SnO2 foils, whose initial densities are respectively 23 % (1.62 g/cm3) and 7 % (0.49 g/cm3) of the solid SnO2 density. The low-density targets were fabricated using monodispersed polystyrene nanoparticles and liquid Sn chloride [18]. After calcination process of the chloride, the lowdensity SnO2 targets have porous structures whose cell size is about 1 µm. Dependence of the EUV-CEs on the laser intensity is shown in Fig. 6. In the case of the solid-density targets, the EUV-CEs depend weakly on the laser intensity, and almost constant CE of 1.2 % is obtained. On the other hand, the EUV-CEs from the low-density targets show relatively strong dependence on the laser intensity, this trend is similar to those for the shorter laser pulse (1.2 ns and 2.2 ns) produced -- optically thinner -- Sn plasmas. The highest CE of 2.2 % was obtained at the optimum intensity of 5 x 1010 W/cm2 for the 7% low-density SnO2 targets. The peak CE for

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the 7 % low-density SnO2 targets is 1.7 times higher than that for the soliddensity Sn targets.

Fig. 6 Dependence of EUV-CEs on initial target density.

Acknowledgement This work was performed under the auspices of a Leading Project promoted by MEXT (Japanese Ministry of Education, Culture, Sports, Science and Technology).

References [1] Silfvast W. T. et al., Appl. Opt. 32, 6895 (1993). [2] Jin F. et al., Appl. Opt. 34, 5750 1994); Spitzer R. C. et al., J. Appl. Phys. 79, 2251 (1996); Shimoura A. et al., Appl. Phys. Lett. 75, 2026 (1999); Choi I. W. et al., J. Opt. Soc. Am. B 17, 1616 (2000); Aota T. et al., Phys. Rev. Lett. 94, 015004 (2005). [3] Nishihara K. et al., in “EUV sources for Lithography” (SPIE, Bellingham, WA, 2006), Vol. PM149, Chap. 11, p. 339. [4] Fujioka S. et al., Phys. Rev. Lett. 95 235004 (2005). [5] Eidmann K. et al., Phys. Rev. E 52, 6703 (1995). [6] Yamanaka C. et al., IEEE J. Quantum Electron. 17, 1639 (1981). [7] Takabe H. et al., Phys. Fluids 31, 2884 (1988).

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[8] Bar-Shalom A. et al., Phys. Rev. E 56, R70 (1997). [9] Svendsen W. et al., Phys. Rev. A 50, 3710 (1994). [10] Tanuma H. et al., Nucl. Instrum. Meth. Phys. Res. B 235, 331 (2005). [11] Tao Y. et al., Rev. Sci. Instrum. 75, 5173 (2004). [12] Tao Y. et al., Appl. Phys. Lett. 87, 241502 (2005). [13] Tao Y. et al., Appl. Phys. Lett. 86, 201501 (2005). [14] Shimada Y. et al., Appl. Phys. Lett. 86, 051501 (2005). [15] Sunaharra A. et al., “Proceedings of the 3rd International EUVL Symposium”, Miyazaki, Japan, 2004. [16] Ando T. et al., to be published in Appl. Phys. Lett. [17] Okuno T. et al., Appl. Phys. Lett. 88, 161501 (2006). [18] Gu Q. et al., Chem. Mater. 17, 1115 (2005).

Laser Physics Research Relevant to Laser-Electron X-Ray Generator A.V. Vinogradov, M.V. Gorbunkov, Yu.Ya. Maslova and Yu.V. Shabalin P.N. Lebedev Physical Institute, Moscow, Russia Summary. A prototype of laser unit for Laser Electron X-Ray Generator is constructed on the basis of the optoelectronic control. The laser system in which an optoelectronic negative feedback is realized by means of a signal reflected from an intracavity Pockels cell polarizer is proposed and tested. The design provides flexible control over pulse train time structure.

1 Introduction Laser produced plasma proved to be a convenient and flexible source of incoherent and coherent soft X-rays probably including water window in the near future [1]. However the scaling of laboratory X-ray lasers and laser plasma X-ray sources to photon energies higher than 5 keV is questionable. Laser plasma based hard X-rays sources are still uncompetitive with conventional X-ray tubes, synchrotrons and free electron lasers. Meanwhile a dramatic (several orders of magnitude) gap exists between Xray tubes and accelerator based X-rays sources in respect of average power, brightness, sizes, cost, monochromaticity, tunability etc. The filling in of this gap would be beneficial for various scientific and commercial applications. In other words a new X-ray source that could bring together the compactness of X-ray tubes and X-ray beam manipulation ability of synchrotron radiation (SR) beamlines without the substantial rise of cost and loss of average power is highly desirable. The applications are biological and medical imaging, material structure and chemical analysis, protein crystallography, microscopy and microtomography for life sciences, medical diagnostics, industrial online X-ray inspection, security and custom control in ports and border terminals. A promising candidate to fill in the gap between conventional and SR sources is laser-electron X-ray generator (LEXG) based on Thomson scattering [2]. The idea to use Thomson scattering of laser radiation by relativistic electrons to extend the output energy spectrum down to hard X-ray of several tens keV range was n [3] and attracted last decade several research groups [4-12]

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Pulse picker

. Fig. 1. The near analogue of the LEXG laser system [13].

A project of LEXG developed jointly by Moscow State University and proposed in Institute of Quantum Radiophysics of Lebedev Physical Institute is aimed at the system containing pulsed synchrotron and a repetitive picosecond laser [11, 12]. Electron bunch is circulating in a storage ring and appears in the interaction chamber (IC) with the period 10-20 ns. Original laser beam time structure is a millisecond train of pulses separated by microsecond-scale interval. Thanks to multiplication in optical circulator the period of laser signal is transformed from microsecond-scale interval into 10-20 ns inside the IC that provides the most efficient coupling of laser and electron beams. Since the microsecond interval is far above a master oscillator’s resonator round-trip (generally about 10 ns), one has to use pulse picking by means of an electrooptical modulator (see Fig. 1). A well-known method to obtain highly stable trains of picosecond pulses is to apply a system of feedback loops, which proved to be efficient in hundred microsecond range [14, 15]. Furthermore, feedbacks allow not only to stabilize the pulse amplitude, but also to obtain regular pulsations with controlled period far exceeding a resonator round trip time Tr [16]. In this case a laser radiation looks like microgroups of picosecond pulses separated by microsecond interval. It is important to note that such mode has an attractive advantage. In fact, after single pulses at 0.5 MHz are picked from a train of pulses at 100 MHz, only 0.5% of average power is utilized. The mode of regular pulsations with 2-microsecond (0.5 MHz) period is

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more favorable, since it provides increase in intensity for the pulses picked in pulsation peaks.

2 Two Feedback Loops-Controlled Laser To investigate the dynamics of a picosecond laser controlled by feedbacks we use the approach describing a mode-locked laser as an object with discontinuous control [16, 17]. In the simplest case of system with one negative feedback (NFB) loop delayed by a resonator round trip the control can be described by means of the so-called logistic mapping

xn +1 = rxn (1 − xn )

(1)

where xn stands for a normalized energy at the n-th pass (a pass corresponds to a laser cavity round trip), r is an overall gain including active medium gain and passive losses, and the term in brackets represents the one-pass delayed feedback loop action. The maximum acceptable gain for steady operation is rmax = 3 [16]. When r exceeds the threshold value rmax, the logistic mapping demonstrates a well-known nonlinear dynamics [18].

Fig. 2. Calculated log of pulsation period T(rmax) over relative feedback sensitivity: curves are in close agreement in the region of negative argument. The upper curve is an approximation.

Another dynamics can be observed in a system controlled by two feedback loops (delayed by one and two round trips) described by the equation

xn +1 = rxn (1 − α xn − xn −1 )

(2)

where α is relative feedback sensitivity, its negative value denotes that feedback loop delayed by a resonator round trip is positive (PFB). The

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analysis shows that if −1 < α < 1 a nonlinear dynamics displayed by (2) differs fundamentally from that of the logistic mapping (1): regular pulsation with period above three round-trips appears. The pulsation period T (rmax) at r = rmax (α) calculated by means of the mapping stationary point stability analysis and the approach based on differential equations (approximation) is presented in Fig. 2. For negative α (i.e. positive and negative feedback combination control) at r = rmax (α) the pulsation is harmonic and the period can be expressed as

T ( rmax (α ) ) =

2π α +1

(3)

Formula (3) implies that regular dynamics with large periods (tens and hundreds of round-trips) can be observed at α close to - 1 (see Fig. 2).

3 Optoelectronic Feedback Designed for Pulsation Mode The above discussion showed that pulsations with period far exceeding a resonator round trip time are expected in a laser controlled by a combination of feedbacks where a negative feedback loop is delayed by one resonator round trip with regard to the positive one. With this aim in mind we designed a laser system in which an optoelectronic negative feedback is realized by means of a signal reflected from an intracavity Pockels cell polarizer. Self-mode-locking [19] in the negative feedback-controlled laser is a known technique for stable ultrashort pulses generation. The laser modelocked by a fast time-shifted negative optoelectronic feedback loop [20] is a very simple and reliable source of light pulses with about hundred picosecond duration. In such a laser the losses caused by an intracavity Pockels cell look like a periodic asymmetric "saw" with a long front and short tail. The tail is forming due to fast charge of the Pockels cell capacity by photocurrent generated in optoelectronic element under ultrashort light pulse. The long front is formed by slow discharge of intracavity cell capacity through the control system resistor. Stable self-mode-locking occurs with temporal delay in feedback control system corresponding to light pulse passage through the Pockels cell at the moment of low intracavity losses. Discharge time should be [20, 21] about several cavity round trip time Tr. Optimal delay for short pulse generation is approximately Tr. Usually the optical control signal is taken at the moment after passage of intracavity Pockels cell polarizer. The control proved to be efficient in laser output stabilization [16, 17].

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The laser dynamics changes dramatically if an optoelectronic feedback is realized by means of a signal reflected from an intracavity Pockels cell polarizer. The diagram of discontinuous control in the laser is shown in Fig. 3. When the laser pulse length varies slightly from pass to pass, the (n+1)-th pulse energy in the cavity En+1 is related to En as En +1 = En G 2 RPn , where G is a gain in a round-trip and R is an output mirror reflectivity (see Fig. 3). Similarly to [5], we use the Pockels cell transmission Pn = P0 (1 − Bn ) where Bn is control signal, and P0 is the initial Pockels cell transmission when feedback is off. In the proposed laser design Bn is the difference between incident light flux on the polarizer and transmitted flux. G2REn-1 - En NFB

Output mirror, R

→G2REn-1

→En

Polarizer, P

Gain medium, G

Fig. 3. The diagram of discontinuous control in a laser with NFB: the control signal is getting from Pockels cell polarizer.

As a result for the recurrence relation we have

(

En +1 = EnG 2 RP0 1 − ( En −1G 2 R − En ) Using r = G 2 RP0 and En = xn

)

(4)

P0 leads to r

P ⎞ ⎛ xn +1 = xn r ⎜1 − xn −1 + 0 xn ⎟ r ⎠ ⎝

(5)

Applying (3) and taking into account the Pockels cell transmission

⎛ U π⎞ P (U ) = cos 2 ⎜ ⎜ U λ 2 2 ⎟⎟ ⎝ ⎠

(6)

where U is a static bias voltage and U λ 2 is a cell half-wave voltage, we estimate the nonlinear dynamics development threshold gain rmax(U) and oscillation period T(U) in two limits.

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When U is far less than U λ 2

T (U ) = 2

2π U λ 2 U

, rmax (U ) = 1 +

π2 ⎛ U ⎞

2

⎜ ⎟ 4 ⎜⎝ U λ 2 ⎟⎠

When U → U λ 2 , T (U ) → 2π , rmax (U ) → 2 . Thus, we conclude that in the laser system controlled by optoelectronic NFB with the control signal getting from the Pockels cell a large period regular pulsation can be obtained. The period increases and the nonlinear dynamics development threshold decreases when the Pockels cell bias voltage U decrease.

4 Laser Dynamics Simulation Results To complete our demonstration of the laser, where the optoelectronic control signal is taken from an intracavity Pockels cell polarizer, however, we still have to show that the regime of pulsations can be reproduced qualitatively by extending the mapping (4) to take into account the laser output radiation fine time structure evolution as well as Pockels cell voltage variation at the time scale of Tr depending on the feedback delay time, Pockels cell capacity discharge time, active medium gain, and the cell bias voltage Ust following the same approach as in our previous works [16,21] The goal is to investigate self mode locking in pulsation regime with corresponding significant control voltage and time-dependent Pockels cell transmission variation. The main question was about the possibility to obtain a single short pulse circulating in a laser cavity. In the numerical simulation spontaneous emission noise was placed in the laser cavity and subsequently transformed by time-dependent transmission P(t) of the Pockels cell. On the other hand P(t) is calculated from the feedback signal proportional to the laser intensity I(t) reflected from the intracavity polarizer. The simulation proved that the discussed laser system allows not only to obtain stable mode-locking in quasi CW mode, but also to generate short pulses microgroups with controlled period far exceeding a resonator round trip time. To show gain sensitivity of microgroup envelope, the trains at gain r = 1.03 and 1.09 are shown in Fig. 4 (in both cases Ust = 0.05 U λ 2 ).

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a

b

Fig. 4. Simulated trains: r = 1.03 (a) and 1.09 (b).

Experiment The experiments were performed using a flash-lamp pumped Nd:YAG laser (∅6.3×60 mm rod was used). A PC-controlled laser pumping based on the incomplete discharge of large capacity allowed us to vary pump duration

Fig. 5. Millisecond lamp pumped YAG-Nd laser designed for mcs scale pulsations. AM active laser medium; M1, M2 cavity mirrors; P polarizer; IA iris aperture; MT – mirror telescope; Pockels cell DKDP electrooptical crystal ; CC feedback control circuits.

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up to 3.9 milliseconds. Laser cavity was made by flat wedge-shaped reflectors of 0.98 and 0.35 reflection coefficient respectively. We introduced an intracavity mirror telescope 3:1 to enlarge a laser mode volume in the active media and thus to raise the laser output. Total cavity length was 150 cm. Iris aperture was used for mode selection. Two-pass Pockels cell was based on a multilayer polarizer (Brewster angle) and 8×8×11 mm3 DKDP a

b

Fig. 6. Traces for a lasing power (a) and a pump lamp running (b), discharge time is 3,9 ms obtained with C8-14 scope; time scale 0.5 ms/div.

(Uλ/2= 3.9 kV) crystal with antireflection faces placed close to the laser mirror. Crystal was installed directly on the control circuit plate. Static bias voltage Ust applied to the Pockels cell was varied in a range 0÷2 kV. A high voltage silicon mesa-structure was used as a control element of an optoelectronic system. Discharge time of intracavity Pockels cell ca pacity was set to 20 ns (2Tr). The control signal was taken from an intracavity Pockels cell polarizer (Fig. 5). Pin-diode and C8-14 storage (low resolution) and digital TDS-3052 (5 GS/s, 500 MHz) oscilloscopes were used for laser emission registration. Control voltage vs time was registered by using of specially made HF voltage divider and fast oscilloscope C7-19 (5 GHz frequency bond). Fine time structure of the laser light was investigated using streak-camera AGAT SF-3M (time resolution < 2 ps) synchronized with laser pulses with specially-made electronic delay system. Pumping pulse shape is shown in Fig. 6, b. Setting an optimal diameter of intracavity iris aperture we obtained a picosecond pulse train of stable amplitude with total number of pulses up to 350000 (Fig. 6, а). By varying Ust and fine angular DKPD crystal tuning we obtained modes of regular pulsations having periods 0.5, 1, 1.3, and 2 microseconds. The experiments showed that despite of significant control

Laser Physics Research Relevant to Laser-Electron X-Ray Generator Fine time structure, 50 ns/div.

gain increase

Pulsations, 2 mcs/div.

627

Overview trace, 0.5 ms/div.

Fig. 7. The development of regular microsecond pulsations and a microgroup fine time structure in millisecond laser. Pulsation period is 200 round trips (2 mcs). The dynamics is shown in three time scales: millisecond, microsecond and nanosecond.

voltage and corresponding time-dependent Pockels cell transmission variation a single pulse is circulating in the laser cavity for all modes. An example of 2 microsecond period pulsation development is shown in Fig. 7. Millisecond oscilloscope traces (see Fig. 8) show that the peak pulsation power (feedback is on) is several times higher than a steady-state power level in free-running lasing (feedback is off, all other conditions being equal).

a

b

Fig. 8. Overview oscilloscope traces: a – feedback is switched off, b – feedback is switched on (time scale 0.5 ms/div). Vertical scales are equal.

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We are grateful to N. A. Borisevich, V. G. Tunkin and V. A. Petukhov for fruitful discussions and to A. M. Chekmarev for help in work. The work was partially supported by the Program of Fundamental Research of RAS, subprogram “Laser systems” and RFBR grant 05-02-17448a.

References 1. R. Toth, J.C. Kieffer, A. Krol, et al.: 'Phase contrast micro-CT with an ultrafast laser-based hard x-ray source', Proc. SPIE, p. 591813-1 – 591813-8, 2005. 2. P. Sprangle, A. Ting, E. Esarey, and A. Fisher: 'Tunable, short pulse hard xrays from a compact laser synchrotron source', J. Appl. Phys. 72, p. 5032, 1992. 3. A. Luccio and A.B. Brik: 'Methods and Apparatus for Producing X-rays', US Patent 4,598,415 July 1 1986, European Patent 0,05032 24.08.1988. 4. Z. Huang and R.D. Ruth: 'Laser-Electron Storage Ring', Rhys. Rev. Letters, Vol. 80, No. 5, p. 976, 1998. 5. R.J. Loewen: SLAC-R-632, June 2003, Ph.D. thesis, Stanford University, Stanford CA. 6. A. Agafonov, V. Androsov, J.I.M. Botman et al.: 'Status of Kharkov x-ray generator NESTOR', Proc. SPIE, 5917, p. 97, 2005. 7. F.E. Carroll: 'Tunable Monochromatic X Rays: A New Paradigm in Medicine', AJR 179, p. 583, 2002. 8. W.J. Brown, S.G. Anderson, S.P.J. Barty et al.: 'Experimental characterization of an ultrafast Thomson scattering x-ray source with three-dimensional time and frequency-domain analysis', Physical Review Special Topics – Accelerators and Beams, 7, 060702, p. 1, 2004. 9. K. Dobashi, A. Fukasawa, M. Uesaka et al.: 'Design of Compact Monochromatic Tunable Hard X-Ray Source Based on X-band Linac', Japanese Journal of Applied Physics, Vol. 44, No.4A, p. 1999, 2005. 10. T. Yanagida, T. Nakajyo, S. Ito et al.: 'Development of high-brightness hard x-ray source by Laser-Compton scattering', Proc. SPIE, Vol. 5918, p. 231, 2005. 11. M.V. Gorbunkov, V.G. Tunkin, E.G. Bessonov et al.: 'Proposal of a Compact Repetitive Dichromatic X-ray Generator with Millisecond Duty Cycle for Medical Applications', Proc. SPIE, 5919, OU1-OU6, 2005. 12. I.A. Artyukov, E.G. Bessonov, A.V. Vinogradov et al.: 'Laser-electron X-ray Generator', Preprint INP MSU 2006-7/806. 13. S. Schreiber, I. Will, D. Sertore et al.: 'Running experience with the laser system for the RF gun based injector at the TESLA Test Facility linac', Nuclear Instruments and Methods in Physics Research A 445, 427-431, 2000. 14. M.V. Gorbunkov, Yu.Ya. Maslova, A.M. Chekmarev et al.: 'Pulse generation of a large number of picosecond pulses microtrains in Nd:YAG laser controlled by negative feedback loop', Proc. of MIPT, Moscow, p. 50, 2005.

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15. M.V. Gorbunkov, A.V. Konyashkin, P.V. Kostryukov et al. 'Pulsed-diodepumped, all-solid-state, electro-optically controlled picosecond Nd:YAG lasers', RUS Quantum Electronics 35 (1), p.2, 2005. 16. I.M. Bayanov, V.M. Gordienko, M.G. Zvereva, S.A. Magnitski, A.P. Tarasevich. A High-Stable Negative-Feedback Picosecond YAG:Nd3+ Laser. RUS Quantum Electronics, 16 (8), p. 1545, 1989. 17. M.V. Gorbunkov, Yu.V. Shabalin: 'Two-Loop Feedback Controlled Laser: New Possibilities For Ultrashort Pulses Generation And High-Level Stabilization', Proc. SPIE, Vol. 4751, p. 463, 2002. 18. H.G. Schuster: Deterministic Chaos. An Introduction, Physik-Verlag, Weinheim, 1984. 19. V.K. Makukha, V.M. Semibalamut, V.S. Smirnov: 'Simulated Emission of Ultrashort Pulses from a Negative Feedback Laser', Sov. Quantum Electronics 4, No.5, p.1023-1027, 1977. 20. D.B. Vorchik, M.V. Gorbunkov: 'Self Mode-Locked Nd-YAG Laser Under Fast Delayed Negative Feedback by Means of High-Voltage Assemblies of Inversely-Shifted Silicon p-n Junctions', Physical Foundations of Electronic Laser Engineering, Proceedings of MIPT, Moscow, p. 4 - 11, 1995. 21. M.V. Gorbunkov, Yu.V. Shabalin: 'Picosecond YAG:Nd3+ Laser with SelfExcitation of HF Oscillations in Optoelectronic Negative Feedback System', Bulletin of the LPI 8, p.38-50, 1998

Laser Electron Generator of the X-Ray Radiation I. A. Artyukov, E. G. Bessonov, A. V. Vinogradov, M. V. Gorbunkov, Yu. Ya. Maslova, N. L. Popov, A. A. Postnov, Yu. A. Uspenski, R. M. Feshchenko and Yu.V. Shabalin P.N. Lebedev Physical Institute of RAS 19991 53 Leninski Pr, Moscow, Russia

Yu. L. Slovokhotov and Ya.V. Zubavichus Institute of elemental organic compounds of RAS, 119991 28 Vavilov st, Moscow, Russia

B.S. Ishanov, A.V. Poseryaev and V.I. Shvedunov Institute of Nuclear Physics of MSU

P. V. Kostrukov and V. G. Tunkin International Laser Center of MSU

Summary. The possibility of the creation and the application prospects of the laser-electron X-ray generator based on the Thompson scattering of the laser radiation on a bunch of relativistic electrons are considered. Such a generator fills the existing gap between X-ray tubes and synchrotron sources, which is several orders of magnitude in terms of the brightness, average intensity, size and also in the construction and exploitation costs. The layout of beam-lines and experimental stations intended for the applications of the X-ray laser-electron generator to the investigation of the elemental composition and material structure and biological objects is discussed.

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1 Introduction The development of the technologies connected to the generation and utilization of the X-ray radiation is an important part of the scientific and technical progress in lots of fields of the industry including metallurgy, chemical and pharmaceutical industry and also in such areas of the human experience as medicine, whole agricultural and food trade, ecological monitoring, social security, work of the custom and boarder terminals etc. For the introduction of many scientific developments in areas the investigators need constant access to X-ray sources. The modern generators of X-radiation can be divided into two main classes. X-ray tubes (with a fixed or rotating anode) and boosters of electrons: synchrotrons and storage rings. The X-ray tubes are used in overwhelming majority of production devices and apparatuses. The tubes with a fixed anode are reliable enough, compact, and simple to service and rather inexpensive - from hundreds up to several thousand dollars. The modern tubes with a rotated anode give in 10-100 times higher emission power, however they cost tens and hundred thousand dollars and is much more complex in exploitation. Common faults of this class of X-ray sources are absence of directivity of X-ray radiation, broad and, at a given material of the anode practically not variable spectrum, rather a small emission power and impossibility of generating bright monochromatic xray radiation. As compared to X-ray tubes, synchrotron accelerators and the storage rings are large power-intensive research installations with a closed path of the electron beam of tens and hundreds meters length. All over the world there are about hundred accelerators intended for deriving of X-ray synchrotron radiation (SR). This radiation has high luminosity, directedness and wide spectrum, with possibility of obtaining tunable monochromatic radiation. However size and cost - tens and hundred millions USD – of the modern synchrotron sources seriously restrict their applications, which do not satisfy the needs of the science and practice. Thus, now there is objective need for a new source of X-rays, which would fill in the gap existing between X-ray tubes and synchrotron centers. An X-ray source adequate to the formulated requirements, can be built on the basis of complex systems, which combine a compact high-current electron accelerator and laser emitting intensive light pulses. X-rays are in this case generated at head on collision of electronic and laser bunches; in other words, the photons of high energies bear as a result of diversion of the electron beam from the linear trajectory in the field of an intensive light wave. The relevant elementary process is well investigated and wears a title Thomson or Compton scattering (depending on quantity of parameter

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EħωL/(mc2)2, determining the size of the quantum contributions, E - energy of an electron, ħωL - energy of the laser photon). From the end of 70th years of XX century the Compton scattering on bunches of relativistic electrons serves as an effective method of deriving γ - photons (down to energies ~ 2 GeV), used in photonuclear reactions. However in generation of photons of lower energies (~ 10 - 100 keV), which have the greatest interest for the applications, the X-ray tubes and synchrotron radiation until recently remained beyond the competition. Now new active solid-state mediums using pumping by laser diodes, diode bars and matrixes, allow to generate and enhance trains of picosecond light pulses in compact devices and with a high efficiency. On the other hand, the modern electron accelerators allow to generate bunches with high luminosity, which can be focused in a spot with the size about 10 microns, and the modern accelerating structures can supply rate of acceleration up to 50 MeV/m, that allows to build installations of the small sizes. The integration of lasers and accelerators in one device enables to create rather a cheap compact source of intensive X-rays for the scientific and applied purposes.

2 Thompson scattering by relativistic electrons The research on deriving gamma and X-rays by the scattering of laser pulses on relativistic electrons has been carried on for more than 40 years [1-7]. In this section we shall give an estimate of intensity and luminosity of the laser-electronic generator and compare it by the last parameter to Xray tubes and sources of SR. For the electrons with energies Ee = γmc2 ~ 25 – 50 MeV and laser photons ħωL ≤ 2 eV, which provide X-ray generation in the range 5-50 kev interesting for us, the inequality holds:

2γ hω L << mc 2

(1)

where γ = Ee/mec2 – is the relativistic factor. It allows viewing collision of electrons with laser photons as the classical Thomson scattering. Complete number of X-ray photons generated at interaction point of a single laser pulse with the electron bunch in this case equals 2

8π ⎛ e 2 ⎞ ⎜ 2 ⎟ = 6,6 ∗ 10 −25 cm 2 n= N L Ne , σ T = s 3 ⎝ mc ⎠ σT

(2)

where σT - Thompson cross-section, NL, Ne –complete number of photons in the laser pulse and number of electrons in the bunch, respectively. In formula (2) it is supposed, that the electron and photon bunches have

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Gaussian transversal distribution with identical rms values. s = 2sL,e =4πσL,e2 ; σL=σe. The energy of the X-ray photon ħω is connected to the laser photon energy ħωL and scattering angle θ with a formula

4γ 2 hω = hω L 2 1 + (γθ )

(3)

It is obvious now, that X-rays of the laser-electron generator are spread in a narrow solid angle ~ 1/γ2 rad2 in the direction of the electron movement. In the proposed source the electron bunches from a linac with frequency f=30-50 Hz are inserted into the storage ring. With the same frequency f=30-50 Hz the laser generates trains of pulses, which are guided to the optical circulator. The X-rays are generated in the interaction chamber at the point, where the density of the laser and electron beams peaks. The average flux of X-ray photons is

Φ = fN , N = nnL nc =

σT s

N L N e n L nc

(4)

where N – number of X-ray photons generated by one laser train, n – number of photons (2), generated during a single encounter of a laser micropulse with the electron bunch, nL – number of laser micropulses in the train, nc –number of circulations in optical recirculator. Obviously nc≈ ns , where ns – number of circulations of the electron bunch in the storage ring.

3 Intensity and brightness of the laser-electron generator To estimate the intensity we shall begin from the laser-electron generator, which design is given in [7] (see Fig.1). Features of this plan are small radius of the ring R0 =0.5 m and use of a quasicontinuous laser of low power PL = 10 W together with a high finesse cavity. In particular [7] authors in (4) supposed nL=1, nc=104, while the experimentally affirmed energy amplification of ultrashort pulses in a passive resonator doesn’t exceed nc ≤ 102 [13]. The basic parameters including intensity of the X-ray beam are given in Table 1. Other scheme of the laser-electron generator is considered in [14] (see Fig. 2) in connection to the problems of angiography. In this case source’s power should provide the exposure of the order of several ms with frequency ~30 Hz. For this purpose the pulse-periodic picosecond laser [14, 15] controlled by optoelectronic feedbacks and having a special time struc-

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ture has been developed: duration of the train is 2 ms, number of pulses in the train nL=103, frequency of consecutive trains – 30 Hz. Table 1 E

ħωL

Ee

σe=σL

keV

eV

MeV

µm

12

1.16

25

30

Ne

6⋅10

NL 9

(1 nC)

6⋅10

11

f , nL

PL,, nc

Φ

MHz

W

THz

90 / 1

10 /10

4

19

(0.11 µJ)

The reference lifetime of the laser radiation in a high finesse optical circulator exceeds two orders i.e. it’s quite realistically to accept nc=102. Radius of the storage ring R0 ≈ 0.5 – 1 m is almost the same as in the previous case. The basic parameters of the source [16, 14] are presented in Table 2. In the scheme of Fig. 2 the second laser with a close wavelength is also stipulated, which enables to produce a dichromatic X-ray beam for noninvasive difference angiography.

Fig. 1. Design of a laser-electron generator.

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Table 2 E

ħωL

Ee

keV

eV

MeV

33

1.16

43

σe=σL

Ne

NL

f , nL

PL,, nc

THz

µm 30

Φ

9

6⋅10

(1nC)

2.7⋅10

16

(5 µJ)

30 Hz,

150 W

3

2

nL=10

nc=10

2.8

The beam brightness Bω is determined by a differential flux dΦ(θ,ϕ)/dΩdω, which is in turn connected to the total (integrated by the spatial angle and frequencies) flux as follows:

Φ = ∫ d Φ (θ , ϕ , ω ) = ∫

dΦ (θ , ϕ , ω ) dΩdω dΩdω

(5)

By definition of the brightness:

Bω (θ ,ϕ ,ω ) =

10 −6 dΦ(θ ,ϕ ,ω )⎪dω =10 s (мм 2 ) ∫

−3

ω

⎡ ⎤ ph , ⎢ 2⎥ 2 ⎣ s mm (mrad ) ⎦ (6)

where in the denominator there is the source area s=2πσe2 in mm2, and the integration is limited by the frequency interval dω=10-3ω. To utilize formula (6) one should express the differential flux of the Thompson laserelectron generator (4) in terms of Thompson differential cross-section:

dΦ = dΩδ (ω − ω (θ ))dω

dσ T fN e N L nL ni dΩ s

dσ T 3 1 + (γθ ) = σ Tγ 2 , dΩ 2π (1 + γ 2θ 2 )4

(7)

4

(8)

where ω(θ) is defined in (3). The presence of δ-function in (7) suggests the monochromaticity of the electron beam. Substituting (7) into (6) one obtains:

Bω (θ ) =

10 −6 dσ T fN e N L n L ni s (mm 2 ) dΩ s

Comparing (9) to (4) it is possible to derive that:

(9)

Laser Electron Generator of the X-Ray Radiation

Bω (θ ) =

10 −6 1 dσ T Φ s (mm 2 ) σ T dΩ

637

(10)

Using the formula (10) the brightness of the laser-electron generator can be determined in the direction of the electron beam motion. For that purpose one should suppose in (10) θ =0 and take into account (8):

Bω =

10 −6 3 2 1,2 ∗ 10 −7 ω γ Φ = Φ s (mm 2 ) 2π s (mm 2 ) ω L

(11)

where Φ - the total X-ray flux (4). It can be shown that the laser electron generator has the brightness by 6 to 7 orders of magnitude lower than the third generation SR sources, but exceeds the performance of the X-ray tubes by 4-5 orders.

4 Applications in spectroscopy and material sciences As it was mentioned above, laser-electron generators open the prospects of obtaining tunable by spectrum X-ray radiation in comparatively compact devices. They can be used for the independent investigations under the Xray beam intensity unachievable with X-ray tubes as well as for the development of methods of equipment testing and for the preparation of samples for the investigation in SR centers. On the other hand focusing and monochromatization of the radiation of laser-electron generator can be done by various methods developed and tested in the SR centers. One can notice that the distribution of the photons of the laser-electron generator beam by energy and angles has a number of special features, which enable to conduct some spectral measurements in the direct beam i.e. without any collimation and monochromatization devices [7, 18]. In this sense there is an analogy with the undulator radiation. The spectrum of the laser-electron generator with aid of (7) can be expressed as:

dEω = hωdΦ =

fN e N L nL ni dω 2 Σ T (ω ) , ωmax = 4γ ω L (12) ω max s

The spectral function ΣT(ω) is determined by angular integration (0<x<1) of (7):

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ω 3x , (13) 2x 2 − 2x + 1 , x = ω max 2

(

Σ T (ω ) = hω maxσ T xϕ ( x) = hω maxσ T

)

If the distribution of the electrons by energy isn’t monochromatic, the function ϕ(x) has a more complicated form than in (13), but the its integral remains equaled to 1. Beam dump KICK

e

INF

e

5; 35; 50 MeV LINAC

IP R>99.9%

X-rays

RFC

R>99.9% t T = 2 μs τ

< 40 ps

R>99.9% Pockels cell 1

P 1 R>99.9% Pockels cell 2

T c = 10 ns

1 ms

<1 ms

λ2

1.5-2 ms P2

λ1

τ

λ2

t

λ1

< 40 ps

T = 2 μs

T = 2 μs

Fig. 2. Idea of a laser-electron generator for angiography.

The maximum energies of X-ray photons correspond to K lines of copper (8 keV) and molybdenum (17.5 keV), which are widely used in applications. One can see that the spectrum has sharp short wavelength boundary and about half of the energy is located in the bandwidth δE/E ≈0.2. Two special features that distinguish it from the “white” SR spectrum are (1) its triangular shape: the intensity of radiation grows with the energy up to the threshold value E0=4γ2ħωL and than drops sharply; (2) relatively narrow continues interval of the photon energies (half-width ~1.5 keV at the threshold energy 8.03 keV and ~3 kev at the threshold energy 17.5 keV). However the intensity interval acceptable for the measurements 0.1I0−I0,

Laser Electron Generator of the X-Ray Radiation

6 2 1

639

5

3

4 Fig. 3 Block-schemes of the stations: (top) combined investigation of the samples with SAXS/WAXS/XAFS/XRF methods ( – sample, 1 – polychromatic X-ray beam, 2 – removable monochromators, 3 – monochromatic X-ray beam, 4 – 1Ddetector, 5 – vacuum chamber for the small angle scattering, 6 – 2D-detector SAXS, 7 – detector of the X-ray fluorescence, 8 – X-ray filter), (bottom) diffraction investigation of the materials and powders including protein crystallography ( – sample, 1 – polychromatic X-ray beam, 2 – removable monochromators, 3 – monochromatic or polychromatic X-ray beam, 4 – goniometer, 5 – 2D-detector, 6 – detector of the X-ray fluorescence; X-ray filter).

where I0 – the maximum intensity, is significantly wider: for the mentioned threshold values it corresponds to the intervals from 5 to 8 keV and from 9 to 17.5 keV. Another special feature of the laser-electron generator is its energy dispersion inside the angle 1/γ: The decrease of the photon energy in the interval where intensity changes from I0 до 0.1I0 corresponds to the change in the scattered angle θ from 0 to 1.2o. On the other hand the angular dispersion by the energy makes it possible to work in the direct beam i.e. to make monochromatic the radiation with use of a collimator without losses for the Bragg diffraction. So at the threshold value of the energy 17.5 keV at the distance 5 m from the source of the radiation the energy interval 12

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− 13 kev (30 – 35% from the maximum intensity I0) corresponds to the distance interval ~10 mm, which can contain several hundreds sensitive elements of a standard 1D detector. So a possibility exists to register EXAFS spectra in the direct beam and also for the development of new diffractometry methods with use of anomalous scattering and other nonstandard X-ray optical schemes. Taking into account on one hand the design of the source (only one quasi synchrotron beam-line or “bunch” of beam-lines with narrow energy bands), and on other hand – the high flexibility of the proposed system it seems reasonable to build a number (2-3) of the multifunctional exchangeable stations for the use with it. Such stations, which cover a set of the main methods, can be (Fig. 3): 1. A station for the combined investigation of the materials and biological samples with X-ray fluorescent analysis (XFA), small angle scattering (SAXS), X-ray scattering in the wide angular range (WAXS) and analysis of the fine structure of the X-ray absorption spectra (XAFS). 2. A station for the X-ray diffraction investigations of monocrystals (including protein ones) and powder samples with possibility to do experiments as using monochromatic radiation with the variable wavelength as by the Lauer method with the polychromatic beam. The first scheme (Fig 3 top), which is intended for the combined investigations of the wide range of materials having arbitrary degree of ordering, allows recording the multilevel information on the close order and elements of the remote order of the atom positions and also on ordering of the sample at the mesolevel (distribution of the nanoparticles by the diameter, the shape of protein globules etc). The second scheme (Fig. 3 bottom) is meant for the most widespread at this time methods of the structural investigations of monocrystals (including biopolymers), which suggests rotation of the sample in the X-ray goniometer. This scheme also enables registering precise diffractograms of the crystalline samples. The measurements without a monochromators in the first scheme allow in particular realizing the standard synchrotron methods of the X-ray fluorescent analysis with the white beam excitation and in the second one – Lauer diffractometry methods. In their design one should take into consideration the special features of the angular and spectral radiation distribution of the laser-electron generator (see above). The block schemes mentioned if necessary can be optimized for the dynamical measurements, which will use the temporal structure of the X-ray beam generated. This work was supported by the Section of Physics Sciences of Russian Academy of Science in the framework of the basic research program “Laser systems based on new active materials and optics of structured materi-

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als”. It was also supported under RFBR (Russian Foundation on Basic Research) grants # 05-02-17448a and 05-02-17162a.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

11. 12. 13. 14. 15.

16.

17.

F.R.Arutyunian, V.Tumanian, Phys.Letters 4 (1963), 176 R.H.Milburn. Phys. Rev. Letters, 10 (1963), 176 O.Kulikov et al. Phys. Rev., 138 (1964), 344. .F.Ginsburg, G.L.Kotkin, V.G.Serbo, V.Telnov, Nucl. Instr. and Meth., 205, 77 (1983) G.M.Gurevich, L.E.Lazareva, V.M.Mazur, et.al, Nucl. Phys. A 351 (1981), 257. C.Schaerf, “Polarized Gamma-Ray Beams”, Physics Today, pp. 44-50, Aug. 2005 R. J.Loewen SLAC-R-632, June 2003 (Ph.D.thesis, Stanford University, Stanford CA). A. Agafonov, V. Androsov, J.I.M. Botman, et.al, “Status of Kharkov x-ray generator NESTOR”, Proc. SPIE, 5917, pp.97-104, 2005 F.E.Carroll, “Tunable Monochromatic X Rays: A New Paradigm in Medicine”, AJR 179, pp 583-590, 2002 W. J. Brown, S. G. Anderson, C. P. J. Barty, et.al, “Experimental characterization of an ultrafast Thomson scattering x-ray source with three-dimensional time and frequency-domain analysis”, Physical Review Special Topics - Accelerators and Beams, 7, 060702, pp. 1 – 12, 2004 K. Dobashi, A.Fukasawa, M.Uesaka, et.al, “Design of Compact Monochromatic Tunable Hard X-Ray Source Based on X-band Linac”, Japanese Journal of Applied Physics, Vol. 44, No.4A , pp.1999-2005, 2005 T.Yanagida, T.Nakajyo, S.Ito, F.Sakai, “Development of high-brightness hard x-ray source by Laser-Compton scattering”, Proc. SPIE Vol. 5918, p. 231238, 2005 C. Gohle, T.Udem, M.Herrmann, et.al, “A frequency comb in the extreme ultraviolet„, Nature,436, 234-237, 2005 M.V. Gorbunkov, V.G.Tunkin, E.G. Bessonov, et.al, “Proposal of a Compact Repetitive Dichromatic X-ray Generator with Millisecond Duty Cycle for Medical Applications„ , Proc. SPIE, 5919, OU1-OU6, 2005 M.V. Gorbunkov, L.A.Fomin, Yu.V. Shabalin, “The effect of radiation stabilization and generation of the picosecond radiation of Nd -YAG lasers with use of nonlinear mirror based on STP crystal”, Cratkye Soobshenia po Fisike LPI, No 12, pp. 14-21, 2000 (in Russian). E.G. Bessonov, R.M. Fechtchenko, M.V. Gorbunkov, A.V. Vinogradov, “The Analysis of Laser Electron X-Ray Generator based on Thomson Scattering„, X-ray lasers 2004, Proc. of the 9th International Conference on X-Ray Lasers, Institute of Physics, Conference Series, #186, pp435-441, IOP, 2005 H.Winick, SLAC-PUB-777 1, March 1998

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18. T.Kaneyasu, M.Uesaka, K.Dobashi, M.Torikoshi, “Dual-energy x-ray CT by Compton scattering hard x-ray source”, Proc. of 2005 Particle Accelerator Conference.

Time-Resolved keV Emission Spectra from Hot, Dense Buried Layer K-Shell and L-Shell Targets J. Dunn, K. Widmann, R. Shepherd, R. Booth, K. B. Fournier, C. D. Eng and S. B. Hansen Lawrence Livermore National Laboratory, Livermore, CA 94551, USA

Summary. We report new time-resolved measurements for 50 nm thick Al and Ge buried layer targets. The top-coat thickness of carbon is varied between 0 and 100 nm. A single beam of the Compact Multipulse Terawatt (COMET) laser is frequency doubled, at 527 nm wavelength, up to 1 J energy in a 500 fs (FWHM) pulse and focused to a maximum of 7 × 1017 W cm-2 with an off-axis parabola. An RbAP (001) von Hamos curved crystal spectrometer with an 500 fs x-ray streak camera is fielded to measure the time history of the Al n = 2 – 1 K-shell emission and the Ge n = 3 – 2 L-shell emission in the 7 – 10 Å waveband. The main objective is to generate and study hot, Te ~100 – 200 eV, dense, ne ~ 1023 cm-3, thermal plasmas in tamped optically thin targets under a range of laser irradiance conditions. We observe short-lived emission lasting a few picoseconds and indications of cooler, denser plasmas with increasing thickness of the tamping carbon layers.

1 Introduction Buried layer targets heated by intense, short pulse laser beams have been reported as a way of creating and investigating hot, dense highly ionized matter [1 – 5]. The laser energy is absorbed within the top or ablator layer and energy, either by thermal or suprathermal electrons, is transported to heat the buried diagnostic layer. The ablator layer helps to tamp the plasma expansion and keeps the diagnostic layer at high density on time frames of several picoseconds. Additional higher Z layers buried more deeply can be used as K-α fluorescence markers to determine the presence of hot electrons [1]. L-shell emission conditions in near-LTE [2], K-shell line shifts attributed to the plasma polarization shift [3] as well as low Z high density plasmas measured by Stark-broadened n = 3 – 1 lines [4] have all utilized this technique in experiments heated by a 400 nm wavelength, 100 fs, high irradiance pulse. Experiments have also been carried out with 527 nm

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wavelength, 500 fs pulses to study K-shell lines and the effect of laser absorption and transport as a function of the laser beam polarization [5]. Time-resolved Bragg crystal x-ray spectroscopy is an essential diagnostic to measure the spectral line emission and determine the electron temperature, density and ionization in the buried layer when heated by subpicosecond pulses. We report recent time-resolved measurements with preliminary results of K-shell and L-shell buried layer spectra.

2 Experimental Description The experiments were conducted on the Compact Multipulse Terawatt (COMET) laser at the Lawrence Livermore National Laboratory. This is a chirped pulse amplification laser with a fundamental wavelength of 1054 nm and a repetition rate of 1 shot every 4 minutes. The final beam size was 4.2 cm diameter with up to 2.7 J laser energy in a 600 ps full width at half maximum (FWHM) stretched pulse. The pulse was compressed to 500 fs (FWHM) pulse then frequency doubled in a KDP crystal under vacuum. The maximum 1ω to 2ω conversion efficiency was 48%. Seven high reflectivity 45° angle of incidence dielectric mirrors for 527 nm wavelength delivered the beam to the target chamber and rejected the unconverted fundamental light. An off-axis parabola with 30 cm focal length focused the laser beam at an angle of incidence of 21.8° to the target. Maximum energy was ~900 mJ focused to a 23 × 12 µm2 focal spot. This gave an irradiance of 7 × 1017 W cm-2. The 1ω and 2 ω laser energy were monitored on every shot and a second order autocorrelator measured the laser pulse width. During an earlier experiment it was discovered that a pre- and postpulse 500 fs laser pulses with ~10% of the energy of the main pulse was present at ±28 ps. This was found to originate in the regenerative amplifier stage and was corrected before the buried layer targets were shot. Figure 1 shows the experimental arrangement. Not shown is a UVvisible grating spectrometer that viewed the plasma in the specular direction. This monitored the harmonic generation produced by collective plasma processes due to the interaction of the main pulse with any preformed plasma. Only the fundamental 527 nm spectral feature was observed and it was concluded that the laser intensity 5 – 10 ps before the peak of the pulse was less than 10-7. The main instrument was an RbAP (001), 2d = 26.121 Å, von Hamos curved crystal spectrometer, with two separate crystals of radius 2.5 and 3 cm, combined with a 500 fs resolution x-ray streak camera [6]. The 2.5 cm and 3 cm radius crystal viewed the target at 45° and 24°, respectively, from the target surface. The spectral

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coverage was continuous from approximately 7.3 to 8.4 Å and 8.3 to 9.6 Å, respectively. The photocathode consisted of a 400 µm thick Si substrate containing an etched slit 120 µm wide by 2.5 cm long. The slit was etched to leave a 40 nm Si3N4 layer and coated with 35 nm Au and 100 nm of CsI. The photocathode was pulsed and the x-ray generated photoelectrons were accelerated and then streaked by the sweep plates. A phosphor coated fiber optic converted the electron 2-dimensional image to optical photons and the signal was increased by an intensified microchannel plate detector. The output was recorded with a fiber-optic 1024 × 1024 pixels charge-coupled device (CCD) (pixel size 24 × 24 µm2) and digitized to 16-bit depth.

Fig. 1. Experimental setup showing von Hamos crystal spectrometer.

3 Experimental Results The targets consisted of silicon wafers coated with 50 nm of a buried diagnostic layer of either Al or Ge. A second layer of carbon varying from 0 – 100 nm was coated in order to tamp the diagnostic layer and minimize the direct interaction of the laser with the Al or Ge. Streaked x-ray spectra were recorded from both the Al and Ge targets for different carbon over-

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coat thicknesses and at different laser intensities. The two crystals produce simultaneous spectra separated by approximately 10 ps on the one streaked image. The target position could be adjusted to select one spectrum to minimize temporal interference between the two spectra. Figure 2(a) shows a streaked spectrum from the 2.5 cm radius crystal from the von Hamos spectrometer for a 50 nm aluminium target buried under 50 nm carbon and irradiated with 350 mJ of laser energy. The dispersed spectrum is sloped in time due to the increased path length the shorter wavelengths have to travel from the source to the streak camera entrance slit [6]. The strongest feature at 7.757 Å, labeled He-α, corresponds to the 1s2 – 1s2p He-like Al resonance line. The two weaker features to the long wavelength side of the He-α at 7.85 Å and 7.95 Å are various Li-like 1s2 2l – 1s2l2l’ transitions and Be-like 1s2 2l2 – 1s2l22l’, respectively [7]. The features are spectrally broad due to Stark effects at high densities in the buried layer and last a few picoseconds.

Fig. 2. (a) Streak camera image showing time-resolved Al n = 2 – 1 x-ray spectrum from 50 nm Al layer buried under 50 nm C. He-like resonance line at 7.757 Å is labeled together with Li-like and Be-like satellite lines at 7.85Å and 7.95Å, respectively. (b) Time history of three spectral features in (a).

Temporal lineouts are taken through the three main spectral features after the spectrum was corrected for the different path lengths and delays, Fig. 2(b). Time t = 0 was chosen as the start of the Al He-α line emission and also corresponds to the onset of the satellite lines. The Li-like and Belike lines turn on quickly and reach peak intensity at approximately +2 ps

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and +3 ps well before the He-like emission at +6 ps. A similar fast evolution of low ionization stages was observed for 100 fs heated thin foil targets [8]. The Be-like emission lasts the shortest time at 3 ps (FWHM) and has effectively terminated before the He-like emission reaches peak intensity. Both the Li-like and He-like emission last for 4 ps (FWHM). This is consistent with increasing electron temperature inside the buried layer and rapid heating that ionizes through to the He-like stage. The layer expands and rapidly cools during the recombination stage.

Fig. 3. (a) Streak camera image showing time-resolved Ge n = 3 – 2 x-ray spectrum from 50 nm Ge layer buried under 50 nm C. Ne-like 3d – 2p resonance lines at 8.93 and 9.11 Å are labeled. (b) Time history of Ne-like 3d – 2p in (a).

A 50 nm Ge layer buried under 50 nm carbon target, Fig. 3, was shot for similar 500 fs laser irradiance conditions to compare with the K-shell buried layer target in Fig. 2. In this case the spectrum was recorded with the 3 cm radius RbAP crystal to study the L-shell Ge n = 3 – 2 transitions at 9 Å. The streaked spectrum in Fig. 3 (a) is largely featureless except for a line identified as the 3d – 2p Ne-like at 8.931 Å. These lines as well as Na-like transitions become more evident under higher irradiance conditions, thinner carbon overcoats or when the laser pulse is stretched to 5 ps. Figure 3(b) is a lineout showing the time history of the Ne-like Ge 3d – 2p line at 8.93Å. The foot at -5 ps is due to low level x-rays from the 2.5 cm radius crystal illuminating the photocathode. The x-ray emission is observed to last for 10 ps (FWHM), approximately twice as long as the He-like Al emission, and is more symmetrical in shape. Simulations and further measurements will be reported in a future publication.

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4 Conclusions We have reported recent results of K-shell and L-shell spectral lines from buried layer spectroscopy experiments heated by a frequency-doubled, 500 fs laser pulse. The use of a 500 fs time resolution x-ray streak camera, precision layered targets and a well-characterized laser pulse is essential to create and measure the evolution of the hot, dense plasma. Ongoing hydrodynamic and atomic kinetics simulations will be compared with the experimental results and will be discussed in detail in the near future.

Acknowledgments The authors would like to thank J. Hunter, R. Van Maren, A. Niles and C. Cadwalader for their excellent technical assistance. Thanks to J. McKenney of Sandia National Laboratory for manufacturing and characterizing the buried layer targets. Work performed under the auspices of the US Department of Energy by the University of California Lawrence Livermore National Laboratory under Contract No. W-7405-Eng-48.

References 1. G.J. Tallents, M.H. Key, P.A. Norreys, D. Brown, J. Dunn and H.A. Baldis, Phys. Rev. A 40(5), 2857-9 (1989). 2. B. K. F. Young, B. G. Wilson, D. F. Price, and R. E. Stewart, Phys. Rev. E 58, 4929 – 4936 (1998). 3. A. Saemann, K. Eidmann, I. E. Golovkin, R. C. Mancini, E. Andersson, E. Förster, and K. Witte, Phys. Rev Lett. 82, 4843 (1999). 4. K.B. Fournier, B.K.F. Young, S.J. Moon, M.E. Foord, D.F. Price, R.L. Shepherd, and P.T. Springer, J. Quant. Spectrosc. Radiat. Transf. 71, 339 (2001). 5. F. Dorchies, P. Forget, P. Gallant, Z. Jiang, J. C. Kieffer, H. Pépin, and O. Peyrusse, Phys. Plasmas 8, 5239 – 5243 (2001). 6. R. Shepherd, P. Audebert, R. Booth, B. Young, J. Bonlie, D. Nelson, S. Shiromizu, D. Norman, J. Dunn, K. Widmann, and P. Springer, Rev. Sci. Instrum. 75(10), 3765 – 3767 (2004). 7. P. Audebert, J. P. Geindre, A. Rouse, F. Fallies, J. C. Gauthier, A. Mysyrowicz, G. Grillon, and A. Antonetti, J. Phys. B: At. Mol. Opt. Phys. 27, 3303 – 14 (1994). 8. P. Audebert, R. Shepherd, K. B. Fournier, O. Peyrusse, D. Price, R. Lee, P. Springer, J.-C. Gauthier, and L. Klein, Phys. Rev. Lett. 89, 265001-1 - 4 (2002)

Novel Attempts to Realize an Innershell X-Ray Laser in Na B. Wellegehausen1, T. Mocek2, S. Sebban3, B.H. Wellegehausen4, L. Koch1 and B. Rus2 1

Institut für Quantenoptik, Leibniz Universität Hannover Institute of Physics, PALS centre 3 Laboratoire d´Optique Applique´, ENSTA 4 Friedrich Schiller Universität Jena 2

Summary. A planned experiment to realize an innershell x-ray laser in atomic sodium by pumping with the Zn x-ray laser at 21.2 nm, presently operated at the PALS laser facility, is presented. According to model calculations, a gain of more than 60 cm-1 is expected for a sodium density of 1016 cm-3 and the given pump laser data.

1 Introduction One of the earliest proposed but so far not realized x-ray laser is based on innershell photoionization of atomic sodium [1]. In this scheme (Fig.1), an inner 2p electron of atomic sodium is ionized by x-rays, resulting in a population inversion on the 2p53s – 2p6 transition in Na+, with possible emission of radiation at 37.2 nm. The optimum pump wavelength for a preferential extraction of a 2p electron, instead of ionizing 2s or 3s electrons, is around 20 nm, as can be seen from the photoionization cross section (Fig.1). While longer wavelengths innershell-photoionization lasers have successfully been operated using incoherent x-rays from laser induced plasmas [2], such an attempt seems to be problematic in case of Na, due to the pump power requirements. Ideal would be to pump this scheme with an x-ray laser at about 20 nm. In the past, two experiments have been undertaken to realize this scheme by pumping with an x-ray laser [4,5], but these attempts finally failed due to either too low power or poor reliability of the used Neon-like Ge or Zn x-ray lasers at 19.6 nm or 21.2 nm, respectively. According to published data [6], the presently operated Neon-like Zn x-ray laser at the PALS centre in Prague promises higher power and better performance, and target experiments are planned for 2007.

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Energy [cm-1]

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Photon energy [eV]

Fig. 1. Partial Na+ - level scheme and photoionization cross section of Na (for details see Ref.3)

In this contribution we will present detailed model calculations and briefly describe the planned experimental setup.

2 Model calculation The innershell photoionization of atomic sodium with x-ray laser radiation can be described by the following rate equations, using the simplified 4 level scheme of Fig 2.

( X-rays > 40eV

Wp

N 0 g0

)3

N 2 g2

A21 N 1 g1 Wg

Fig. 2. Simplified 4 level scheme

37.2 nm -

e -collisions

5

2p 3s

2

3

P

3

P1 Na +

1

2p6 1 S0

0

2p 6 3s

Na

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Rate equations dN 0 dt

= − N 0W p (t ) − N 0W g (t ) − N 0 N el C

dN el dt

= N 0W p (t ) + N 0Wg (t ) + N 0 N el C

dN1 dt

= N 0Wg (t ) + N 2 A21 + N 0 N el C

dN 2 dt

= 14 N 0W p (t ) − N 2 A21

dN 3 dt

= 34 N 0W p (t )

In these 5 equations, N0 is the density of sodium atoms in the ground state (2p63s), N1 and N2 are the population densities of the lower (2p6 1S0) and upper (2p53s 1P1) laser levels and N3 is the population density of the 2p53s 3 P level manifold, which however does not contribute to the laser process itself. Wp describes the total pump rate to the excited 2p53s states of the sodium ion and Wg the corresponding pump rate for the lower laser level (sodium ion ground state). According to the level degeneracies, only ¼ of the pump rate Wp is used for the upper laser level. The pump rates Wp,g are given by Wp,g = Ip/hνp* σp,g, where Ip is the intensity of the x-ray pump laser (hνp: photon energy) and σp.g are the photoionization cross sections for extraction of an inner p-electron, leading to the population of the upper laser level, and of an outer s-electron, leading to the population of the Na+ ground state. According to Fig. 1 and the data of Ref. 3, σp is about 8 Mb at the pump wavelength of 21.2 nm and σg is about a factor of 200 smaller. With the ionization of sodium atoms electrons are produced, which may then populate ionic levels by collisional excitation of sodium atoms. Of special importance thereby is the population of the lower laser level, leading to a reduction of the population inversion. This population of the lower laser level is described by the rate NelC, where Nel is the electron density. The collisional coupling rate C is estimated as 10-7 cm3/s (Ref. 7). From the equations, the inversion density ΔN = N2 – g2/g1*N1 can be calculated, where g2 and g1 are the degeneracy factors of the levels, with g2= 3 and g1 =1. With the inversion ΔN the gain coefficient g is then given as g = σstim*ΔN, with the stimulated emission cross section σstim. Assuming a Doppler broadened linewidth at a temperature of about 400 oC and a lifetime τ of the upper laser level of 400 ps (A21 = 2.5x109 s-1), σstim amounts to 5x10-14 cm-2. At a temperature of 400 oC the sodium density is about 1016 cm-3. For numerical calculations of the gain, the intensity, duration (pulse shape) and spatial change of the pump pulse (depending on the focussing) have to be chosen. Also the starting density N0 may change in pump beam

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direction and perpendicular to it, which depends on the used sodium oven. In the following, calculations of the inversion density and gain coefficient for specific scenarios (assuming constant intensity and density) will be presented and discussed. Assuming pulses with a sech2 pulse form and different peak intensities, a pulse duration (FWHM) of 100 ps and a starting sodium density of 1016 cm-3, the time development of the relative inversion density ΔN/N0 shown in Fig.3 is obtained. Population inversion is achieved in a certain time window, first at an intensity of about 109 Wcm-2 just around the maximum of the pulse. With increasing intensity this window shifts to earlier times and the inversion density finally saturates due to the depletion of the sodium density N0. The inversion density at the maximum intensity of 1013 Wcm-2 corresponds to a gain coefficient of about 28 cm-1.

Fig. 3. Time behaviour of the relative inversion density ΔN/N0 in units of τ (1/A21 = 400 ps)

To achieve a larger gain for the given density of 1016 cm-3, pulses with shorter pulse duration have to be used, as can be seen from Fig.4. For a pulse duration of 50 ps a gain coefficient of 65 cm-1 can already be obtained at a pump intensity of 5x1011 Wcm-2. To reduce the saturation at higher pump intensities, which is due to the depletion of the sodium density, the initial particle density has to be increased further, as can be seen from Fig. 5. For a given pump intensity and pulse duration an optimum density exists, which for the 50 ps pulse duration and intensity of 5x1011 Wcm-2 is around 2.5x1016 cm-3, leading to a gain coefficient of more than 100 cm-1

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Fig. 4. Gain versus pump intensity for different pulse durations (sech2 pulse) at a sodium density of 1016cm-3

Fig. 5. Gain versus sodium density for different pulse durations (sech2 pulse) at an intensity of 5x1011Wcm-2

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3 Planned experiment In the planned experiment, the x-ray laser radiation will be focussed with an off axis paraboloid into the sodium vapour which is generated in an

Fig. 6: Time dependent gain (in unit of τ = 400 ps) for the measured Zn-x-ray laser pulses (pulses superimposed at maximum intensity)

oven. The vapour streams out of a nozzle head, which has 800 µm holes on both sides and a length which can be varied between 5-15 mm. The oven is located in a vacuum chamber, which can be attached to the target chamber of the x-ray laser. The x-ray laser delivers pulses with energies between 1 mJ - 10 mJ and pulse durations of 150ps (single pass) and 250 ps (double pass) (Fig.6), with the larger energies for the double pass geometry. Assuming a pulse energy at the sodium target of 0.25 mJ/1 mJ for the 150 ps/250 ps pulses and a focus radius of 50 μm, the 150 ps/250 ps pulses deliver peak intensities of 0.75x1011cm-2 and 2.2x1011Wcm-2. For a sodium density of 1016 cm-3 these pulses then yield maximum gain coefficients of 52 cm-1 and 62 cm-1 (Fig.6). The large gain is due to the steep raising of the pulses and comparable to the gain for a 75 ps sech2 pulse (Fig.4). For interaction lengths of about 5mm-10mm and assuming constant pump intensity, saturated amplification should be possible.

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4 Conclusions The presented calculations yield high gain in a wide parameter range. Planned more detailed calculations will include changes of the pump intensity within the vapour due to the focussing and absorption, and also changes of the vapour density especially at the nozzle exit. These effects may slightly reduce the gain. But as the x-ray laser data are assumed conservative and further improvements expected, good chances for realization of the innershell x-ray laser in sodium exist.

References 1. 2. 3. 4. 5. 6. 7.

M.A. Duguay and P.M. Rentzipis; Appl. Phys. Lett. 10,350 (1967) W.T. Silfvast and O.R. Wood II; J. Opt. Soc. Am. B4, 609 (1987) J.J. Yeh and I. Lindau; Atomic Data and Nuclear Data Tables 32, 1 (1985) S. Meyer et al.; Inst. Phys. Conf. Ser. No 151, 173 (1996) S. Meyer et al.; Inst. Phys. Conf. Ser. No 159, 313 (1998) B. Rus et al.; Phys. Rev. A 66, 063806 – 12 (2002) W. Lotz; Z. Physik 216, 241 (1968)

310 Angstroms X-Ray Lasing Under Beta-Decay of Tritium M. Yu. Romanovsky1 and V. K. Bityukov2 1 2

A.M.Prokhorov General Physics Institute of RAS Moscow State Institute for Radiotechnics, Electronics, and Automatics

Summary. The beta-decay of atomic tritium produces the ion 3He+ at the first exited state 2s with the probability of 25%. This state can irradiate two photons (two-photon lifetime is about 0.01 ms) or one photon (the lifetime is 173 s). The stimulated emission of one-photon may depress the two-photon decay. This is a soft X-ray laser with the wavelength 310 angstroms (40.8 eV). The first problem of two-photon decay depression is solved by largereflectivity mirrors for 310 A. The periodic array of non-dispersive, periodically positioned, quasi-dielectric cylinders in vacuum oriented along the axis of X-ray emission has narrow-band reflection of about 100% for wavelength closed to the distance between dielectric cylinders. Such array with quasi-dielectric cylinders periodically located at about 300 angstroms chess table can be realized by forthcoming lithography methods. Two such mirrors shape the proper resonator for generated emission and form good divergency of (coherent) X-ray beam. The second problem of 310 A radiation absorption by tritium atoms in bounded-free electron transitions may be solved by application of (strong) permanent magnetic field to the tritium sample. The magnetic field produces the spectrum of permitted free electron energy in one direction (of X-ray propagation). While the energy of possible free electron 27.2 eV is out of this spectrum, the bounded-free transition is forbidden, and the absorption of stimulated emission is depressed by several orders and becomes negligible small. The theoretical limit of X-ray continuous laser power is 0.15 mW per cubic cm of liquid atomic tritium. The required magnetic field is about 300 kGs.

1 Introduction: irradiation of tritium under the beta-decay. The beta-decay of any nucleus provides the nucleus with the additive charge +e. After the small time of the beta-decay (it is about the flight time of decayed electron through the atom), the electron system of the atom becomes in a non-stationary state. All electrons have some additional energy with respect to new stationary states. The deepest K- and L- electrons have the energy

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E

− K ,L

Z 2e2 = 2rB (n − δ − ) 2

before the beta-decay, and the energy

E

+ K ,L

( Z + 1) 2 e 2 = 2rB ( n − δ + ) 2

after the beta-decay, where Ze is the charge of initial parent nucleus, n is the principal quantum number (n = 1 for K-electrons and n = 2 for Lelectrons), rB is the Bohr radius, δ- and δ+ are quantum defects of atomic states of initial and product nuclei. To obtain a population inversion, the L states of the product nuclei should have less energy that K state of the parent one. It means that

( Z + 1) 2 e 2 Z 2e2 ΔE = E − E = − + ≤0 2rB (2 − δ + ) 2 2rB (1 − δ − ) 2 + L

− K

Since δ- ~ δ+ ~ δ < 1, this inequality does not fulfill for any pair of nuclei, taken place in beta-decay, except one. Auger-processes start in any nuclei (except one) immediately after the beta-decay [1], and normally do not accompany by any X-rays since the effective “width” of state in an atom with product nucleus (of “product” ion) is very large. There is one atom where radiation processes permitted not only by energy, but due to the fact the electron in a product atom appears in some stationary state. This is atomic tritium. The product ion is 3He+ is produced by beta-decay of tritium. Indeed, the energy of the ground state of tritium (Z = 1, δ- = δ+ = 0) E1T = - e2/2rB while the energy of the first excited state of + 2 2 2 3He (Z = 2, n = 2) ion is E2He = - 2 ·e /2rB·2 = E1T. The probability to appear at this state is about 25% [2]. The process is fast due to the absence of large transformation of a wave-function. At the same time, there are no mechanisms of an energy transfer for transitions to the ground state (the probability is about 70%, see, for example, [2]) as well as to other excited states (total probability 5%). It means, looks, that these lasts transitions occur while some body (nearest atom) collides with the decayed tritium (3He+ ion) and rates of these transitions are (very) slow. Thus, there is a long-life temporal population inversion on the transition 2s – 1s in 3He+ ion. Indeed, the beta-decay of atomic tritium leads to an appearance of the part (denote this part as α) of ions 3He+ at the meta-stable state 2s. There

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are 3 possible decays of this state: two-photon decay to 1s state, and the cascade transition to 1s state via Lamb transition to 2p state. The last process is very slow and can be neglected. The third possible decay is the forbidden one-photon M1 transition to 1s state (the electro-dipole and electroquadropole transitions are forbidden) [3]. Thus the radiation of tritium can be calculated easily. The two-photon component is very wide: from zeros for 0 eV and 40.8 eV quanta energy to the maximum of quanta with the 20.4 eV energy. The one-photon component with quanta energy 40.8 eV (wavelength λ = 310 A) is narrow (its natural width is about 19 orders less than the width of the two-photon component), but the maximum is 12 orders larger (the total ratio of 7 orders is the ratio of lifetimes of one-photon transition τ1 ~ 175 s and twophoton transition τ2 ~ 0.92·10-5 s). The spectrum of tritium radiation (it is, in fact, the radiation spectrum of an ion 3He+) is presented on Fig.1. The total rate of tritium emission under the beta-decay (the radiation of ions 3He+) is

v = αΛ -9

where Λ = ln2/T= 1.78·10 s, T is the period of tritium half-decay. The rate of two-component decay is

v2 = αΛ

τ1 ≈v τ1 + τ 2

while the rate of one-photon decay is τ2/τ1 ~ 0.5·10-7 times less.

Fig. 1. The radiation spectrum of tritium under the beta-decay in arbitrary units: the radiation spectrum of an ion 3He+. The width of one-photon radiation is 19 orders less than the width of two-photon radiation (the scale along X-axis is not kept).

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The total power of quantum radiation of ℏ ω1 = 40.8 eV is

P1 = αΛhω1 N 0

τ2 τ1

where N0 is the total number of (tritium) atoms. The one cubic cm of liquid atomic tritium (N0 = 5·1022) irradiates P1 ~ 3α·10-11 W spontaneously, the total power of this two-photon is about one mW. Note that the total power of beta-decay of atomic tritium is

Pβ = ΛN 0

Emax

∫ f ( E )dE 0

where f(E) is the energy spectrum of decayed electrons. The value Pβ ~ 0.15 W for one cubic cm of liquid atomic tritium, i.e. Pβ is two orders larger than the total radiation power. The radiation of tritium is isotropic. To create X-ray laser with the beta-decayed tritium as active medium, several problems have to be solved. The first problem is to get atomic tritium with high enough density. It is in most technical. The second problem is to depress two-photon radiation. It is solved through a creation of conditions for one-photon stimulated radiation with the wavelength λ = 310 A. Such conditions achieve due to good reflectivity resonator (high reflectivity mirrors) for λ = 310 A. This problem is solved [4]. At least, losses of stimulated one-photon radiation (per one pass of resonator) should be less than the gain (per one pass of resonator), i.e. these losses should be depressed specially.

2 High-reflectivity mirrors for λ = 310 A. The first problem of two-photon decay depression is solved by largereflectivity mirrors for 310 A. The periodic array of non-dispersive, periodically positioned, dielectric cylinders in vacuum oriented along the axis of X-ray emission has narrow-band reflection of 100% for wavelength closed to the distance between dielectric cylinders [4]. Such array with dielectric cylinders periodically located at about 300 angstroms chess table can be realized by usual lithography methods. Two such mirrors shape the proper resonator for generated emission and form good divergency of (coherent) X-ray beam.

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In Fig. 2, the reflection coefficient is shown as a function of the wavelength expressed in units of array step Dg. The solid-blue and dashed-red curves correspond, respectively, to dielectric constants ε = 2 and ε = 4. As one can see the array becomes a perfect reflector within a fairly narrow wavelength range centered at the resonant wavelength that is slightly larger than the period Dg. Similar results have been obtained for dielectric grating structures. The resonant pattern is associated with the so-called Wood anomalies [5], and can be explained by the existence of trapped modes or guided wave resonances [6].

Fig. 2. Calculated zero-order reflection coefficient for a periodic array of dielectric cylinders in vacuum described in the text. Results are presented as a function of the wavelength of the incident radiation measured in units of the period Dg. The solid blue and dashed red curves correspond, respectively, to the array of cylinders with dielectric constants ε = 2 and ε = 4.

Of course, all medium (of cylinders) can not be considered as dielectrics for X-ray radiation: such radiation excites currents in cylinders (heads). Nevertheless, the volume of such currents is very small due to the cylinders radius, and losses may be considered as negligibly small. Indeed, the cylinders mirror can be compared with the metal grating mirror [4]. The reflection coefficient from “dense” silver grating is about 85% with zero transmission (losses are about 15%) while the grating holes square is about 3%. The square of cylinders head is about 0.7%, therefore total losses are much less than 1%, which is quite enough for the proposed X-ray laser. The good (theoretically, very closed to one) reflectivity for λ = 310 A plays the role in a solutions of damp losses. As well, this perfect reflectiv-

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ity leads to the stimulated emission of λ = 310 A with a sharp space diagram and to the depression of two-photon radiation. Thus, the periodic array of non-dispersive, periodically positioned, dielectric cylinders in vacuum oriented along the axis of X-ray emission solves two problem of Xray laser by tritium: the depression of two-photon radiation (all energy will be forwarded to the one-photon stimulated emission) and increase of final power output of X-ray laser. Moreover, the sharp space diagram of stimulated emission permits to solve the problem of radiation losses.

3 Damping of radiation losses inside an active medium. The third problem of 310 A stimulated emission is the (large) radiation absorption. There are two types of absorption: by bounded electron transitions in 3He+ ions which transited to ground state, and by bounded-free electron transitions in by tritium atoms. Since the concentration of 3He+ ions is small, this type ob absorption can be neglected. The absorption of 40.8 eV quanta radiation in tritium is much more larger. The cross-section of this process can be estimated by well-known Kramers formula 3

σ vn = 7.9 × 10 −18

n ⎛ ωn ⎞ ⎜ ⎟ cm 2 2 Z ⎝ω ⎠

where ωn is the minimal frequency needed for an ionization of hydrogen atom from the n state. For tritium Z = 1, n = 1, and σ1n = 2.9·10-19 cm2. The bound-free absorption coefficient in tritium is proportional to the density, and for liquid tritium (density n0 = 5·1022 cm-3) is equal 14600 cm-1. Even for moderate (gaseous) tritium n ~ 1019 cm-3, this absorption coefficient remains large enough to prevent any stimulated emission (the gain is not so large). How to solve this problem? It is necessary to transform the spectrum of free electrons, appeared due to an absorption of stimulated radiation with λ = 310 A. This spectrum should have the forbidden energy band near the 27.2 eV. It is impossible to realize uniformly in space, but possible for free electrons propagated in the definite direction. Indeed, the magnetic field produces the discrete spectrum of particles, moving at the direction perpendicular to the field direction. Classical motion of charged particles in this case goes along circles, radiuses of these circles depend on particles energy continuously. Quantum effect is the change of the continuous radi-

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uses spectrum (in one direction!) to a linear spectrum. The differences between two nearest values of possible energy ΔE is

ΔE =

ehH = hωL mc

where H is an amplitude of (permanent) magnetic field, e is an electron charge, m is an electron mass, ωL is the Larmor frequency (see, for example, [7]. This energy difference should be larger than the energy difference of stimulated emission arises by line broadening ℏ Δω, i.e.

ωL > Δω If the permanent magnetic field provides this inequality, the energy value of 27.2 eV becomes forbidden for free electrons, moving along the axis of stimulated radiation. Since only these electrons can absorb quanta of stimulated radiation due to the momentum conservation law, the absorption coefficient along the X-ray axis becomes depressed strongly. Experimentally, this fine depression can be achieved by tuning of the magnetic field amplitude.

4 Estimates. Since the total radiation of tritium under the beta-decay in good resonator goes at the wavelength of 310 A, the output power of stimulated emission may reach the value

P1s = αΛhω1 N 0 Thus the theoretical limit of X-ray continuous laser power is 0.15 mW per cubic cm of liquid atomic tritium, α = 0.25. Of course, an experimental preparation of liquid atomic tritium is doubt: atomic tritium with gas densities is much more achievable. The gas atomic tritium has to be prepared specially. The gas with room temperature and normal pressure, the expected output laser power is about 0.1 μW per cubic cm. The broadening of 310 A X-ray laser radiation in above normal gas conditions has the non-uniform character (collision broadening is small). The recoil linewidth ΔωR ≈ 4·1012 s-1, the Doppler linewidth ΔωD ≈ 0.4·1012

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s-1, thus the total non-uniform linewidth Δω = ΔωR + ΔωD ≈ 4.4·1012 sThis limits the magnetic field above the value

1

H > mcΔω / e

or, for normal gas atomic tritium, H > 2.2·105 CGS. Such magnetic field can support the existence of tritium in form of atomic gas.

Fig. 3. The possible experimental scheme of atomic tritium X-ray laser. The gaseous atomic tritium is contained in the tube. Cylinder array mirrors are located in vacuum near the side windows of the tube.

The possible experimental scheme of 310 A X-ray laser based on the beta-decay of atomic tritium can be the following (Fig.3). The tritium tube can have the volume up to 102 – 103 cm3, therefore the expected X-ray laser power output may be up to 1 mW while α = 0.25. Thus, the combination of three devices: the tube with gaseous atomic tritium, high reflectivity mirrors (cylinders array), and strong magnetic field may provide X-ray lasing of λ = 310 A with output power up to 1 mW.

References 1. K.Siegbahn. Beta-and Gamma-rays Spectroscopy. Amsterdam (1955). 2. P.V.Elyutin, V.D.Krivchenkov. Quantum mechanics. Moscow: Science (1976) [in Russian]. 3. Berestetskii V. B., Landau L. D., Lifshitz E.M., Pitaevskii L. P. Quantum Electrodynamics. Oxford, UK: Pergamon Press (1982). 4. A.G.Borisov, S.V.Shabanov. J. Comp.Phys., 209, 643 (2005). 5. R.W. Wood, Phys. Rev. 48, 928 (1935) 6. R. Magnusson and S.S. Wang, Appl. Phys. Lett. 61, 1022 (1992);

310 Angstroms X-Ray Lasing Under Beta-Decay of Tritium 7. 8. 9. 10. 11.

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S. Peng, G.M. Morris, Opt. Lett. 21, 549 (1996); T. Peter, R. Br¨auer, O. Bryngdahl, Optics Communications 139, 177 (1997); K. Koshino, Phys. Rev. B 67, 165213 (2003); L. Pilozzi, A. D’Andera, R. Del Sole, Phys. Rev. B 54, 10763 (1996). L.D.Landau, E.M.Lifshitz. Quantum mechanics: non-relativistic theory. 3rd ed., Oxford, UK: Pergamon Press (1991).

Capillary Discharge Soft X-Ray Laser at University of L’Aquila: Laboratory Survey A. Ritucci, G. Tomassetti, A. Reale and P. Zuppella Physics Department of University of L’Aquila, gc LNGS-INFN, via Vetoio 67010 Coppito L’Aquila, Italy

Summary. We report on different experimental investigations regarding the use of the 0.3 mJ, 0.3 Hz, 1.7 ns, 46.9 nm Ar laser developed at the University of L’Aquila. Firstly, we have investigated the potentiality of the EUV laser in the ablation of hard dielectrics such as CaF2 and LiF crystals, which are largely transparent to the visible and to the ultraviolet laser light. We determined the ablation thresholds and the ablation rates for these two crystals and compared the results with the values obtained with other kinds of visible-ultraviolet laser systems. Secondly, we investigated a method to manipulate the intense soft X-ray laser beam based on the use of hollow waveguides. We used monocapillary tubes in a multireflection regime to achieve a substantial modification of the intensity distribution of the beam. These results can be of great interest for several applications of these soft X-ray laser sources.

1 Introduction Among the variety of soft X-ray lasers, which are recently under fast development in several laboratories worldwide, the capillary discharge soft X-ray Ar laser operating at 46.9 nm remains, to now, the most reliable one [1-2]. This laser is the most suitable for a large number of laboratory investigations for its simplicity of use, its compactness and the relatively large output energy per pulse. Many of such investigations may be of relevance in the field of applied science and the basic physics [3-4]. Moreover they can represent a valuable starting point in view of the applications of the new, high rep-rate, tabletop EUV lasers in laser-produced-plasmas having shorter wavelengths and smaller pulse durations [5]. The aim of this paper is to report some experimental investigations, which have been performed by the use of the 46.9 nm Ar laser, recently developed at the University of L’Aquila [2]. The laser under consideration operates at the reprate of 0.3 Hz, with 0.3 mJ/pulse and 1.7 ns pulse duration.

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2 EUV Laser Ablation Today, laser ablation has a significant role in the field of applied science for the processing of different kinds of materials and/or for their characterization. From the general point of view, laser ablation depends on different experimental parameters such as the pulse laser energy and duration, the energy fluence and strongly on the penetration depth of the laser light through the material. In this work we have focused our attention to hard dielectrics, such as CaF2, LiF, BaF2 or SiO2, which have relevant interest for several applications such as for miniaturized optical devices. These crystals are characterized by very large band gap (e.g. Eg ≈12.0, 13.6-14.5 or 9.1 eV for CaF2, LiF and BaF2 respectively [6]), so that they are largely transparent from the infrared up to the vacuum ultraviolet (where hν <Eg). In order to improve the ablation quality, several experimental investigations on these materials have been typically performed employing ns vacuum ultraviolet excimer lasers (see for example refs. [7] and references therein) or ultra-intense optical picosecond- and femtosecond-laser pulses [7]. As a larger absorption of the radiation by the material generally leads to an improved quality of the ablated region, significant improvement should be expected by the use an EUV laser. Another considerable advantage in the use of the EUV is the high spatial resolution of the processing. In fact, using a corrected optical system one can expect an ablation spot diameter lower than 1-2 µm [8]. In this section we present a description of the laser ablation of CaF2 and LiF crystals by focusing our 46.9 nm, 1.7 ns Ar laser and analyzed the ablated surfaces using Scanning Electron Microscopy (SEM) and a vertical profilometer. We experimentally determined the etch rates of these crystals and the ablation thresholds and compared the assessed values with those found in literature using lasers with a longer wavelength. 2.1 Experimental setup The irradiations were performed by focusing the laser on the samples by a 12 cm-focal-length spherical Ir mirror, located 2 m far from the capillary output with an incidence angle of 5° (reflectivity ~15%) (see, fig. 1). The fluence was varied by changing the position of the sample along the optical axis of the mirror. The simplicity of this focusing system had several limitations due to the strong optical aberrations of the beam spot on the target. The coma due to the 5° incidence angle produced an elongated shape of the beam, an irregular illumination of the sample and a non-planar wavefront of the radiation. The spherical aberration limited the beam fo-

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cusability to only a few tens of micrometers. Moreover, it should be noticed that by moving the sample along the optical axis of the mirror, we have changed not only the fluence, but also the curvature of the wavefront. This last effect was neglected because of the small numerical aperture (NA=0.05) of the focusing mirror. The values of the fluence were determined by measuring the beam energy and the area of ablated craters with an estimated accuracy of about 20%.

Fig. 1. Scheme of the experimental setup used for the laser ablation and an AFM image of a typical ablated structure.

Despite the poor focusing resolution, we reached a maximum laser fluence of 3 J/cm2, which is well above the ablation thresholds. In these measurements, we operated in a multi-shot irradiation mode using 25 shots for each ablation. The CaF2 samples consisted of 2-mm thick plates optically polished on both sides, while the LiF samples consisted of 1-mm thick plates polished on one side. The samples were placed in an evacuated environment at the pressure of 10-4 Torr. The ablation was studied analyzing the craters produced on the surfaces through a vertical profilometer (TENCOR) and an Atomic Force Microscope (AFM). Scanning Electron Microscopy (SEM) was used as a complementary experimental technique, for the inspection of the ablated surface. 2.2 Results and discussion The behavior of the ablation rates versus the fluence is shown in figs. 2 and 3 for LiF and CaF2, rispectively. The experimental points have a threshold behavior for both materials, which can be fitted by the standard expression [9]: L = d·ln(F/Fth), where L is the ablation rate, F and Fth are the irradiation fluence and the fluence threshold respectively, and d is a

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Fig. 2 Experimental (points) ablation rate vs the fluence for LiF. The line is a theoretical fitting.

Fig. 3 Experimental (points) ablation rate vs the fluence for LiF. The line is a theoretical fitting.

characteristic ablation depth, related to the effective absorption length of the radiation in the material. The results of figs. 2-3 present several interesting aspects. Firstly, we find very low ablation thresholds: 0.11 J/cm2 for LiF and 0.06 J/cm2 for CaF2, while with the nanosecond 248 nm laser beam the typical values are in the range of 20-40 J/cm [10]. Secondly, the best fit of the experimental data provides for d the values of 20 and 14 nm for LiF and CaF2, respectively. These values, which are in agreement with the optical penetration depths (α-1 ~14 nm and ~10 nm) assessed for λ = 46.9 nm from Ref. [11], are about five orders of magnitude smaller than in the deep UV. This is due to the large photon energy (hν = 26.4 eV) of our laser, which can induce efficient excitations of electrons from the valence band into the vacuum level of the crystal. This strong interaction introduces new ablation conditions for these large band gap dielectrics, which could be of significant interest for the fine processing of these materials. The topography of the ablated areas depends strongly on the laser fluence. At the lower fluence, the inhomogeneous distribution of the laser intensity produces an inhomogeneous heating of the surface and an irregular profile of the crater. By contrast, at values >1 J/cm2, the fluence is sufficiently high to produce evaporation of material over the whole beam cross section. The ablated crater has, in this case, a conical shape with regular vertical profile and deepness >1-1.5 µm. The analysis performed at the AFM (Fig. 1) for the large fluence confirms the regularity and the deepness of the ablated region. This behavior in the vertical profile of the craters is found both in the case of LiF and CaF2. Figures 4 (a) – (b) show the SEM images of LiF irradiated with the fluence of 0.8 J/cm2 (a) and 3 J/ cm2 ((b). Irregular reliefs on the ablated region can be reasonably attributed to the irregular distribution of the laser fluence due to the diffraction of the beam and not to liquid waves formed by the melting of the surface. This analysis shows also that the ablation processes at 46.9 nm is accompanied by the formation of micro-sized cracks inside the irradiated area.

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These cracks are due to the strong thermoelastic stress on the surface and to the brittleness of the materials. An interesting behavior is that the cracks are observed already very close to

Fig. 4 SEM image of an ablated region of LiF with fluence of (a) 0.8 J/cm2 and (b) 3 J/cm2.

6 µm

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Fig. 5 Ablated spot on LiF with fluence > 3 J/cm2 and using an improved optical configuration.

the ablation threshold at very low irradiation fluences and increase with the number of pulses. These cracks stand along preferential directions, which should correspond to the cleavage planes of the crystal. The higher density of short microcracks at the periphery (see Fig. 4 (a)-(b)) of the craters can be attributed to the different thermoelastic forces acting inside and at the edge of the laser spot. As the fluence is increased from the threshold, the evaporation of material is more efficient, cracks become less evident and a cleaner condition of ablation is found. Fractures on CaF2 samples are typically less evident and of smaller dimensions. They present irregular shape homogeneously distributed through the irradiated area. Approaching 3

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J/cm2, the mechanical stress of the surface becomes so large (see fig. 5) to detach away from the surface macroscopic pieces of material and the quality of ablation is lost. The presence of cracks even close to the ablation threshold is in contrast to what is generally expected by the shortening of the laser wavelength and suggests the necessity for the modeling and a better understanding of the ablation processes induced by EUV and soft Xrays. Concerning the resolution fig. 5 show an ablated spot obtained at a large fluence (>3 J/cm2) using an improved focusing system. The central hole has diameter of only 6 µm. The fluence in this case is so large to destroy substantially the crystal in proximity of the hole.

3 Capillary waveguides in the EUV Soft X-ray lasers are generally obtained without any optical cavity by the single pass amplification of a lasing line through elongated hot plasma columns. Unfortunately, the amplifying plasmas are often characterized by large density gradients where the laser emission can experience large refraction effects. As a consequence, the intensity distribution of a soft X-ray laser can have unusual and not uniform profiles, which are quite difficult to control. As an example, our laser is characterized by an annular shape with the divergence of 4.5 mrad. This beam profile may be inconvenient for several kinds of applications. The need for the manipulation of the beam of such a kind of coherent soft X-ray radiation pushes the need for testing different kinds of optical elements. In this section we have investigated the possibility to use hollow glass capillary waveguides to modify the intensity distribution of the soft X-ray laser beam. The soft X-ray propagation in different kinds of capillary optics (both in the form of mono- and poli-capillary structures) has been well studied for several years and it has been successfully employed on different kind of sources: synchrotrons, incoherent plasma sources (laser plasmas and z-pinches) and x-ray tubes (see for example refs. [12-13]) at wavelengths typically <1-3 nm. Here, to manipulate the laser beam we used simple glass monocapillaries. In particular, the targets consisted of hollow glass tubes with variable lengths, 3.5-18.5 cm, and different inner diameters in the range of 280-880 µm. The laser was focused at the entrance of the waveguides, by a spherical mirror realized by Sc/Si multilayer having a maximum reflectivity at normal incidence of about 30%. The transmitted fraction of the soft X-ray laser energy was determined by measuring the laser energy before and after the waveguide channel by

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Fig. 6 (Points) Experimental transmittance of the waveguides versus the length of the capillary. The solid line represents a fit of the experimental data.

means of an X-ray vacuum photodiode and a digital oscilloscope. An aluminum filter, mounted on a fine nickel mesh, was used to avoid the saturation of the detector. The measurements of the near and far-field structures of the beam intensity after propagation through the targets were performed using an integrated detection system composed by a multi-channel plate (MCP), a phosphorous screen and a charged coupled device (CCD) camera, which was located at different distances from the capillary output in the range of 1- 60 mm. Figure 6 shows the transmittance of the guides versus the capillary length. Despite the absence of any special treatment, we can notice a relatively large value of the transmittance. In particular, the transmittance ranges from ~92% for a 3.5 cm long guide, to ~58% for 18.5 cm. We should observe that the higher value observed at 18.5 cm in respect to the value found at 11 cm may be attributed to the statistical variations of the inner-wall characteristics of the capillaries and to differences arising in the optical alignment. The values of the transmittance T of the guide is determined by the wall reflectivity R of the capillary tube through the expression: T ≈ RN, where N is the number of reflections that the radiation experiences inside the channels (N ≈L/(4f#·r), where f# is the f-number of the focusing system and r and L the inner radius and the length of the waveguide, respectively). In our case the waveguides operate in a multireflection regime with N ranging from 3 to 12. The solid line in fig. 2 represents the result of a theoretical fit of T calculated for the first set of capillaries. Here an average inner radius of ≈ 300 µm was considered. We find for R a value of 94-95% that is in good agreement with the theoretical

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value reported in ref. [11] at the grazing angle of about 2.5°. Accordingly, an absorption of 5-6% at each reflection can be inferred for this kind of waveguides.

Fig. 7 Images of the intensity distribution of the guided beams obtained after propagation through hollow capillary guides. (a) Near field intensity distribution of the beam 1-mm far from the output of a 9 cm long waveguide. (b) Typical intensity distribution of the laser obtained by free propagation of the beam beyond (6 cm far) the focal point of the spherical mirror. The evident mesh structure is due to the holder of the aluminum filter. (c)-(d)-(e) Intensity distributions of the guided beams measured at 6 cm from the capillary outputs. The capillary lengths are: (c) 4 cm, (d) 9 cm and (e) 18 cm, respectively.

Figure 7 illustrates the effect of waveguiding on the intensity distribution of the beam. Fig. 7 (a) shows a typical laser beam profile measured in the near field zone obtained at 1 mm distance from the output end of a 9cm long tube. Herein, we note a full width diameter at half maximum of 1 mm diameter. The modification of the intensity distribution of the beam can be, more effectively, observed in the far-field zone. Preliminarily, we present in fig. 7 b) the distribution of the laser intensity of an unguided beam after 6 cm from the focus of the mirror. In this figure, it is clearly shown the irregular typical annular structure of the beam and the modulation of intensity induced by the mesh of the filter support. Figures 7 (c)(d)-(e) compare the profiles of the laser beam, obtained with 4, 9 and 18.5 cm capillary lengths, respectively. These profiles have been obtained in a quasi-far field zone at 6 cm from the output end of the guide. From the

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comparison of these pictures and of their line profiles it emerges a progressive and considerable modification of the intensity distribution of the beam generated by the increase of the number of reflections with the capillary length. As a result of these multiple reflections the laser shape changes from a quite irregular one, where it is still possible to notice the presence of the modulation induced by the mesh of the filter, to a distribution approaching a flat top profile. These experimental results demonstrate the large potentialities of hollow capillary channels for the efficient manipulation of EUV laser beams. These effects could be of practical interest for several applications of these sources such as for the EUV laser-basedmicroscopy, EUV laser-ablation and controlled material processing. In conclusion we have firstly used the soft X-ray laser beam to investigate the ablation of large band gap dielectrics. Due to the large absorption of the EUV laser beam, we found very low ablation thresholds and ablation rates for LiF and CaF2, which are substantially different from what can be found with conventional optical or excimer laser radiation. The use of a soft X-ray laser should lead to a more efficient ablation processes of these materials. Secondly, we have investigated a method for the manipulation of the intensity distribution of the beam by the use of hollow waveguides. In capillary pipes as long as 18 cm we found a substantial modification of the intensity distribution, which reaches an almost flat top profile.

References 1. B. R. Benware, C. D. Macchietto, C. H. Moreno, J. J. Rocca, Phys. Rev. Lett. 81, 5804,1998. 2. G. Tomassetti, A. Ritucci, A. Reale, L. Palladino, L. Reale, S. V. Kukhlevsky, F. Flora, L. Mezi, A. Faenov, T. Pikuz, A. Gaudieri, Opt. Comm. 231, 403 2004. 3. F. Brizuela, G. Vaschenko, C. Brewer, M. Grisham, C.S. Menoni, M.C. Marconi, J.J. Rocca, W. Chao, J.A. Liddle, E.H. Anderson, D.T. Attwood, A.V. Vinogradov, I.A. Artioukov, Y.P. Pershyn, V.V. Kondratenko, Opt. Express 13, 3983, 2005. 4. A. Ritucci, G. Tomassetti, A. Reale, L. Arrizza, P. Zuppella, L. Reale, L. Palladino, F. Flora, F. Bonfigli, A. Faenov, T. Pikuz, J. Kaiser, J. Nilsen, A.F. Jankowski, Opt. Lett., 31, 68, 2006. 5. H. Daido, Rep. Prog. Phys., 65, 1513, 2002. 6. Klocek P. eds. Handbook of Infrared Optical Materials, Dekker, New York, 1991.

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7. J. C. Miller, R. F. Haglund-Jr, Laser ablation and desorption, in Experimental methods in the physical sciences, J.C. Miller, R. F. Haglund eds.,Academic press, San Diego, 1998, Vol. 30, and references therein. 8. S. Le Pape, Ph. Zeitoun, M. Idir, P. Dhez, J. J. Rocca, M. François, Phys. Rev. Lett., 88, 183901, 2002. 9. S. Nolte, C. Momma, H. Jacobs, A. Tunnermann, B. N. Chichkov, B. Wellegehausen, H. Welling, J. Opt. Soc. of Am. B 14, 2716, 1997. 10. M. Reichling, J. Sils, H. Johansen, E. Matthias, Appl. Phys. A, 69, 743, 1999. 11. Data from NIST, website: http://www-cxro.lbl.gov/optical_constants 12. V. Kantsyrev, R. Bruch, M. Bailey, A. Shlyaptseva, Appl. Phys. Lett. 66, 3567, 1995. 13. S.B. Dabagov, S.V. Nikitina, M.A. Kumakhov, N.S. Ibraimov, G.A. Vartaniants, A.N. Nikitin, L. Spielberger, Nucl. Instrum. Meth. B 103, 99,1995.

Compact EUV Lasers Based on Low-Inductive Capillary Discharges V.A. Burtsev, E.P. Bolshakov, N.V. Kalinin, V.A. Kubasov and V.I. Chernobrovin The D.V. Efremov Scientific Research Institute of Electrophysical Apparatus, 196641, Saint-Petersburg, Metallostroy, Russia

Summary. In the given paper results of elaboration, numerical and experimental modeling, and also research of radiation sources on the base of low-inductive capillary discharges are presented. Author’s approach is to use a running wave of sliding avalanche discharges for gas pre-ionization and main z-discharges for collisional excitation pumping. Full-scale testing showed, that this approach allows to create compact radiation sources. Numerical predictions in further increasing of input power efficiency are informed.

1 Introduction Application of fast capillary discharges for last years is one of the main ways in developing compact sources of coherent EUV radiation on plasma of multiply ionized ions. Actually, the laser of capillary type on neon-like ions of argon with wave length of 46.9 nm was found the very compact and rather effective source [1]. However attempts in creation of more short-wave lasers on capillary discharges were not crowned yet with success though sufficiently high coefficients of amplification have been obtained on many kinds of ions [2]. The fact is that with reduction of wavelength the needed specific pumping power sharply grows. The complex processes of energy storage, power sharpening and their fast onset in the discharges to obtain non-equilibrium plasma influence also full efficiency of such sources. Optimization of these processes is the main task of given work. On the last Conference on X-Ray lasers the authors proposed their own approach to create compact and effective sources of capillary type [3]. This approach was based on using a running wave of sliding avalanche discharges for gas pre-ionization and main z-discharges for collisional excitation pumping in low-inductive capillary load, supplying through long

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transmitting line. Sliding discharges use this line in opened regime at double voltage of incident wave; main discharges use it in closed regime at double current of incident wave. This is possible if one applies lowinductive capillary loads with close spacing of return current-carrying cylindrical conductor, when Lcap≤ ρτ, ρ – wave resistance of transmitting line, τ – rise time of incident voltage pulse. In following works This scientifictechnical approach was developed in a series of papers [4-7].

2 Experimental modelling of EUV source on low-inductive capillary discharges

2.1 Full-scale model EUV source In accordance of accepted approach a full-scale model EUV source has been designed and manufactured. At creation of the experimental installation a generator of high-voltage pulses which provides on the matched load a voltage pulse with amplitude up to 100 kV, HWFM of ∼ 100 ns at rise time of ∼ 8 ns has been applied. In the base of this generator an artificial double storage-forming line, produced with using of technology of pulse low-inductive roll condensers on oil-paper isolation, was laid [3]. As a capillary load a ceramic tube with internal diameter of 5.5 mm, external diameter of 10,5 mm (return current-carrying coaxial conductor had internal diameter of 11 mm) and length which can be varied (L/l ~1,4 nH/cm) was used. The generator was connected to a current-collecting low-inductive unit of the capillary load through 8-cable 9 Ohm transmitting line with length of 10 m [7, 8].

2.2 Fast Photographing of Plasma on the Model One-Cable EUV Source For modeling and researching of processes, occurring at the formation of running wave of sliding avalanche discharges and the ignition of main discharges one of 8 cables of the transmitting line was connected directly to a capillary load, similar to the capillary load of the full-scale EUV source. The main experimental results have been obtained with the tube length of 50 mm at changing of gas pressure in the very wide range (0.001-1000

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Torr). Among them it is necessary to note following. The dependence of travel time of sliding discharge running wave versus initial gas pressure has a wide minimum in the range of 0.1-100 Torr [4]. The field of 0.1-1 Torr, interesting in respect to creation of EUV lasers get to drop-down part of this dependence, on which ionization collisions of slow electrons with atoms are determinant. The second result, which was obtained on the model one-cable source in the same wide range of gas pressure, is the amplitude dependence of signals from photo multiplies versus pressure [4-6]. It turned out, that there are two kinds of light signals. The first kind is observed at more low pressure and characterized by more short rise time of discharge current pulse and dominating ultraviolet component in total light radiation. The second kind is characterized by red-orange component and observed at more high gas pressure. Signal of first kind insensibly converts to second kind as the gas pressure increases [5,6]. At the pressure of 30-300 Torr both kinds of discharges are registered simultaneously. Recently for studying this phenomenon a fast photographing of discharges from the muzzle of capillary tube was undertaken by CCD camera in frame regime with time expose of 1.8 ns. The first image, obtained at t=3 ns, corresponds the phase of sliding avalanche discharge (Fig.1). As one can see, sliding discharge gives week ring-like degraded luminescence; it is avalanche Townsend discharge, named also as dark discharge. Following images present the phase of main longitudinal discharge with week pinching at ~ 35 ns.

t=3 ns

20 ns

35 ns

60 ns

Fig. 1 A set of images, obtained by CCD camera in different moments at p=0.1 Torr argon. U0= 60 kV.

Other situation is observed at more high gas pressure. When the light pulse acquires the character of the second kind the main discharge converts to spark shape or channels, thermally expanding as Joule energy dissipates (Fig.2). At p=1 atm the main discharge from the very outset has the shape of sliding sparks (low brightness, left picture on Fig. 3) and only high brightness allows to reveal a ring-like shape of radiating plasma,

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demonstrating its thermal expansion to axis (high brightness, right picture on Fig.3).

Fig. 2 Images of the discharge, obtained by CCD camera at different brightness. U0=60 kV. Argon at p0= 120 Torr.

Fig. 3 Time integrated photo of the discharge, obtained by digital camera at different brightness of images. U0=70 kV. Air, 1 atm.

So, two kinds of light signals, observed early in very wide range of pressure changing, are connected with changing of discharge structure from diffuse (low pressures) to near wall spark one (high pressure). It needs to note, that at the gas pressure, typical to EUV lasers (0.1-1 Torr), discharges possess diffuse structure both on sliding avalanche and main longitudinal phases. 2.3 Testing of the Full-Scale EUV Source Now the full-scale EUV source is passing the stage of testing and adjusting. The source was provided with a current shunt 1 on one of transporting cables, a coil of Rogovsky 2 in the grounded flange 3 before the construc-

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tive plane film condenser 4 and a foil shunt 5 nearly the entrance of the capillary tube 6 with the high voltage electrode 7 (Fig.4). These detectors allow evaluate roles of different elements of circuit, including the plane

Fig. 4 Scheme of current detectors.

film condenser. In Fig.5 one can see preliminary results of registering EUV radiation by help of Si-diode and 2 μ Al filter, placed on axial position of 4 cm from the muzzle of the source (upper trace). The arraignment for differential pumping and collimating of radiation has been moved. On the lower trace the discharge current, registered by shunt on one of cables, is presented. The first feature of this trace corresponds to the current of incident wave and then the current of sliding discharge phase. Radiation signal consists from long time spontaneous part and very short part (several ns) immediately before current maximum, caused by amplified EUV radiation.

3 Numerical Modelling of the Full-Scale Capillary Source The purpose of following numerical calculation is to show opportunities of the full-scale model source in generation of EUV radiation and to obtain additional information to limited experimental results. Again, the radiative MHD code with account of non-equilibrium ionization, transport of radiation and the system of energy supply, described by equivalent scheme, was applied [6].

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Fig. 5 Preliminary results of EUV registration by Si-diode. 40 ns/div. p0 = 0.1 Torr, Ar. U0= 58 kV.

Carried out calculations at p0 = 0.75 Torr, lcap= 5 cm showed effective plasma compression with final plasma column parameters on the axis: δ ~25, Te ~188 eV (see Fig.6). Near-axis plasma column with radius of 0,3 mm would have almost full ionization (equilibrium average ion charge z ≈ 17 instead maximal possible value Zn=18, where Zn is nuclear charge for argon atoms). But non-equilibrium average ion charge in this area is only Z~9 and a factor of non-equilibrium ΔZ=Z-z~-8. So, plasma column with

Fig. 6 Temporal dependences of relative parameters: discharge current I/I0, vacuum radius of plasma shell r/r0 (r0 – inner radius of capillary), coefficient of plasma compression δ, electron and ion temperatures Te, Ti (Rydberg constant, equal 13,6 eV), equilibrium and nonequilibrium average ion charge z and Z correspondingly (Zn=18- total charge of argon nucleus). I0= 22 kA.

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plasma density of ni ~ 4.1017 cm-3 and temperature T~ 190 eV has ionization non-equilibrium and one can wait in this column a laser effect on neon-like Ar8+ on wave-length of 46,9 nm. A new step was done in numerical RMHD calculations – the first attempt in analyzing of energetic balance and evaluation of efficiency of input energy. The purpose of this calculation is to show the ways of optimization of different mechanisms of obtaining needed plasma and to reveal opportunities for increasing of input energy efficiency. As one can see on Fig. 6, at first a current pumping of constant inductance Wl0= L0I2/2 occurs. Here, L0 consists from constant inductance of the current collecting unit L00 and constant inductance of the capillary tube Lco. Then Joule mechanism of plasma heating takes effect, but more sufficient contribution in creation of plasma column with needed parameters makes a work of magnetic piston against plasma. To increase this contribution it is possible by heightening of total current or reducing of initial gas pressure. But it needs to note, that at the same time magnetic energy, stored in variable capillary inductance will increase too. There are reserves in reducing of magnetic energy, stored in constant inductance Wl0 , and in unused energy (W0-Wgmax), but it is a matter of serious complex optimization and analyze.

Fig. 7 The example of energy balance of capillary discharge. Wg- used energy of generator, Wl0- magnetic energy, stored in constant inductance, Wj- Joule heating, Wp- work of magnetic piston, Wlv- magnetic energy, stored in variable inductance of capillary discharge.

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4 Programming of Input Power for Increasing of Total Efficiency In this section results of numerical calculations, directed on searching of more effective methods of power input in capillary discharges are presented. The idea consists in using of radially expanding plasma column after pinching by means of reducing in wave resistance of transporting line in required moment, that is characterized by increasing discharge current

Fig. 8 Temporal dependencies of relative parameters the same on Fig.5. ion charge z and Z correspondingly (Zn=18- total charge of nucleus for argon). U0= 100 kV, I0=100 kA, ρ=2 Ohm before the arrow and ρ-1 Ohm after the same arrow on upper graphic, and I0-200 kA, ρ=1 Ohm on lower graphic. p= 1 Torr Ar.

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(in given moment a second transmitting line was connect up). This occurs in that moment when plasma, passing the pinch, starts to extend outside. The opposite movement of plasma and flying on it second current layer is accompanied by increasing in efficiency of energy input, that gives the contribution in full efficiency of installation. The carried out calculations have shown, that at the use at the first a line with wave resistance of ρ=2 Ohm, and then equivalent line with resistance of ρ=1 Ohm allows to reach some plasma with average ion charge with number of Z =15. At the same time the application from the very beginning of the line with the wave resistance of ρ= 1 Ohm hardly enables obtaining of charge number of 14 (increase of input efficiency reaches 1.5) . The obtained result gives grounds for carry out the further optimization calculations with the purpose of increasing in efficiency of energy input in capillary discharges in conditions of ionization nonequilibrium.

5 Conclusions •

The model single-cable source can be used for creating of manyrange radiation sources with adjusting of regimes by simple changing of initial gas pressure.

•

laser effect has been obtained on the full-scale EUV source with low-inductive capillary, supplying through long transmitting line and using pre-ionization of gas by sliding discharges.

•

Carried out preliminary numerical study of energy balance on fullscale source allowed to reveal opportunities in optimization of such devices.

•

Numerical researches have showed prospect of input power programming for efficiency increase of the EUV sources of ionization type.

Acknowledgments This work was supported by the grant N 06-08-00828 of the Russian Foundation for Basic Research.

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References 1. J.J. Rocca, V. Shlyaptsev, F.G. Tomasei et al,. Phys. Rev. Letters, 73, 21922195, 1994 2. J.J. Gonzalez, M. Frati, J.J. Rocca, V.N. Shlyaptsev, A.L. Osterheld., Phys. Rev. E., 65, 026404, 2002 3. V.A. Burtsev, E.P. Bolshakov, A.S. Ivanov et al, “Electrodischarge radiation source of capillary type”, In Proc. of 9-th International Conference on x-ray lasers ICXRL-2004 (May 24-28, 2004, Beijing, China), pp.167-170. 4. V.A. Burtsev, E.P. Bolshakov, A.S. Ivanov et al.,“Fast z-discharges in lowinductive capillary tubes”, In Proc. of 15-th Intern. Conf.on high power particle beams BEAMs-2004 (July 18-24, 2004, St.-Petersburg, Russia), pp. 450453. 5. V.A. Burtsev, E.P. Bol′shakov, A.S. Ivanov, N.V. Kalinin, V.A. Kubasov, R.F. Kurunov, V.G. Smirnov, V.I. Chernobrovin, V.I. Engelko: “Electrophysical problems in creation of compact and effective sources of short-wave radiation on plasma of capillary discharges”, In Proc. of 15-th Intern. Pulsed Power Conf. (Monterey, USA, June 13-17, 2005), In press (October 2006). 6. V.A. Burtsev, E.P. Bol′shakov, N.V. Kalinin, V.A. Kubasov, V.G. Smirnov, R.F. Kurunov, V.I. Chernobrovin, V.I. Engelko: “Electrophysical problems in creation of compact and effective sources of short-wave radiation on plasma of capillary discharges”, IEEE Transactions on Plasma Science. Special issue on pulsed power science and technology. In press (November 2006). 7. V.A. Burtsev, E.P. Bolshakov, N.V. Kalinin, V.A. Kubasov, R.F. Kurunov, V.G. Smirnov, V.I. Chernobrovin: “Sources of radiations on the basis of capillary discharges”, Intern. Conf. on Micro and Nanoelectronics 2005 (Moscow-Zvenigorod, Russia, October 3-7, 2005). Proc. SPIE, 2006 (in press).

Experimental Comparison of Capillary Pinching Discharge in Argon and Nitrogen A. Jancarek, L. Pina, M. Vrbova, M.Tamas, R.Havlikova, S. Palinek, P. Vrba*, K. Kolacek*, J.Schmidt* and J. Strauss* Czech Technical University, Brehova 7, 11519 Prague 1, Czech Republic *Institute of Plasma Physics, AS CR, 18221 Prague 8, Czech Republic

Summary. Experiments with CAPEX-U apparatus were done to more understand the differences between Ar and N active media created during the pinch compression, respectively. Capillary discharge current, X-ray narrow band radiation and EUV spectrum temporal behavior were measured. Results of laboratory experiments for both gas fillings under various currents and initial pressures are shown. Computer simulations show that current quasi-period shortening and higher amplitude is needed.

1 Introduction Basic requirements on the X-ray laser recombination pumping realized through the capillary pinch decay are following. Plasma should be heated during the pinch compression to get high density of bared nuclei N7+. After that the plasma should be quickly cooled during the pinch expansion to get a column of under-cooled plasma. The inversion population at the Balmer α transition of hydrogen-like nitrogen is created via three body recombination process. To get measurable gain the pinch should be carefully designed and the peak value of upper level population should be of order 1015 cm-3. We report here results of laboratory experiments with pinching discharge in alumina capillary filled by nitrogen or argon and computer simulations.

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2 Experiment The experiments were performed with the CAPEX-U device recently developed in the Institute of Plasma Physics, Czech Academy of Sciences [1]. The experimental setup is shown as Fig. 1.

Fig. 1. CAPEX-U experimental setup

Alumina capillary 230.5 mm long with the inner diameter of 3.2 mm was filled by nitrogen or argon. Regulating the throughput of nitrogen or argon the gas pressure in capillary is controlled. The discharge volume is preformed by 10 μs current pulse with the amplitude of 18 A. The shape of the main current pulse, measured by means of a Rogowski coil, has form of a damped sinus. The measurements reported here were done with the current peak value 45 and 55 kA. Electric current pulse profiles and EUV radiation were recorded simultaneously, see Fig.2.

Fig. 2. Time dependence of current and EUV signal for nitrogen and argon

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For the various filling pressures in the range of 10 Pa < p0 < 580 Pa intensive pulses of radiation (Fig.2. red line) were detected by vacuum diode. The time delay of the radiation pulses was meassured between the start of current pulse to first peek of EUV signal. PIN diode and Ni filter was used for measurement with nitrogen, see Fig.6. The delay for both gasses is increasing with increasing filling pressure, see Fig.3. The dependance of X-ray signal on pressure can be seen on Fig.4.

Fig. 3. Dependence of X-ray peek delay to capillary discharge current edge

The highest amplitude of the X-ray radiation pulse is observed with the initial filling pressure about p0 = 275 Pa for nitrogen and 30 Pa for argon, the peak delay is about 90 ns resp. 65 ns in this case. The reproducibility of current in all meassurements is ±3 kA.

Fig. 4. X-ray signal dependence on nitrogen resp argon pressure

Time-resolved spectra with gating time 30 ns were measured by means of MCP chevron and cooled CCD camera.. Spectra of capillary discharge in nitrogen and 55kA current are shown on Fig.5. There were three gating times. Also PIN diode measurement of X-ray signal behind 2μm Ni filter for various pressures was done. Example of detected signals is on Fig.6.

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Fig. 5. Nitrogen spectra for various pressure gated in various time.

Fig. 6. X-ray signal behind Ni filter for 55 and 68 kA current.

3 Computer Simulations Our interpretation of the experimental results is based on the computer simulations of the pinch dynamics done by means of the NPINCH code [3]

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and on the ion kinetics evaluations done by means of the FLY code used as a post processor [4]. The dependences of the pinch characteristics on the time for various pressures is seen from Figs 7-8. The pinch time is increasing with increasing initial pressure. At low initial pressures the evaluated peak values of the electron temperature Te allow us to expect high densities of helium-like nitrogen ions. If the gas pressure is increased and the peak value becomes lower than 100 eV, the plasma ionization state should be lower than =5. Instantaneous emission spectrum (Fig.8) evaluated by means of the FLYSPEC subprogram for N0 = 1.4x1016 shows that the He-like lines dominate in the whole spectral range. 4E+020

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4 Conclusions Comparing results of pinch emission for argon and nitrogen (in the same capillary pumped by the same electric current pulse) we have observed that for the same pinch delays higher initial pressures of nitrogen should be installed. This is in a good correspondence with pinch scaling law [5] which claims that the characteristic time is increasing with increasing multiple of atomic number and initial atom concentration. The parameters of our experimental device are not yet fully optimized for the recombination pumping of the hydrogen-like nitrogen. Emission spectra recorded and simulated are in reasonable correspondence and confirm the presence of helium-like nitrogen ions around the pinch time. Following the results of our simulations further increase of the current amplitude and/or shortening of the current quasi-period is needed.

Acknowlegment This research has been supported by a grant MEYS CR under the Research Project MSM 6840770022 and under the project 1P2004LA235-INGO.

References 1. 2. 3. 4. 5.

J. Schmiedt et al.: Comparing of calculated and experimental results of CAPEX-U device, Czech.J.Phys., 56, Suppl.B, B371-B376, 2006. P. Vrba et al.: Role of initial vapour density in Z-pinch, Nukleonika 46 Supplement 1 S25-S27, 2001 N. A. Bobrova et al.: Plasma Physics Reports, 22, 387-402, 1996. R. W. Lee, J. T. Larsen.: J.Q.S.R.T. 56, 535-556, 1996. R. C. Elton: X-Ray Laser, Academic Press, New York, 1990.

Analysis of Laser Pumping by Capillary Pinching Discharge in Argon and Nitrogen P. Vrba, M. Vrbová, A. Jančárek, L. Pína, M. Tamáš, R. Havlíková, S. Palínek, G. Tomassetti* and A. Ritucci* CTU, FNSPE Břehová 7 CZ-115 19 Prague 1, Czech Republic, *University di l’Aquila, INFM, 67010 Coppito, l’Aquila, Italy

Summary: A comparative study of the capillary pinching discharges in argon and nitrogen is presented. Requirements on plasma parameters needed for laser collision and recombination pumping are stated. The results of the computer modelling are compared with previously published experimental results for argon laser and with recent experiments done with the same capillary filled by nitrogen.

1 Introduction Our aim is to get lasing at 13.38 nm with hydrogen–like nitrogen N6+ ions. The inversion population is expected at the quantum transition corresponding to the Balmer alpha line. Collision recombination in under-cooled plasma, created during the expansion stage of capillary pinch, is considered as the pumping way. We have performed computer modelling and predicted system parameters where a measurable gain is expected [1]. Peak values of electric current higher than that for Ar8+ laser pumping are required. To check the validity of our model we have done experiments with l’Aquila apparatus, previously optimised for Ar8+ laser [2].

2 Z-pinch plasma properties required for collision and recombination pumping To get efficient collision pumping of Ar8+ laser the discharge plasma should have a high density of Ar8+ ions and plasma electron temperature Te, should guarantee prevailing excitation of the upper laser level. In the same time, the electron density Ne should be lower than threshold value for collision mixing. It is well known that proper pumping conditions are achieved in over-heated plasma during the pinch collapse.

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For the recombination N6+ laser pumping, the primary process of upper laser population is a three-body recombination, which may be achieved in a non-stationary under-cooled plasma, when the plasma with high density of bare nuclei is expanded after the pinch. The decisive plasma property is the history of plasma electron temperature. A high concentration of fully stripped ions N7+ should be created during the pinch collapse and then the electron temperature decrease should outrun the relaxation of ionisation.

Fig. 1. Time dependences of current and PIN diode signal

3 Experiments An apparatus, previously realized for argon capillary laser [2], was used for the experiments with nitrogen. The current profile had the form of dumped sinus with the peak value about 21 kA (see Fig. 1, black line). To get information about the pinch position and temperature time dependences of emitted radiation in the wavelength range 1.9- 5 nm were recorded by a pin-diode behind 1 μm thick nickel foil (Fig. 1, red line). Time integrated spectra in the spectral region 10 – 21 nm emitted in the axial direction have been also recorded (see Fig. 2 (a)).

4 Computer modelling Simulations were done for the parameters related to the experiments. Time dependences of axial temperatures and electron densities and plasma tra-

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jectories (r0 = 1.6 mm, Imax = 20 kA, and T1/4 = 75 ns for Ar and T1/4 = 65 ns for N) for various initial pressures are seen from Fig. 3.

Fig. 2. Spectra of the radiation from the pinching plasma in nitrogen (a) time integrated spectra, (b) instantaneous spectra evaluated at the pinch time.

Previously, the same simulations together with detailed kinetic evaluations [3,4] were done for argon laser in TIT [5] and the results proved our computer model. We have suggested to follow the trajectory of pinching plasma in the “space Ne-Te” (see Fig. 4a). Labels along the trajectory represent the time delays in nanoseconds. The pinch time tp = 35 ns and reasonable gain is calculated on the interval of one nanosecond, with the peak value at 33.2 ns when Te = 100 eV and Ne = 5. 1018 cm-3. We may guess

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rium ionisation state Z = 8 and where Ne is slightly lower than the value for collision mixing. The collision pumping takes place during the pinch collapse or before the pinch time. In our case (related to the Fig. 3a,b), we judge only the parts of trajectories before the pinch times (Fig. 4b). The optimum pressure is estimated to 0.2 torr. For the recombination pumping of hydrogen like nitrogen ions high electron temperature should be achieved during the pinch collapse and then the plasma should be quickly cooled during the pinch expansion. To find out suitable pumping conditions the pinch trajectory is followed in the space tau-Te and Ne–Te simultaneously (see Fig.5). Under the current experimental conditions, the inversion population is not achieved because, for low values of gas pressure the plasma density

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is too low (even in the pinch time) to get measurable gain. If the pressure is increased, the peak value of Te is not high enough to get fully ionized nitrogen. The measurable gain factor is expected if the peak value of current is bigger. The corresponding trajectories are shown as dashed in Fig. 5 in this case.

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5 Evaluation of the emission spectra Kinetic code FLY is used as a postprocessor [1] to estimate instantaneous ionization state, energy level populations of Li-, He- and H-like ions and spectra. Under the conditions in our experiment the H-like ion densities are al least one order lower than the He-like ion densities for any initial gas

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pressure (see Fig. 5). Consequently, the He-like lines dominate the emission spectra (see Fig. 2b).

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6 Conclusions Results of experiments and computer modelling are in a good agreement for both argon and nitrogen gas fillings. The identified spectral lines correlate with the evaluated pinch plasma temperature. A higher value of the peak current is needed to achieve laser effect with N6+. This work was supported by the Ministry of Education, Youth, and Sports of the Czech Republic by grants on the projects MSM 6840770022 and LN00A100.

References 1. 2. 3. 4. 5.

Vrba, P. et al.: “Modelling of a nitrogen x-ray laser pumped by capillary discharge”, Central European Journal of Physics 3, 564 – 580, 2005. Ritucci, A et al.: “Sub-milliradiant divergence soft-X-ray laser by active plasma waveguiding in z-pinch capillary discharge”, Europhys. Lett., 63. 694 - 700, 2003. Bobrova, N.A. et al., Plasma Physics Reports, 22, 387- 402, 1996. Vrba, P. et al.: “Argon filled capillary discharge for EUV laser pumping” 28th ECLIM Proceedings, Roma, 626 – 630, 2004. Yasushi Hayashi et al., Jpn. J. Appl. Phys. 42, 5285 - 5289, 2003.

CAPEX-U – A New Driver for Discharge-Pumped Lasers Working on the Wavelength Below 15 nm K. Kolacek, J. Schmidt, V. Prukner, O. Frolov, J. Straus, V. Stelmashuk, M. Martinkova*, V. Matejec** and I. Kasik** Institute of Plasma Physics, Academy of Sciences of the Czech Republic, *Faculty of Nuclear Sciences and Physical Engineering, CTU in Prague, **Institute of Radio Engineering and Electronics, Acad. of Sci. of the CR

Summary. CAPEX-U device is a pulse-power apparatus capable to deliver a “short-circuit” discharge current ~120 kA in a quarter-period ~80 ns. Its characteristic features are direct optical access to both discharge electrodes, and laser triggering of the main spark gap (for exact synchronization of detectors and applications). It is described, how CAPEX-U joint with SHOW device will be used for soft X-ray amplification on nickel-like silver ions (generated by exploding wire in water), and how the pressure at the SHOW axis was measured.

1 Introduction Prof. G. Pert of University of York, UK, enunciated in his concluding remarks to 9th International Conference on X-ray Lasers in Beijing, China (May 24-28, 2004) that practically no experimental progress was made since previous Conference in Aspen (USA, May 27-31, 2002) to bring lasing to shorter wavelengths. Therefore, our effort was to contribute to fill this gap in the field of electrical (discharge) pumping. At present there are two main ways to amplified spontaneous emission (ASE) in soft X-ray region in discharge (practically in all cases capillary discharge) plasma 1. The first way is based on electron-collisional recombination pumping scheme. Unfortunately, reproducibility of such laser is very poor and nowhere in the world is in routine operation. The second way to population inversion in capillary discharge devices uses electron-collisional excitation pumping scheme. It prefers Ne- or Nilike ions. While Ne-like Ar laser (λ = 46,9 nm) is very stable and works at present in at least four laboratories, its scaling to shorter wavelengths re-

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quires to use (Ne-)/Ni-like ions of metal vapours. Such step has not yet been successful 2 mainly because of difficulty with feeding these metal vapours into the capillary. However, even if their feeding is solved they will condense on the capillary wall making it conducting, which will exclude its further use. Therefore, we suggest to supply metal vapours by a wire explosion, and to substitute solid capillary wall by a liquid one. Moreover, to add another degree of freedom, we suggest performing wire explosion at various pressures that could be generated by focused shock wave in ambient liquid (water). The apparatus SHOW (SHOck Wave) with water-filled experimental chamber has been designed, assembled and tested. In future this SHOW device will be joined with CAPEX-U (CAPillary Experiment Upgrade) apparatus that will explode wire in SHOW-chamber-axis as soon as the shock wave arrives. Numerical modeling of this situation requires some experimental data about the shock wave dynamics and focusing. Therefore, the aim of this paper is to investigate the shock wave structure and to determine the diameter of the shock wave focus and pressure in it.

2 Apparatus The apparatus consists of the driving part of CAPEX-U (CAPEX-U rid of capillary) that will in future explode wires in the load-part - SHOW device. The new device CAPEX-U (see in more detail 3 and Fig. 1) is capable to deliver in the load the shortcut current ~120 kA in less than 100 ns. It has:

Fig. 1. Left: apparatus CAPEX-U. Right: apparatus SHOW – schematic diagrams.

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• co-axial pulse forming line that is charged from its side (not axially as CAPEX); therefore, both capillary ends are optically accessible, which enables much easier adjustment of the apparatus, of the diagnostics, as well as of the applications; • larger transverse dimensions (∅550 x ∅426 x 730 mm in comparison with ∅262 x ∅158 x 675 mm of the CAPEX); it yields more flexibility for charging voltage, discharge current, as well as for pre-pulse; • four-channel laser-triggered spark gap as the main switching element (CAPEX uses single-channel spark gap working in a self-breakdown regime) that enables reliable synchronization of the diagnostics as well as of the applications. SHOW device generates cylindrical converging shock wave in water to compress the channel arisen out of wire explosion 4. It is (see the right part of Fig. 1) water filled experimental chamber with isolating (Plexiglas) flanges and cylindrical stainless steel shell ∅400x200 mm serving as the ground electrode. Its inner surface is covered by porous ceramics (almandine) that, when voltage is applied, creates strong electric field at the output of pores and limits the current (reducing contact of metallic wall with conducting water). The second electrode is a co-axial mesh or a foil (if water between electrodes has a higher conductivity than the rest of experimental chamber) transparent for acoustical wave. When voltage pulse is applied the coronalike multi-streamer discharge generates a strong cylindrical acoustic wave that propagates towards the second electrode and through it further to the chamber axis. Near the axis it changes into a shock wave with strongly increasing pressure amplitude. This pressure was measured by a shadowgraphy technique, and by piezoelectric and fibre-optic sensors (see in more detail 5).

3 Measurement The shock wave structure was measured by a schlieren method. Unfortunately, the shock wave induced inhomogeneity at the focus was so large that the deflected beams went out of schlieren lens aperture. Therefore, a new diagnostic technique – off-axis shadowgraphy – was developed for pressure measurement near the focus. Besides that application of piezoelectric and fibre-optic sensors to pressure measurements were tested. Schlieren method. The expanded laser beam (2nd harmonic of Nd:YAG) was directed along the SHOW device axis. The paraxial region of SHOW device was imaged by lens (f=310 mm/∅80 mm) on the chip of CCD camera; undeflected beams were stopped by schlieren target (see Fig. 2, left).

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Shooting with laser at various delays after multi-streamer discharge depicted a medium stage of shock wave development (example (107 μs after the discharge) is shown in Fig. 2, right). Unfortunately, at the later stage of development the deflections of probing rays were so large that they did not fall into schlieren-lens-aperture.

Fig. 2. Left: schematic diagram of schlieren diagnostic. Right: schlieren image (58,75x 47mm) of the shock wave; inner circle – compression phase, outer circle – dilution phase

Off-axis shadowgraphy. The expanded laser beam was directed along the SHOW axis similarly as in the previous case. However, the imaging lens shielded by horizontal slit (57x20 mm) was placed in off-axis position to use for imaging the rays with higher deflections than in the former method (undeflected rays do not fall into lens-aperture at all (see Fig. 3, left). Such measurements (an example is shown in Fig. 3, right) were repeated for a few

Fig. 3. Left: schematic diagram of the off-axis shadowgraphy. Right: shadowgram of the shock wave; double-arc on the left depicts rising parts of the index of refraction (from undisturbed to the maximum, and from the minimum to undisturbed), single arc on the right shows falling part of index of refraction (from its maximum to its minimum).

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off-axis positions and for a few delays to find the deflection, at which the signal disappears. From this deflection the maximum pressure in the inhomogeneity was inferred to be ~30 MPa at 20 kV charging voltage. A slight disagreement with pressure estimate made according to 4 (70 MPa) is attributed to boundary layer effects that were neglected during evaluation. The probing-laser-delay after the discharge and the radii of curvature of individual arcs on the shadowgrams gave position of individual shock-wavephases in the given time (see Fig. 4). From the graph the radius of shock wave focus 2,8 mm, and focusing time 122-125 μs after the multi-streamer discharge were determined.

Fig. 4. Position of the shock wave

Piezoelectric pressure sensor. The active part of the sensor was cut from silver-ink-metallised piezo-film sheet (MSI sensors), contacted by conducting stick, fixed on plastic (PMMA) rod of the diameter 10 mm and placed in the SHOW axis. This piezoelectric sensor was connected to highimpedance input of the near-staying battery-powered oscilloscope (see

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Fig. 5 left). The signals were smaller than it was expected, probably because the sensor thickness (110 μm) was small in comparison with characteristic dimension of the shock wave (~3,5 mm). Fibre optic pressure sensor. The fibre-optic pressure measurement is based on idea of changed fibre transmission due to pressure induced change of ratio of cladding/core index of refraction. The fibre (core: quartz, ∅210 μm, index of refraction ncore=1,457, cladding: plastic, ∅250 μm, index of refraction nclad=1,41-1,44) was selected to have as close ncore to nclad as possible. Fibre was sealed in the axis of SHOW with a little camber (to exclude fibre stretching due to pressure-induced axial movement of flanges). Fibre input was first illuminated through a chopper (for preliminary adjustment), then by continuous light of HeNe laser and the transmitted light was detected by the fast photodiode SFH 2030 (see Fig. 6, left). It turned out that initial fibre transmission at the shock wave arrival falls. Then with new fibre the transmission increases to values much higher than the initial one (see Fig. 6, right), while with used fibre (probably with cladding corrupted) the transmission proceeds to fall much faster to the drop value roughly proportional to the charging energy. This method will be calibrated in a hydraulic press (in a quasi-static regime) as soon as it is available.

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4 Conclusion SHOW device in its water-filled cylindrical experimental chamber generates a shock wave that focuses on the chamber axis. Along this axis a silver wire will be stretched that will be exploded by CAPEX-U device as soon as the shock wave arrives – creating an environment for amplified spontaneous emission on nickel-like silver atoms.

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This paper presents pressure measurements near/on the SHOWchamber-axis in/around the moment when shock wave arrives. Unfortunately, none of these methods is absolutely reliable: piezoelectric sensors are probably too thin to measure a real pressure of a few mm thick shock wave, moreover they are destroyed during one or two shots; fibre-optic sensors need further calibration; schlieren method failed due to large deflections. Therefore, the most reliable seems the off-axis shadowgraphy that yielded radius of shock wave focus 2,8 mm and pressure amplitude 30 MPa at 20 kV charging (which is less than one half of the value predicted by the model (70 MPa)); however, the measured value can be underestimated, because boundary layer effects were neglected during evaluation.

Acknowledgement The experimental part of this work was supported by the Grant Agency of the Czech Republic under Grant 202/06/1324 and the theoretical part by the Ministry of Education, Youth, and Sports of the Czech Republic under Grant 1P2004LA235.

References 1. K.Koláček: 'Principles and present state of capillary-discharge-pumped soft X-ray lasers', Proc. SPIE, 5228, 557-573, 2003 2. A.Rahman, E.C.Hammarsten, S.Sakadzic, J.J.Rocca, J.F.Wyart, 'Identification of n=4, Δn=0 transitions in the spectra of nickel-like cadmium ions from a capillary discharge plasma column', Physica Scripta, 67, 414-419, 2003 3. J.Schmidt, K.Kolacek, V.Bohacek, .V.Prukner, O.Frolov, and J.Straus, 'Design of laser-triggered driver for fast capillary discharge', Czechoslov. J. Phys., 54, C321-C325, 2004 4. K.Kolacek, J.Schmidt, V.Prukner, P.Sunka, O.Frolov, J.Straus, M.Martinkova, 'Wire exploding in a focus of converging cylindrical shock wave in water – introductory remarks', IEEE 15th IPPC, Monterey, Ca., USA, June 13-17, 2005, to be published 5. V.Prukner, K.Kolacek, J.Schmidt, J.Straus, O.Frolov, M.Martinkova, 'Coronalike multistreamer dis-charge in water for cylindrical shock wave generation', Czechoslov. J. Phys., 56, B342-B348, 2006.

Towards Nitrogen Recombination Soft X-Ray Laser Scheme in a Capillary Discharge Z-Pinch N. S. Kampel, A. Rikanati, I. Be'ery, U. Avni, A. Ben-Kish, A. Fisher and A. Ron Department of physics, Technion, Israel institute of Technology, Haifa, Israel, 32000.

Summary. In recent years z-pinch configuration is considered for implementing a nitrogen recombination X-Ray Laser at λ≈13.4nm. The required plasma conditions at the pinch time are Te~140eV and Ne~1020cm-3. Lasing can occur after the plasma cools to Te<60eV, in a time scale of a few nanoseconds (<5nsec). A capillary discharge z-pinch apparatus was built (Imax≈60kA, τ¼=70nsec), and examined by means of radiation measurements with filtered X-Ray diode (XRD). By using different filters it is possible to identify the emission from He-like and H-like nitrogen. We show that at the pinch time the electron temperature is well above 80eV, and the total cooling period, to Te<60eV, is shorter than 5nsec. Future complementary XRD and spectroscopic measurements are being planned.

1. Introduction It is well known that a recombination based soft X-Ray laser (XRL) has better scaling with energy in comparison to the collisional ionization scheme [1]. Accordingly, our goal is to implement a recombination laser, at λ~13.4 nm (3Æ2 transition in H-like nitrogen) [2]. The required initial conditions for achieving the XRL are: a transient nitrogen plasma column where ~50 % of the atoms are fully stripped, i.e. Te~140 eV. An electron density of Ne~1020 cm-3, for a dominant 3-body recombination process [1,3]. Furthermore, in order to get a significant population inversion, the plasma should cool to an electron temperature below 60 eV, at a cooling rate faster than 5nsec, the time scale of the 3-body recombination. In recent years the z-pinch scheme has been considered as a candidate for the implementation of a nitrogen recombination XRL [4,5]. Choosing the right z-pinch parameters may lead to the appropriate plasma conditions as described above. The pinch temperature and density can be varied by changing the maximum current and the initial density. For an efficient en-

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ergy coupling to the pinch, the pinch time should coincide with the current pulse time scale. As for the cooling duration, it is expected to follow the time scale of the rarefaction wave, which depends on the plasma column diameter and the sound velocity of the plasma. In relevant schemes, this time scale is a few nanoseconds long [6,7]. In this work, a capillary discharge Z-Pinch apparatus was implemented, according to the criteria mentioned above. A high voltage pulse power, Imax=60 kA and τ¼≈70 nsec, was coupled to a 5mm diameter, 90 mm long capillary. The capillary was initially filled with N2 gas at 0.4-2 Torr (10167×1016 cm-3). The pulse equivalent RLC circuit parameters are: R≈0.5 Ω, L≈160 nH, C=12 nF, V0=280 kV. It should be noted that the nitrogen gas was pre-ionized with a 50 A, 2.5 μsec pre-pulse before the main current. First, the plasma parameters were studied in order to find suitable conditions for achieving lasing. Estimating the highly ionized plasma conditions requires measuring the N+7 ion abundance. However, N+7 ions do not emit line radiation, which are easy to identify. Therefore we used simple steady state rate equations [8], in order to get a rough estimate about the N+7 ion abundance from measuring the N+5 and N+6 abundance in the plasma. Radiative recombination N+6

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Measuring the ions emission was done using two filters: Ti 2 μm and Be 7.5 μm. The Ti filter was used for measuring the contribution of N+5 ions emission, whereas for the N+6 ions emission we used the Be filter. The filters transmission, shown in Fig.1, was calculated using the material absorption coefficients [9]. It should be noted that the Ti filter also transmit N+7 recombination spectrum at E>800eV, which is not shown in the figure. The expected signal, with various filters is proportional to η=∑λIλΛλTλ, where Iλ is the line intensity, Λλ is the plasma opacity and Tλ is the filter transmission. The line intensity for each ionization stage at a given plasma parameters (temperature, density and characteristic length) was calculated using the atomic code FLY [10]. In order to compare the expected signal strength at different plasma parameters, we normalized η according to the maximum signal, as shown in Fig.2a. The characteristic length of the plasma in our case is 0.1-1 mm, due to the off axis pinholes apparatus we are using. As expected, the maximum signal for the two filters is at different temperatures. Additionally, it can be seen that the relative emission of the plasma as a function of the temperature does not depend on the density or on the opacity. b

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4. Experimental Results The emission was measured, using the different filters, through off axis pinholes which are located 10mm from the capillary and ~60mm from the detector. For these measurements we built a sub-nanosecond high efficiency X-Ray Diode (XRD). The high quantum efficiency was achieved by using cesium iodide coated photocathode. We estimate the response of this photocathode to be ~1800 C/MJ. For comparison, the quantum efficiency of polished-carbon photocathode was measured to be ~4 C/MJ. The emission from the pinch was measured, using these filtered XRD's, for different initial gas pressure of 0.4-2 Torr (1016-1017 cm-3) of N2 molecules. The results of four of these measurements are shown in Fig.3. The pinch time (time of the first peak) was compared to a snow-plow model [11] and found to be 30-35 % (~15nsec) longer in all the measurements. The XRD signals for both filters have a similar profile. Therefore we examined the ratio between the signals (Be/Ti) throughout the pinch (±4 nsec), which turned out to be time independent. This means that for the duration of the pinch, the ions abundance does not change significantly i.e. the temperature is constant. 1.1

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From these measurements, and from the knowledge about z-pinch behavior [4,6], we can deduce the following about the plasma: The emission starts when the shock wave hits the center and starts heating the plasma. The emission reaches a maximum value, at the pinch time, when the shock wave reaches the end of the plasma. At that stage a rarefaction wave enters the plasma and starts cooling it. The first radiation peak ends when the rarefaction wave reaches the center, after about 5nsec. Hence the cooling time of the plasma must be shorter than 5nsec as expected. Since the emission vanishes at this stage, the cold plasma temperature can be estimated to be below 60 eV (see the Ti transmission in Fig.2a. As previously discussed, the two filters were designed to transmit line emission from N+5 or N+6 ions. In order to verify this we designed two additional filters, which are also shown in Fig.1. The N+5 line emission part in the Be filter was measured using Be and Cr filter. From this measurement we estimate that the N+5 lines emission part in the measurements with the Be filter is less than 1/7. A filter made out of Ti and Cr was designed to check the Ti filter. The transmission of this filter is ~20 % of the Ti filter transmission at the N+5 lines wavelength, and therefore it drastically reduces the N+7 recombination spectrum. We compared the measurements with the Ti filter and the Ti and Cr filter, at the same initial conditions, for estimating N+7 recombination contribution. This comparison gave a 1.5 times stronger signal, than expected with the Ti filter. This can be attributed to two significant effects: N+7 recombination radiation which is not taken into account or to the decay in the quantum efficiency of the cesium iodide photocathode. We believe that the majority of the difference is due to the decay in the photocathode efficiency. This issue will be checked in the near future. From these measurements we deduce that the Ti filter reflects the N+5 ions abundance and measurements with the Be filter reflects N+6 and N+7 ions abundance. Fig.2b shows the normalized measured XRD peak signal, that can be compared to Fig.2a. The figure is shown as a function of the inverse initial pressure, since the inverse of the density is proportional to the temperature [4]. Therefore we show the measured emission per atom as function of an equivalent temperature. From the measurements with the Be filter we can see that there is a significant abundance of N+6 ions. According to the steady state rate equations [8] we can conclude that there is a significant abundance of N+7 ions in the plasma, and that the plasma temperature is well above 80 eV. Fig.2 (a and b) shows that there is a disagreement between the calculated (expected) signal, due to line emission (Fig.2a), and the measured signal, due to the plasma emission (Fig.2b). Unlike the calculated signals, the measured signals rise as the plasma temperature increases (at lower ini-

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tial gas pressure) for both filters. This can be attributed to N+7 continuum radiation or to the non steady state plasma condition. At low initial pressure the signals drop, which is not understood.

5. Conclusion Nitrogen Z-Pinch plasma was investigated as a basis for a recombination XRL. A Z-Pinch driven by a 60kA peak current with τ¼≈70ns was constructed. The plasma conditions were investigated using high quantum efficiency cesium iodide XRD with appropriate filters. These filters were designed to measure the N+5 (Ti filter) and N+6 (Be filter) ions line emission. It was demonstrated that, at the hot stage of the pinch there is a significant abundance of N+7 ions, with temperatures well above 80eV. Furthermore, the total cooling of the plasma to Te<60eV is shown to be less than 5nsec. These parameters are promising for implementing a nitrogen recombination XRL scheme. Future measurements with XRD and various filters are planned in-order to estimate the radiative recombination part in the XRD signals. Additionally a spectroscopic setup is under construction.

6. References 1. Elton R. C.: 'X-Ray Laser', Academic Press, New York, 1990. 2. Hulin S., Dobosz S., Monot P., D'Oliveira P., Auguste T., Jacquemot S., Bonnet L., Lefebvre E.: 'Recombination X-ray laser in H-like nitrogen', J. Phys. IV France 11 (2001) Pr2-189-192. 3. Korobkin D., Goltsov A., Morozov A, Suckewer S., 'Soft X-Ray Amplifica tion at 26.2nm with 1 Hz Repetition Rate', PRL, 81, 1607 (1998). 4. Lee K., Kim J. H., Kim D., 'Analytical study of the dynamics of capillary discharge plasmas for recombination x-ray lasers using H-like ions', Physics of plasmas, 9, 4749 (2002). 5. Vrba P., Vrbova M., Jancarek A, Pina L., Havlikova R.: 'Dense Z-Pinches: 6th International Conference on Dense Z-Pinches', 2005 6. Ben-Kish A., Shuker M., Nemirovsky R. A., Fisher A., Ron A., Schwob J. L.: 'Plasma Dynamics in Capillary Discharge Soft X-Ray Lasers', PRL, 87, 015002 (2001). 7. Rocca J.J., Shlyaptsev V., Tomasel F. G., Cortazar O.D., Hartshorn D, Chilla J. L. A.: 'Demonstration of a Discharge Pumped Table-Top Soft-X-Ray Laser', PRL, 73, 2192 (1994). 8. Griem H. R., Lovberg R.H.:'Plasma Physics', Vol 9, Part A, Chapter 9, Academic Press, New York 1990.

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9. NIST website: ' http://physics.nist.gov/PhysRefData/FFast/html/form.html' 10. FLY: Atomic Kinetics and Spectroscopy Code Suite, Cascade Applied Sciences, Inc. 11. Ryutov D.D., Derzon M.S., Matzen M.K., 'The Physics of fast Z-Pinches', Reviews of Modern Physics, 72, 167 (2000).

On the Influence of Preionization Current Directions on X-Ray Lasing in Capillary Discharge V. I. Afonin, O. N. Gilev and A. M. Gafarov RFNC -VNII Technical Physics named after acad. E.I. Zababakhin, Snezhinsk, Russia

Summary. Experiments carried out on SIGNAL facility have shown that X-ray lasing in Ne-like Ar plasma of fast capillary discharge occurs when directions of preionization current pulse and main current pulse are the opposite. When the currents directions are the same we don’t observe the X-ray lasing. In this report we give the interpretation of this effect. The role of the preionization current pulse is not just formation of partially ionized gas to quickly tear the plasma away from the capillary walls when the main pulse comes (Z-pinch effect) but also formation of stabilizing magnetic field (in the case of oppositely directed current pulses).

1 Introduction There are many factors influencing X-ray lasing in Ar plasma of capillary discharge and the problem of stability of plasma compression by magnetic field is the most distinguished. This task had been solved by the preliminary Ar ionization by low-amplitude current prepulse and a number of experiments confirmed it [1, 2]. But the mechanism of instabilities elimination by the pre-ionization current is still uncertain. Indeed process of discharge evolution in preionized gas in contrast to breakdown in neutral gas is preferable for uniform plasma column formation. But large-scale axial-azimuth instability of such column including the case of capillary discharge may arise on its electron temperature and density fluctuations during evolution of ionization-thermal instability [3]. Let us estimate typical scale-length D of plasma column axial nonuniformity created by electric discharge with current maximum at 40 kA and rise-time of 60 ns in a capillary with diameter of 4 mm filled with Ar to pressure of 0.64 torr. The dynamics of such discharge was numerically simulated in [4]. According to the simulation by the time t1~10 ns from discharge start plasma with temperature Te1~3 eV and average ion charge

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Z1=1 is formed near walls, effective compression begin at t2=20 ns when Te2~5÷10 eV, Z2~3÷6. Then using the estimate of typical strata size [3]: D=

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2 Experimental Facility and Diagnostics Setup Experiments were performed at SIGNAL electrophysical facility having inductive energy storage and plasma circuit breaker [5, 6]. This facility depending on operating mode provided a load with the current with amplitude of 20÷40 kA and rise-time of 20÷50 ns. As a load the ceramic (Al2O3) capillary of 157 cm length, 3 mm inner diameter filled with Ar to pressure of 0.2÷1.0 torr was used. Gas-injection system allowed pressure controlling with accuracy of 5%. The SIGNAL provided good pulse repetition: current amplitude straggling was < 6%, rise-time straggling was < 14%. Current pulse had step-like form with rise-time rate of ~1012 A/s (see fig. 1). 10

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used. Mirror was inserted in the registration channel between the capillary and XRD at a grazing angle of 22.5° to the beam optical axis (see fig. 3).

Fig. 3. Setup of soft X-rays yield measurement: 1 - capillary; 2 - Si-mirror; 3 – slit; 4 – XRD.

XRD registration range is ε~10÷40 eV. From the higher energies side it was limited by sharp falling of Si-mirror reflectance (cut-off energy ~40 eV), from lower energies side – by significant decreasing of golden photocathode sensitivity near 10 eV. XRD signal measurements were performed with TDS-3052 oscilloscope having 500 MHz bandwidth and 5 GHz sampling frequency. Alignment of the registration channel was carried out with He-Ne laser. To constrain registration solid angle and to improve signal to noise ratio was the rectangular slit (3x15 mm2) installed in front of the photocathode. The measurement of a radiation from pre-ionized plasma was executed to examine plasma uniformity. The measurement was performed with the framing camera based on photon imaging detector. In these experiments a 4 mm diameter and 130 mm length glass capillary filled with 0.67 torr of Ar was used. Pre-ionization current amplitude was 12 A.

3 Experiments results and discussion Carried out at different Ar pressure and main pulse amplitudes as well as at different delays (2÷40 μs) between beginning of pre-ionization current Ip and the main pulse Im the experiments showed absence of XRD peaks in all cases when currents directions were coincident (see fig. 4). In case of opposite directions of currents, in the XRD signal at ~35 ns after main current switch to capillary we observed distinctive narrow peak from X-ray lasing effect of ~1 ns duration (see fig. 5). In both cases time interval between Ip and Im was 16 μs and initial Ar pressure in the capillary was 0.78 torr.

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It is necessary to note that in our experiments maximal XRD signal peak of 63 V was observed when pre-ionization current switched on in ∼20 μs before the main pulse and Argon pressure was 0.6 torr [6]. In fig. 6 are the frame images acquired in the optical band of luminescence of argon plasma excited by pre-ionization current in the capillary.

Fig. 6. Image of luminescence of Ar plasma excited by pre-pulse. Delay from beginning of the current is 200 ns. Frame duration: a-10 ns; b-20 ns.

In the fig. 6a one can notice a small-scale nonuniformity of plasma luminescence due to nonuniformity of its electron temperature or/and electron density. This is evidence of evolution of the ionization-thermal instability. It is clear that there's a possibility of development of ionizationthermal instability and large-scale MHD instability when the main pulse is passing through arisen temperature and density disturbance. Thus the experimental results seem more intriguing showing that in the case of opposite directions of pre-ionizing and main pulses the lasing has place, in the case of coincident directions lasing is absent. It is evident that in the first case there is more stable regime of plasma compression by the main pulse and in the second it is less stable. What is this governed by? First of all let us evaluate typical electron temperatures and densities of the plasma excited by pre-ionization current. According [7], there at 90 A

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current the electron density of N~(2÷3)×1015 sm-3 and capillary resistance were recorded. Ar plasma at 90 A has the same resistance (initial pressure 0.2 torr). Using [8]: ⎛ 6 ×10 21 T 32 e J Z = Te ⋅ ln⎜ ⎜ N ⎝

⎞ ⎟ ⎟ ⎠

(where JZ – ionization potential of an ion with Z=1 charge, Te – electron temperature) one can find hydrogen plasma temperature Te~0.92÷0.94 eV. Since the conductivities of argon and hydrogen plasmas are identical then argon plasma will have the same temperature. So from mentioned above relation follows N~(2÷3)×1014 sm-3. Though capillary length is not mentioned in [7] it is easy to show that using obtained estimate of plasma temperature for capillaries of typical diameters used in laser experiments one can obtain typical capillary length thus confirming validity of temperature estimate. Indeed, combining expressions for plasma conductivities: σ=

1.76 × 1013 Te (Λ 10) Z

3

one can find

2

and

σ=

LR , S

3

L=

19.6 RSTe 2 (Λ 10) Z

(where S - sectional area of capillary of length L (sm), R – plasma resistivity (Ohm), Λ – coulomb logarithm). From this using typical capillary length of 0.3÷0.4 sm, Te~0.92÷0.94 eV, R~5 Ohm and Λ=6 it follows that L~10÷18 sm. Therefore, at currents of tens of amperes there forms a plasma in capillary with Te ~1 eV and N~1014 sm-3 and degree of ionization of ~0.1. Let us consider a capillary with plasma as a cylindrical conductor. It’s well known that if alternating current flows through a conductor then when it changes the electrical field of induction appears which contributes to this changing at the periphery and impedes it on the conductor axis (skineffect). For instance, when current falls it amplifies current on the conductor axis and weakens current at the periphery. And if current grows then current at the periphery intensifies, current on the axis decays. The first case occurs when the main pulse flows in the opposite direction to preionization pulse, the second case when the main pulse flows in the same direction to preionization pulse. In the first case current decays at the periphery and grows on the axis. The region between them is occupied by azimuth magnetic field of the axis current. Under temperature Te~1 eV the penetration depth X~c(τ/4πσ)0.5 of

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V. I. Afonin, O. N. Gilev and A. M. Gafamov

the main current into plasma for 1 ns could be X~0.05 sm. But current growth to ~1 kA during this time leads to subsequent heating of the plasma shell and moderation of the current diffusion. According to calculations, during first 10 ns near capillary walls there forms plasma with temperature of Te~3 eV and with mean ion charge of Z~1. Then the diffusion depth of inner current magnetic field through such plasma shell for 10 ns amounts to just X~0.07 sm. Therefore the azimuth magnetic field, which formed in the region between the central current column and the plasma shell, can exist during quite a long time. So one can expect [9,10] that, the first, the field growing towards the system axis, plays role of stabilization when plasma shell compresses in it (under the action of the main pulse magnetic field), the second, the plasma shell stabilizes long-wave perturbations of the axis current column like conductive coaxial housing. In the second case when the directions of the main current and preionization current coincide, the stabilizing magnetic field doesn’t form in the capillary and plasma proves to be less stable.

4 Conclusion In summary, in the experiments carried out on the SIGNAL facility there was observed a soft X-ray lasing in Ne-like Argon plasma when the main current pulse flows in the opposite to the preionization pulse direction. In the case of coincident currents directions the x-ray lasing wasn’t observed. We assume that preionization current role isn’t just creation of ionized gas for further plasma fast tearing from capillary walls during the main current pulse (Z-pinch effect) but also creation of stabilization magnetic field.

Acknowledgments We gratefully acknowledge fruitful discussion with Dr. Vladimir Lykov and also Konstantin Safronov for the help in this work.

References 1. A.V.Vinogradov, J.J.Rocca. Qvant. Elec. 2003. №1. p.33. (in russian). 2. G. Niimi et al., Proc of 28-th IEEE Int. Conf. on Plasma Science and the 13-th IEEE Int. Pulse Power Conf. Las Vegas, 2002, p.746. 3. V.I. Afonin, Phys. Plasma, 2001, v.27, p.614. (in russian). 4. V.S.Imshennik, N.A.Bobrova, Dinamika stolknovitelnoy plasmy, Moscow, Energoatomizdat, 1997, p.320 (in russian). 5. A.M.Gafarov et.al. PTE. 2001. №1, p. 80 (in russian). 6. O.N.Gilev et. al.,Phys. Plasma, 2006, v.32, №2, p.160-165 (in russian).

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7. N. Sakamoto et al. Proc. of 15th Int. Conf. on High Power Particle Beams, St. Petersburg, 2004, p.722. 8. V.I. Derzhiev, V.I.Zhidkov. Izluchenie ionov v neravnovesnoi plotnoi plasme, Moscow, Energoatomizdat, 1989, p.160 (in russian). 9. L.A. Artsimovich, Upravljaemye termojadernye reaktsii, Moscow, Fizmatlit, 1961, p.468 (in russian). 10. V.E. Golant, A.P. Zhilinskiy. Osnovy fiziki plasmy, Moscow, Atomizdat, 1977, p.384 (in russian).

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