Pulsed Power

9(y) :::: 0.95 - l .03y 2 •

From formula (3 . 1 ) it follows that the plot of the dependence (lg j) IE 2 = f(l/E) is a straight line. This, however, is the case for the FE current densities j :s: 1 08 Ncm2 • For higher current densities, the function j (E) is almost independent of work function
9

f2i E312yE r.-112 ov-;;; e

(3 .2)

'

where s0 is the dielectric constant; e and m are the electron charge and mass; YE is a factor, determined by the emitter shape and size, whose value is of the order of unity, and re is the radius of the emission area. (b)

(c)

.. (e)

(g)

., (h)

�

(i)

•

Figure 3.1. Various types of emiSSion centers leading to vacuum breakdown: microprotrusions (a), dielectric inclusions (b), oxide and other inorganic dielectric films (c), adsorbed gas layer (d), grain boundaries emerged on the surface (e), micro particles {f), products of oil vapor cracking (g), edges of craters produced by breakdowns (h), and pores and cracks (i)

Chapter 3

32

A vacuum breakdown is initiated in the main by the FE current from microprotrusions present on the cathode surface. The electric field at the tips of microprotrusions is enhanced many times compared to the average field; therefore, the notion of the factor of electric field enhancement �E is introduced. This factor is defined as the ratio of the actual electric field at the protrusion tip to the average macroscopic field Eav = Vld, where V is the voltage across the gap and d is the electrode separation. Relationships between the factor �E and the irregularity parameters were found for simple protrusion geometries (Latham, 1 995). For the practically useful range of �E values, one can use simple approximate relations between �E and hlr, where h and r are the microprotrusion height and tip radius, respectively. For instance, for an ellipsoid with �E = 7-1 00 we have

ah �E = - + 1, r where a is of the �E = 1 0- 1 000

(3.3) order of unity; for a cylinder with a spherical tip and

h �E = - + 2, r

(3.4)

and for a cone with a spherical tip, cone angle e = 5-1 0°, and �£ = 20-3000 (3 .5) 2.2

Vacuum breakdown criteria

The breakdown criteria are of importance in characterizing the phenomenon of vacuum breakdown. We now consider the main criteria associated with pulsed and de voltages. In a study of the pulsed breakdown of a vacuum gap with a point tungsten cathode whose tip radius and cone angle were known (Mesyats and Proskurovsky, 1 989) it was established that the time delay to breakdown, td, and the density of the FE current from the point tip are related as (Fig. 3 .2) 2 1· td = const 1 •

(3.6)

It can be seen that, in accordance with formula (3.6), on the double logarithmic scale, all experimental points fall well on a straight line with the slope equal to 2. It follows that the product of the squared current density by the time delay to the explosion of a field emitter is an almost constant quantity over wide limits of td andj.

THE VACUUM DISCHARGE 1 09

33 j [Ncm2] 108

107

1 09

1 08 1 07 1 06 s �

";;;' 1 05 1 04 1 03 1 02 1 01 1 00

0.5

0.7

0.9

Eo

1.1 1 .3 · 1 0-8 [V/cm]

1 .5

1 .6

Figure 3.2. Explosion delay time as a function of electric field (I) and current density (2) for a tungsten field emitter

From this plot we find that P td = 4 · 1 09 A2 ·s/cm4• Also given in Fig. 3 .2 is the dependence of the explosion delay time td on the electric field at the emitter tip, E0, for the same experimental points. As the electric field Eo is increased from 7· 1 07 to 1 .3 · 1 08 V/cm, the critical current density increases from 4.5 · 1 07 to 2.2 · 1 09 A/cm2, which in tum causes the time delay to the point explosion to decrease from 4· 1 o-6 to 1 · 1 o-9 s. This suggests a very strong dependence of the breakdown delay time on the electric field at the point tip. Formula (3 .6) is also valid for plane-parallel electrodes having microprotrusions on the surface. Thus, the criterion for a pulsed breakdown to occur in a vacuum gap between a point cathode and a plane anode is relation (3.6). On the other hand, from the studies of electrically exploded conductors it is well known that (3.7)

where td is the explosion delay time, the quantity h is called the specific action for the explosion, and j is the current density in the conductor. The quantity li is determined by the metal type and only weakly depends on current density. Therefore, this quantity can be considered invariable for a given metal over a certain range of current densities. The electrical explosion of metals is discussed in details in Chapter 1 5 and by Mesyats (2000), Burtsev et a/. ( 1 990), and Chace and Moore ( 1 959, 1 962). Thus, the data presented in this chapter provide strong grounds to believe that for a point cathode the breakdown phase ends with the electrical explosion of the point

Chapter 3

34

tip. After that, the spark phase begins which is associated with explosive electron emission. The values of h for several metals are given in Table 3 . 1 (Mesyats, 2000). Table 3.1.

Metal

Cu

h

4.1

AI 1 .8

Au 1 .8

Ag 2.8

Ni

Fe

1 .9

1 .4

Alpert et a/. ( 1 964) investigated the breakdown of vacuum gaps of spacing 1 0-4-1 em at a de voltage. They established that for metals, such as Al, Cu, Au, Pt, Mo, W, and other, the breakdown electric field is independent of gap spacing. For instance, for tungsten it is (6.5 ± 1 } 107 V/em (Fig. 3 .3). In accordance with formula (3 . 1 ) for the FE current, this fact can be interpreted so that breakdown occurs as the FE current density reaches a certain value, i.e., j = const2 .

(3.8)

Relations (3.7) and (3.8) are criteria, respectively, for pulsed and de breakdown of vacuum gaps. They in fact imply that a vacuum breakdown occurs as a result of the electrical explosion of a cathode microprotrusion where the energy density reaches high values due to the heating of the microprotrusion by the FE current. 1 08

2:::.

e 1 07

.... c

�

� 1 06 ws

1

c

w-4

2

0

0

0

w-3

3

0

...s.� �

ovo

v ov 0

a

a

a

1 00

w-z w-1 d [mm]

101

Figure 3.3. Local breakdown electric field at a cathode as a function of electrode separation for tungsten electrodes. Points 1, 2, and 3 are taken from different publications

The above vacuum breakdown criteria imply that the breakdown voltage is directly proportional to the gap spacing, Vbr d. However, a number of experiments have shown that there is no direct proportion between Vbr and d, but Vbr oc da. , where a < 1 . This is a manifestation of the so-called "total voltage effect". At first glance, it seems that this effect contradicts to the breakdown mechanism associated with microexplosions. This, however, is not -

THE VACUUM DISCHARGE

35

the case. The explosion of cathode microregions due to the concentration of energy in them is a universal process. The total voltage effect implies that the FE current is too low for a microexplosion to occur and some other phenomena should be involved to intensify the energy concentration in cathode microvolumes. All these phenomena result in the formation of plasma at the cathode that substantially promotes the microexplosions. A vacuum breakdown may occur even if the electric field is considerably lower than that determined by criteria (3.7) and (3 .8), provided that plasma comes to the cathode from an external source. The minimum energy necessary for a plasma capable of initiating breakdown to be generated at the cathode is - 1 o-s J (Mesyats, 2000). In the presence of anode plasma, this energy is several orders of magnitude greater. The average electric field necessary for breakdown to occur may be in this case lower by one or two orders of magnitude than that required in the absence of plasma at the cathode. There exist two mechanisms for the initiation of a vacuum breakdown by the cathode plasma: due to the enhancement of the current density at cathode microprotrusions and through the charging of dielectric films and inclusions by the current of the plasma ions, followed by the breakdown of these films. In the second case, the density of the breakdown-initiating plasma is lower than in the first one by several orders of magnitude (Mesyats, 2000). There are other factors affecting the electrodes of vacuum gaps and leading to breakdown, such as laser irradiation, an impact of an accelerated microparticle on an electrode, the action of an electron beam, fast heating of electrodes, etc., best studied of which are laser irradiation and an impact of a particle. Of key importance in all these cases is that a high energy is concentrated in a cathode microvolume, giving rise to explosive electron emission. Despite the fact that breakdown can be initiated by different ways, the major physical effects involved are the generation of plasma and the interaction of the plasma with the cathode surface, resulting in the formation of an explosive emission center. The minimum energy required for the initiation of breakdown in a vacuum gap by an accelerated microparticle impinging on the cathode is - l o-s J, as in the case where the plasma of a spark acts immediately on the cathode. When plasma is generated at the anode, this results in an ion flow directed toward the cathode. This ion flow, on the one hand, heats the cathode and creates conditions for the generation of cathode plasma and, on the other hand, may lead to the charging of dielectric films and inclusions followed by their breakdown. As this takes place, microexplosions occur at the cathode, initiating a vacuum breakdown in the main gap. In this case, the generation of cathode plasma is substantially promoted by the gas adsorbed at the cathode surface.

Chapter 3

36 THE ECTON AND ITS NATURE

3.

An electrical explosion at the surface of a metal is accompanied by emission of electrons whose current is some orders of magnitude higher than the FE current. This emission was discovered by Mesyats ( 1 966, 1 998) who gave it the name explosive electron emission (EEE). EEE is thermoelectron emission from cathode regions heated to high temperatures due to microexplosions. This emission occurs by individual portions of electrons, which have received the name ectons (Mesyats, 1 966, 1 998, 2000). The term "ecton" was formed from the first letters of the words Explosive Center or

Electron Cluster.

According to the mechanism proposed by Mesyats (Mesyats, 1 966, 1 998, 2000; Smirnov, 200 1 ), during an electrical explosion at a cathode, an electric current will be emitted from the zone of the explosion. Since the FE current density before an explosion generally reaches 1 09 A/cm2, this will result in a substantial "shift" of the explosion toward very high temperatures, which are many times greater than the critical point temperature. Let us use the Richardson-Schottky formula 1

. AT2 exp =

(

-

e

)

,

(3.9)

where A = 1 20.4; a = 3 .79 · 1 0-4,

THE VACUUM DISCHARGE

37 emission & evaporation zone liquid phase solid phase

emission & evaporation zone

(b)

liquid phase

Figure 3.4. Geometry of an emission center on the tip of a point cathode (a) and on the surface of a plane cathode (b)

This effect is clearly demonstrated by the dependence of current density j on time t plotted for different currents emitted from microregions of the surface of a plane copper cathode (Fig. 3.5). These plots were constructed based on the predictions of the erosion-emission model of an ecton (Mesyats, 2000). In terms of this model, an explosion is replaced by the evaporation of the cathode material from overheated emission centers. The Joule heating of the metal, the evaporation effects, the cooling by heat conduction, and the electron emission effects are taken into account.

100

t [ns]

Figure 3.5. Time behavior of the explosive emission current density at a copper cathode

38

Chapter 3

Let us consider a conical emitter exploding at an initial FE current density � 1 09 A/cm2 • Supposing that a considerable portion of the energy required for the tip of a point to explode is supplied due to the heating of the point in the condensed state, we can determine the principal parameters of the ecton. For this case, the specific action can be considered to be Ji

c I'expl In Ko To '

=p

(3 . 1 0)

where Texpl is the temperature at which the explosion occurs, To is the initial temperature, p is the specific mass, c is the specific heat, and Ko is the coefficient of proportionality between resistivity and temperature. For a current I emitted from the point tip, by solving the heat problem, one can find the temperature distribution in the tip by the formula (3 . 1 1 ) Using formula (3 . 1 1 ), one can also determine the radius rexpl at which the temperature Texpl becomes higher than the formal critical temperature associated with the explosion:

re xpl =

[

Ko

J� 12 (t)dt

1 67r2 p c sin 4 (8/4) ln(Texpl /To )

]114

(3. 12)

It is assumed that the whole of the metal confined within this radius will explode, and the resulting plasma will be removed from the cathode. The first assumption underlying this ecton model is that relation (3 . 1 2) should be involved in formula (3 . 1 0) li obtained experimentally. In view of the fact that for all cases of interest we may put sin (8/4) - (8/4), we obtain (Mesyats, 2000)

(3. 1 3) We already mentioned that the ecton lifetime is limited due to the rapid cooling of the explosive center by heat conduction, the ejection of heated atoms and ions of the cathode metal, and the decrease in current density with increasing the radius of the emission zone. The second assumption is that the ecton zone cools only due to heat conduction and an increase in radius of the explosion zone. An ecton ceases

THE VACUUM DISCHARGE

39

to operate when the radius rexpl becomes equal to the distance "A. for which heat is transferred by conduction. In this case, we have (3 . 1 4)

pc

where a = ').) is the thermal diffusivity. Let us designate the radius within which this assumption is valid as re, the operating radius of an ecton at the cathode. Then from (3. 1 3) and (3. 1 4) for I = const we obtain (see Fig. 3 .6) 2/

r.e = ---=-1t (ah )I /2 94 '

(3. 1 5)

and the ecton operation time

=

2

I fe n2 a 2 h e 4

.

(3 . 1 6)

The mass of the material removed during the ecton operation is (3. 1 7) Substitution of re from (3 . 1 3) into (3 . 1 7) yields

Me

J 3p -- 31t2 (ah )3/2 e 4 . 2

---==-''--­

(3 . 1 8)

The electron charge transferred by the ecton will be (3 . 1 6),

=

qe

n2 a 2 h 9 4

.

qe Ite , or, in view of

The mass per unit charge lost by the cathode will be Yi Yi

= i p (�

)112

=

= Melqe ,

(3. 1 9) or (3.20)

It follows that in terms of our model, the mass per unit charge lost by a cathode depends only on the properties of the cathode material. Table 3.2.

Metal

Cu

a. , cm2/s a1 , cm2/s

1.17

p,

g/cm3

Ag 1 .74

Au

AI

1 .28

0.94

Mo 0.55

Fe

Ni

0.64

0.23

0.23

w

0.42

0.55

0.50

0.35

0. 1 3

0. 14

0.07

0. 1 2

8.90

1 0.50

1 9.30

2.70

10.20

1 9.30

7.90

8.90

40

Chapter 3

To estimate the parameters of the processes that occur during the operation of an ecton, we give the values of the thermal diffusivity in the liquid and solid phases for several metals listed in Table 3 .2 (Mesyats, 2000). The values of the specific mass for these metals are also given.

4.

THE VACUUM SPARK

We shall consider the current of a vacuum arc for the case where a rectangular voltage pulse arrives at a vacuum gap through a transmission line. A typical waveform of the current flowing through such a gap is shown in Fig. 3 .6, where td is the breakdown delay time and fs is the switching time, which is generally measured between the points at which the current makes up 1 0% and 90% of the peak current. Numerous investigations have shown that, irrespective of the applied voltage and electrode geometry, the time fs depends on the cathode material and on the cathode-anode gap spacing, and that d/t5 1 06 cm/s (Fig. 3 .7). The current is pure electronic, which is evidenced by its deflection in a magnetic field and by the x radiation from the anode (Mesyats and Proskurovsky, 1 989). �

----....__ ts

1---l

--,.jr---2 ns

Figure 3.6. Spark current oscillogram, taken with a capacitive voltage divider, for d = 0.5 mm,

V0 = 50 kV. The voltage pulse arrived at the test vacuum gap through a coaxial cable. The first spike was due to the displacement current through the vacuum gap

Figure 3. 7. The switching time as a function of gap spacing for aluminum (1), copper (2), and molybdenum electrodes (3) (a) and the delay time as a function of average electric field for molybdenum (1), copper (2), aluminum (3), lead (4), and graphite electrodes (5) (b)

THE VACUUM DISCHARGE

41

This current is the current of explosive electron emission resulting from the appearance of a great number of secondary ectons, the origin of which will be discussed below. The electron emission from the cathode of a vacuum gap proceeds by portions, ectons, which appear in great numbers. Therefore, for high currents, the discrete character of this emission can be neglected and approximate dynamic current-voltage characteristics can be constructed which relate the gap current and voltage to the gap spacing and to the time. In the general form, the spark current is determined by the modified Child-Langmuir relation (Mesyats and Proskurovsky, 1 989) I(t) = A V 312 F(vtld) ,

(3 .2 1 )

where V is the time-varying voltage across the spark gap, v i s the velocity of expansion of the plasma generated by cathode microexplosions, d is the cathode-anode gap spacing; the constant A and the function F depend on the cathode and anode geometry. If current is measured in amperes and voltage in volts and if vt � d/2, we have for a plane anode and a point cathode A = 37· 1 0-6 and F = vt/d , while for plane-parallel electrodes A = 44· 1 0-6 and F = (vt/d)2 • The current-voltage characteristic of a spark can be calculated more rigorously (Mesyats and Proskurovsky, 1 989). In doing this, the applied electric field is assumed constant. The relationship between the relative current and the time, I(T) , is plotted in Fig. 3 .8, a, where I = RIIV0 and T = vtld. These curves are obtained for different values of (3.22) where n is the number of simultaneously operating EEE centers and R is the resistance of the discharge circuit, which is equal to the wave impedance of the transmission line through which the pulse arrives at the gap. If we, as usual, define the relative time during which the spark current rises as the time of the current rise from 1 0% to 90% of its peak value, T5, we then get 15 = dT's(B)/v.

(3.23)

The function T5(B) is plotted in Fig. 3 .8, b. Let us analyze the results obtained. 1 . The form of the function I(T) fits well to the breakdown current waveforms (see Fig. 3 .7). 2. The time it takes for the spark current to increase from zero to its peak value is independent of the parameters of the external circuit; it is directly proportional to the gap spacing and inversely proportional to the velocity of propagation of the emitting plasma front.

42

Chapter 3

3. The switching time Ts (or fs) is measured between the 1 0% and 90% levels of the peak current (voltage), and the change in Ts (or fs) is thus associated only with the deformation of the J(t) curve. 4. Formulas (3.22) and (3 .23) show a weak dependence of the time fs on n, resistance R, and voltage V0, and the function Ts(B) admits both a slight increase and a decrease in time fs with increasing V0• (a)

0

(b)

0.4

0.2

T

0.8

0.6

0

2

B

4

Figure 3.8. The calculated current as a function of time in relative units (a) and the relative switching time as a function of parameter B (b)

As mentioned, a cathode microexplosion is followed by the generation of plasma at the cathode. This plasma contains singly, doubly, triply, and other multiply charged ions (of AI, Cu, Mo, and other metals); its temperature is 4:-5 eV and its spatial distribution is nonuniform. Immediately in the cathode region, the plasma density is 1 02 1 cm-3 or even more and it falls in inverse proportion to the squared distance (Mesyats and Proskurovsky, 1989; Mesyats, 2000). The plasma expansion velocity for six metals is presented in Table 3.3. This is the velocity of motion of the leading layers of the plasma, estimated using the measured gap closure time. The mass velocity is somewhat lower; it is determined from the mechanical action of the plasma jet on the cathode surface. Table 3.3. Cathode plasma expansion velocity AI Cu

Pb

Mo

Ni

w

v,

1 .0

1 .8

1.4

1 .8

Metal

1 06 cm/s

1 .8

1 .7

The plasma exerts on the cathode in the microexplosion zone a pressure of the order of 1 09 Pa. This pressure is exerted on the liquid phase of the metal. The matter is that during the operation of an ecton a liquid-metal pool is formed on the cathode surface due to Joule heating. The pool radius is approximated by the formula (3.24) where a is the thermal diffusivity and fe is the ecton operation time. The pool radius is generally of the order of 1 0-4 em (for Cu, AI, Mo, and other

THE VACUUM DISCHARGE

43

metals) (Mesyats and Proskurovsky, 1989; Mesyats, 2000). This short-term (te � 1 o-s s) pulsed pressure causes the liquid metal to splash out in the form of jets and droplets, whose velocities are of the order of 104 crn!s. This is evidenced by the micrograph of a crater formed on a cathode by a current of -100 A during 20 ns, given in Fig. 3 .9. In this micrograph, solidified metal jets and droplets are seen. For a copper cathode, the number of metal droplets is 2· 1 07 c-t and the most probable droplet diameter is - (0. 1-0.2) J..lm (Mesyats and Proskurovsky, 1989).

Figure 3. 9. Micrograph of the surface of a plane copper cathode, taken after a single current pulse of duration tp = 20 ns

Thus, the liquid and plasma phases of the metal are formed on the cathode. Therefore, the mass removal from the cathode, or the cathode erosion, occurs both in liquid and in plasma form. For conical point cathodes with a small cone angle, erosion takes place mainly in the liquid phase. For a linearly rising spark current (/ = Kt), the reduced mass lost by the cathode (erosion rate) in the liquid phase is given by the formula (Mesyats, 2000) Yt

=

4pK vz1vz

3J';. 9(3h:)314

,

(3.25)

where p is the mass density of the cathode, tp is the duration of the spark current, 9 is the cone angle, and lim is the specific action of the current required to heat the metal to the melting point (see Table 3.1). If the spark voltage V varies insignificantly, the rate of current rise for a point cathode is

K = 37

· 10-6V312 v

-----

d

'

(3.26)

44

Chapter 3

where v is the expansion velocity of the cathode plasma and d is the gap spacing. Let us estimate y1 for copper ( Jim � 1 09 A2 s/cm4) , putting K = 2· 1 07 A/s, tp = 4· 1 0-8 s, and 0 = 1 0°. Thus we get y1 = 5· 10-4 g/C. Figure 3 . 1 0 presents the dependence of y1 on the cone angle obtained experimentally for Mo and W (Mesyats, 2000).

I Q-3

10

20 e [deg.]

30

40

Figure 3. 10. Reduced mass lost by a conical cathode versus cone angle. Cathode material: Mo (1, 3) and W (2, 4); fp = 5 (1, 2) and 20 ns (3, 4); V0 = 20 kV; d = 2 mm

As can be seen from Fig. 3 . 1 0, the reduced mass lost by a conical point decreases with increasing angle 0. For large angles, the mass removal in the plasma phase prevails. Let us denote the reduced mass lost by a cathode in the form of plasma (ions) by y;. We estimate this quantity by formula (3 .20) of the simplest ecton theory: Y ; = tP(alh)1 12 • Using the data for copper given in Table 3 . 1 and Table 3 .2, we obtain for y; � 7 · 1 0-5 and 6·10-5 g/C solid and liquid copper, respectively. Table 3.4 lists experimental data for the reduced mass lost by a cathode in the plasma phase for four metals (Mesyats, 2000). Table 3. 4.

Metal

Y; ,

I 0-5 g/C

w

Au

Ag

Cu

16

9.2

4.2

4.0

An important question is by which mechanism new ectons are formed after the appearance of a primary one (bearing in mind that the spark current flows continuously). This occurs due to the explosion of liquid-metal jets or neighboring microprotrusions on their interaction with the plasma generated by previous ectons. The existence of liquid-metal jets is testified by the cathode crater shown in the micrograph in Fig. 3.9. The fact that plasma is

45

THE VACUUM DISCHARGE

generated by cathode microexplosions is supported by the photographs of the luminosity in a vacuum gap, taken at an exposure time of 3 ns (Fig. 3 . 1 1 ) The essence of this effect is as follows: If a cathode protrusion (or a liquid-metal jet) is surrounded with plasma, the density of the current flowing through the protrusion base will be �1 times greater than that at its surface. (�1 S/S0, where S is the total area of the protrusion surface and S0 is the cross-sectional area of the protrusion base.) The appearance of ectons immediately in an emission center is due to the interaction of a liquid-metal jet with dense plasma, while their formation near an emission center results from the interaction of dense plasma with the cathode microprotrusions present in this region. Recall that the criterion for the appearance of ectons within 1 o-9 s under the action of dense plasma on a cathode microprotrusion is nivi ;::: 1 028 �1- 1 cm-2 s- 1 (Mesyats, 2000). .

=

(a)

DI = 1 .5 Dz = 1 .5

(b)

(c)

(d)

D1 = 1 1 D2 = 5.6

D 1 = 22 Dz = I I

Figure 3. 11. Photographs of the cathode and anode plasma luminosity (3 ns exposure time) for d = 0.35 mm; V0 = 3 5 kV; copper electrodes; pulse rise time = I ns; D1 and D2 are camera diaphragms. The frames correspond to t = 4 ns, I = 0 (breakdown phase) (a); 8 ns, 20 A (b); 22 ns, 1 50 A (c), and 34 ns, 230 A (d) (arc phase)

Now the question arises of why the current density is enhanced. Immediately in the microexplosion zone, the ion current density is not over - 1 07 A/cm2 • For a liquid-metal jet to explode within 1 0-9 s it is necessary to have a current density of 1 09 A/cm2, i.e., �1 should be ;::: 1 02• For a jet having the shape of a cone, �1 � 2/8, where 8 is the cone angle. For the cathode spot of a copper-cathode arc, we have 8 � 0.5 (Mesyats, 2000) and, hence, �1 � 4; that is, the factor of current density enhancement is too small. For a

46

Chapter 3

cylindrical jet, we have pj 2h/r, where h and r are the jet height and radius, respectively. The quantity� pj coincides in value with the electric field enhancement factor pE, which, for a pulse duration of 5-50 ns, is not over 1 0-20 (Mesyats and Proskurovsky, 1989). It follows that pj � 1 02 cannot be achieved for a conical or cylindrical jet. A much higher degree of current density enhancement is attained with a sphere attached to the apex of a cone. This is the case where a droplet breaks off a liquid-metal jet. As this takes place (Fig. 3 . 1 2), the current density in the droplet-cone bridge increases by a factor pj = 4rilr2, where rd is the radius of the droplet and r is the radius of the bridge. The process of breakout of the droplet will last a time of the order of t = rdlvd, where vd is the velocity of motion of the droplet. Since vd - 1 04 crnls, the breakout time will be - 1 o-9 s. For the bridge to explode within the time t, the current density should be j�

(�r ( � r � h ,

(3.27)

Liquid metal jet

"� Cathode Figure 3. 12. Sketch of a liquid-metal jet at which an ecton is formed. rm is the radius of the molten metal zone, r. is the length for which the ecton zone is heated; Pm is the plasma pressure on the liquid metal; Pe is the plasma pressure at the instant the ecton ceases to operate, and I is the current

Proceeding from the fact that during the spark phase of a discharge the current from the cathode occurs in the form of individual portions of electrons (ectons) we estimate the number of ectons and the rate at which they come in the gap. In the foregoing, we supposed that every ecton cycle is

,

THE VACUUM DISCHARGE

47

accompanied by one liquid-metal droplet leaving the cathode. This takes place when the rates of current rise are not very high: dlldt � 1 08 A/s. In this case, the charge of the ecton electrons will be qe :::::: 1/yd , where Yd is the number of droplets per unit charge. The total number of ectons formed during the spark phase is determined by the relation

Its 1 its N0 = 0 Idt = yd 0 Idt, qe

_

(3.28)

where fs is the duration of the spark phase. If the evolution of the spark current is approximated by a linear function, the total charge built up during the spark phase is given by

(3.29) where Ia is the peak current, which corresponds to the current of the vacuum arc. Since fs - d/v, then

No = !h._ = IadYd . 2v qe For Ia = 100 A, d =

(3.30)

1 em, Yd = 2 · 1 07 c-t (for copper) (Mesyats and Proskurovsky, 1 989), and v :::::: 2 · 1 06 cm/s, relation (3 . 30) gives the number of ectons generated during the spark phase of a vacuum discharge N0 :::::: 1 03• There is another, highly efficient, way of initiating secondary ectons where the cathode plasma affects the cathode surface containing dielectric films and inclusions. The ion current of the plasma charges the dielectric, the latter is broken down, and the plasma resulting from this event promotes the formation of a new ecton. The electron beam that is formed at the cathode due to EEE is then accelerated and, arriving at the anode, heats the latter. This heating results in the formation of anode plasma, liquid metal, and metal vapors, which generally appear with some delay relative to the appearance of the cathode plasma. The velocity of the cathode plasma may reach 1 06 cm/s (Mesyats and Proskurovsky, 1 989).

5.

THE SURFACE DISCHARGE IN VACUUM

A knowledge of the mechanism of a discharge over a dielectric surface in vacuum is of great importance since dielectrics are widely used in high­ voltage vacuum devices. A major application of this type of discharge is associated with electrical insulators. A spark over a dielectric in vacuum may serve as a source of ultraviolet radiation, which can be utilized, in

48

Chapter 3

particular, for pumping gas lasers and in pulsed switching devices. For instance, spark gaps with this type of discharge are convenient for peaking pulses; they are also used as triggers in triggered vacuum switches. Of particular importance is the use of surface vacuum sparks in metal-dielectric cathodes for the production of high-power electron and ion beams. In this section, we shall focus attention on pulsed discharges (in accordance with the scope of this monograph). This type of discharge is sometimes referred to as the sliding discharge or flashover. Comparing the phenomenology of a sliding discharge with that of a discharge between metal electrodes in vacuum, one can see that a dielectric introduced in a vacuum gap reduces abruptly the electric strength of the gap. Here we are up against a number of phenomena that do not occur in a vacuum gap. Among them are the enhancement of the electric field at the cathode due to the presence of metal-dielectric microgaps, the charging of the dielectric surface by electron bombardment, and the appearance of a gas medium in the discharge gap as a result of the gas desorption from the insulator and its destruction. The presence of a dielectric in a vacuum gap results in an enhancement of the electric field in the region of the cathode-dielectric contact due to the existence of microgaps. Kofoid ( 1 960) investigated the processes occurring at a metal-dielectric contact on application of an electric field. The electrode and the insulator were immersed in a magnetic field normal to the electric field to remove electrons from the discharge gap. These electrons were "dumped" onto grounded plates coated with a phosphor. The voltage between the electrodes at which the phosphor starts to fluoresce is a criterion for evaluating the intensity of the contact phenomena. The electron yield from the contact increases with dielectric permittivity. This has the result that the pulsed voltage at which a luminosity appears at the cathode decreases almost sevenfold as the dielectric permittivity s is increased from 6.6 (steatite) to 1 800 (barium titanate). An increase in electric field in the contact region resulting from the plane-to-point change in cathode geometry also increases the electron current. A change of the cathode material has a slight effect on the electron yield from the contact. The electric field at the cathode-dielectric contact is enhanced because the surfaces of both the dielectric and the cathode are not perfectly smooth. They touch one another only by their protrusions (Fig. 3 . 1 3). To roughly estimate the electric field at the contact, one may idealize the contact geometry. Let us denote the averaged microgap width by 1:1 and the dielectric thickness by d and assume that the gap length is much less than its width so that the field in the gap could be considered uniform except for the edges. The field strength in the gap Ec can be found as that in a gap connected in series with a dielectric:

THE VACUUM DISCHARGE

49

(3 .3 1 ) Based on formula ( 3 .3 1 ) , two conclusions can be made. First, if dis 11 « 1 , then (3.32) where E = Vld is the average electric field in the gap. Thus, the electric field in the gap is enhanced dl11 times. This is the case of a high-s dielectric. Second, if d/s /1 » d, then (3.33) that -is, the electric field is enhanced s times. This corresponds to the case of a dielectric with comparatively low s.

Dielectric Figure 3.13. Sketch of a dielectric-cathode contact. rc is the tip radius ofthe sharpest cathode protrusion, Ll is the average width of the cathode gap, and d is the thickness of the dielectric.

(a) the point in contact with the dielectric and (b) the point inside the cathode gap

However, the field at the cathode microprotrusions is even higher due to its geometric enhancement. For microprotrusions of height h and tip radius rc. if h < 11, we have (3 .34) where �E is the electric field enhancement factor. The value of �E lies in the range 10- 1 00. Hence, the total field enhancement factor for high s is of the order of dh ll:!.rc . For d = 1 em, 11 = 1 0-3 em, h = 1 0-4 em, rc = 1 0-5 em, and V = 1 04 V, the electric field at the surface of a microprotrusion (e.g., such as protrusion b in Fig. 3 . 1 3) will be 1 08 V/cm. A protrusion of this type will

50

Chapter 3

explode within - 1 0-9 s (see Fig. 3.2), giving rise to the cathode plasma, explosive electron emission, and the cathode spot. The leading role of the cathode in a discharge is supported by numerous data [see, e.g., (Kofoid, 1 960)]. The electron current from the cathode increases with voltage V, cathode surface roughness (�E), and dielectric permittivity s. Besides a field-emission-induced explosion, there is another possibility of the initiation of a cathode microexplosion, which is associated with a microdischarge over the surface of a dielectric from a microprotrusion being in contact with the dielectric (protrusion a in Fig. 3 . 1 3). In such a discharge, plasma will move from the protrusion, producing a displacement current. This current closes through the protrusion and heats it, and the protrusion eventually explodes. The probability of this type of explosion increases with dielectric permittivity. This will be discussed in detail in Chapter 22 as regards with the operation of metal-dielectric cathodes. The site where a micropoint is in contact with a dielectric is called a triple junction. At such a junction, the cathode metal, the dielectric, and the insulating medium touch each other. In our case, this is a metal-dielectric-vacuum junction. As shown below, the processes occurring at triple junctions play a fundamental role in surface discharges; in particular, they govern the operation of metal­ dielectric cathodes. Important evidence for the microexplosions occurring at the cathode is provided by the luminosity spectra measured early in a discharge. In the experiment described by Bugaev and Mesyats ( 1985), barium titanate (s = 1 800) and titanium dioxide ceramics (s = 80) were used. The cathode was a tungsten needle. At near-threshold voltages, the lines of the cathode metal (W I, W II) as well as the lines of neutral barium (Ba 1), singly ionized barium (Ba II), and titanium (Ti I), being constituents of the dielectric, were detected in the spectrum of the discharge luminosity. As the pulsed discharge voltage increased, these lines became more intense and new lines pertinent to the ceramics appeared in the spectrum. For the pulse duration shortened to 2 ns, the dielectric disintegrated at higher voltages. However, the spectral constitution of the luminosity and the sequence of appearance of lines in the spectrum remained unchanged. The data reported by Bugaev and Mesyats ( 1 985) suggest that the lines of the cathode metal appeared in the discharge luminosity spectrum almost simultaneously with those of the dielectric. It should be borne in mind that the spectral sensitivity of the setup used in this experiment in the region of the W I lines (4302 A) is about half that for the other lines detected. Therefore, the frequency at which the W I lines appeared in each series is underestimated. If we know the species composition of the discharge plasma at a dielectric and the times at which the lines of the cathode metal and dielectric appear in the discharge spectrum, we can determine the characteristic times

THE VACUUM DISCHARGE

51

of the processes leading to the explosive disintegration of the cathode protrusion and dielectric. Assuming for the size of a microprotrusion r � 1 o-4- 1 o-s em, we obtain the local electric field at the protrusion tip E � (1-9)· 1 08 V/cm. For this field, the density of the field emission current from the protrusion will be of the order of 1 09 A/cm2 • At this current density, the explosion and the appearance of plasma at the cathode will occur in fd � 1 0- IO s. If the electric field in the cathode region is lower than that mentioned in the previous section, the cathode microexplosions may occur and the cathode spot may appear only following the processes taking place at the dielectric surface. It was demonstrated (Bugaev and Mesyats, 1 985; Boersch et al. , 1 963; Gleichauf, 1 955) that the predischarge current consists of two components: microdischarges and a steady-state current. Microdischarges occur at voltages far below the breakdown voltage and result in short-term self-extinguishing current bursts. The steady-state component is due to the charging of the dielectric surface. As a voltage is applied to the gap, some electrons from the cathode region arrive at the insulator. Since the secondary emission coefficient for a dielectric is greater than unity, the region bombarded by the electrons will be positively charged. As this takes place, the field component that attracts electrons to the insulator surface is enhanced. Thus, the positive charge can be extended up to the anode. In this case, the conditions at the dielectric are stabilized if the yield of secondary electrons is less than unity throughout the dielectric surface. The appearance of a positive charge at the dielectric surface gives rise to a redistribution of the potential over the dielectric length. As a result, the electric field decreases at the anode and increases at the cathode. In the general case, we have a potential distribution with a rise at the cathode rather than a linear one. Smith ( 1 964) and Watson ( 1 967) investigated the dependence of the breakdown electric field on the inclination angle of the dielectric surface to the cathode surface for short applied voltage pulses. They used insulators shaped as truncated cones and found the breakdown electric field as a function of the cone half-angle for different insulator materials. For an angle of 45°, the flashover voltage was a maximum and severalfold greater than in the case of a cylindrical insulator. This dependence holds for a magnetic field applied orthogonal to the dielectric surface (Avdienko, 1 977). A study of the kinetics of development of a pulsed discharge over the surface of forsterite ceramics on the nanosecond scale was performed by Bugaev and Mesyats ( 1 965, 1 967). The electric field in the cathode region was either uniform or nonuniform. For examination, an electron-optical image converter allowing frame photography and a fast oscilloscope were used. Both

Chapter 3

52

instruments offered a time resolution of -10- 1 0 s. The luminescence over the dielectric surface originated at the cathode, but not immediately after the arrival of the pulse. The time from the pulse arrival at the dielectric to the appearance of luminosity varied from discharge to discharge; however, the time between the appearance of luminosity and the onset of current rise, 't, was almost invariable. It is important that for td 't luminescence started immediately (within 1 0- 1 0 s) after the arrival of the pulse. It is noteworthy that the time 't exactly equals the minimum delay time td that results from a statistical analysis of the flashover delay times for this ceramics. Initially, the luminescence was discrete in character. The luminosity consists of several bright spots of diameter less than 0. 1 mm. Subsequently, it moved toward the anode with a velocity of 2. 7 · 1 07 cm/s, increasing in width and becoming brighter. At the instant the luminosity approached or touched the anode, an intense flash occurred. Within a time shorter than o-9 s, the luminosity brightness increased by several orders of magnitude. As the current increased, a bright channel was formed at the dielectric surface instead of a diffuse luminosity. As the cathode luminosity appeared, the current in the gap increased, reaching -1 A within 3 ns, and at the onset of an abrupt current rise (I � 1 0 A) the discharge phase began that lead to an arc. The velocity of propagation of the discharge, v, increased linearly with electric field and at E = 220 kV/cm it reached - 1 08 cm/s. The discharge propagation velocity increased from 2 · 1 07 to 4· 1 07 cm/s as the residual gas pressure in the chamber was increased from 1 o-3 to 1 Pa (Bugaev and Mesyats, 1 967). Thompson et a/. ( 1 980) examined the light patterns of a surface discharge over a dielectric in a uniform field with the use of continuous sweep. They obtained essentially the same results; however, the propagation velocity of the glow from the cathode was substantially greater than in the experiment described by Bugaev and Mesyats ( 1 967) because of the greater E. Figure 3 . 1 4 presents the vacuum dielectric flashover delay time td as a function of the pulsed electric field E for different values of the thickness of cylindrical forsterite tablets (d = 0.3, 0.9, and 2 mm) (Bugaev and Mesyats, 1 965). The voltage pulse rise time was shorter than 1 o-9 s. As the electric field £ was increased from 1 50 to 450 kV/cm, the time td decreased from 400 to 1 ns. The electric field was determined by the formula E = V.)d , where Va is the voltage amplitude. In all these cases, the time it took for the current to reach its amplitude value was less than 1 o-9 s for both the pulsed and the de discharge mode. The switching time was shorter than 1 ns in all cases.

=

I

53

THE VACUUM DISCHARGE 400 �------� 200

s

�

�

d = 2.0 mm

1 00 40 20 10 4 2 L--L----L---�--� 1 00 200 300 E [kV/cm}

Figure 3. 14. Discharge delay time tct as a function of electric field for forsterite tablets of different thickness

A great deal of empirical information on electrical insulation and discharges in vacuum and on surface discharges over dielectrics in vacuum was analyzed by J. C. Martin (Martin et al., 1 996). This information is especially useful in developing super-high-power pulse systems such as high-current charged particle accelerators, x-ray generators, pulsed lasers, and the like. We shall return to the surface discharge over a dielectric in Chapter 22 where metal-dielectric cathodes are considered.

REFERENCES Alpert, D., Lee, D. A., Lyman, E. M., and Tomaschke, H. E., 1964, Initiation of Electrical Breakdown in Ultrahigh Vacuum, J. Vac. Sci. Techno!. 1:35-50. Avdienko, A. A., 1 977, Surface Breakdown over Dielectrics in Vacuum, Zh. Tekh. Fiz. 47: 1 697- 1 7 0 1 . Barbour, J. P., Dolan, W. W., TroJan, J. K . , Martin, E. E . , and Dyke, W. P . , 1 953, Space­ Charge Effects in Field Emission, Phys. Rev. 92:45-5 1 . Boersch, H., Hamish, H., and Ehrlich, W., 1 963, Oberflachene Ladungen i.iber Isolation in Vacuum, Zt. Ang. Phys. 15:5 1 8. Bugaev, S. P. and Mesyats, G. A., 1 965, Time Characteristics of a Pulsed Discharge over a Dielectric-Vacuum Interface on the Nanosecond Scale, Zh. Tekh. Fiz. 35: 1202-1204. Bugaev, S. P. and Mesyats, G. A., 1 967, Investigation of the Mechanism for a Pulsed Surface Breakdown over a Dielectric in Vacuum. II. The Nonuniform Field, Ibid. 37: 1 86 1 - 1 869. Bugaev, S. P. and Mesyats, G. A., 1985, Pulsed Discharge over a Dielectric in Vacuum. In Pulsed Discharges over Dielectrics in Vacuum (in Russian, G. A. Mesyats, ed.), Nauka, Novosibirsk. Burtsev, V. A., Kalinin, N. V., and Luchinsky, A. V., 1990, The Electrical Explosion of Conductors and Its Use in Electriphysical Systems (in Russian). Energoatomizdat, Moscow.

54

Chapter 3

Elinson, M. I. and Vasiliev, G. V., 1 958, Field Emission (in Russian). GIFML, Moscow. Chace, W. G. and Moore, H. K., eds., 1 959, Exploding Wires, Vol. I . Plenum Press, New York. Chace, W. G. and Moore, H. K., eds., 1 962, Exploding Wires, Vol. 2. Plenum Press, New York. Gleichauf, P. H., 1 955, Electrical Breakdown over Insulators In High Vacuum, J. Appl. Phys. 22:394-398. Weast, R. C., Astle, M. J., and Beyer, W. H., eds., 1 989, Handbook of Chemistry and Physics. CRC Press, Boka Raton. Kofoid, M. J., 1 960, Effect of Metal-Dielectric Junction Phenomena on High Voltage Breakdown over Insulators in Vacuum, AlEE Trans. 6: 991 -998. Latham R. V., ed., 1 995, High Voltage Vacuum Insulation: Basic Concepts and Technological Practice. Academic Press, London. Martin, T. H., Guenther, A. H., and Kristiansen, M., eds., 1 996, J. C. Martin on Pulsed Power. Plenum Press, New York. Mesyats, G. A., 1 966, Doctoral Thesis Study of the Generation of High-Power Pulses of Nanosecond Duration. Tomsk Polytechnic Institute Mesyats, G. A. and Proskurovsky, D. I., 1 989, Pulsed Electrical Discharge in Vacuum. Springer-Verlag, Berlin-Heidelberg. Mesyats, G. A., 1 993, Ectons in Electrical Discharges, Pis'ma Zh. Tekh. Fiz. 57:88-90. Mesyats, G. A., 1 998, Explosive Electron Emission. URO-Press, Ekaterinburg. Smirnov, B. M., 200 1 , Physics ofIonized Gases. Wiley, New York. Smith, J ., 1 964, Insulation of High Voltage Across Solid Insulators in Vacuum. In Proc. 1st Int. Symp. on Insulators ofHigh Voltages in Vacuum, Boston, Mass., p. 26 1 . Thompson, J. E., Liu, J., and Kristiansen, M., 1 980, Investigation of Fast Insulator Surface Flashover in Vacuum, IEEE Trans. Plasma Sci. 8: 1 9 1 - 1 97. Watson, A., 1 967, Pulsed Flashover in Vacuum, J. Appl. Phys. 38:20 19.

Chapter 4 THE PULSED DISCHARGE IN GAS

1.

ELEMENTARY PROCESSES IN GAS-DISCHARGE PLASMAS

The overwhelming majority of nanosecond high-power pulse generators use spark gaps as switches. Therefore, the formation of pulses in these generators is strongly influenced by the processes occurring in the discharge plasma. The initial phase of the discharge, from the application of a voltage pulse to the onset of generation of conducting plasma, determines the delay time and jitter of the spark gap operation. The rate of formation of high­ conductivity plasma in the gap is responsible for the rate of voltage rise (the higher this rate, the shorter the pulse rise time). The limiting frequency for stable operation of a generator is determined by the time it takes the spark gap to recover its electric strength. Moreover, when using spark gaps, it is important to know the factors that affect the breakdown voltage of the spark gap. Spark discharges, in different phases of their operation, contain both weakly ionized nonequilibrium plasma of the glow-discharge-plasma type and comparatively strongly ionized quasi-equilibrium plasma of the arc­ plasma type. In the first-type plasma, the average electron energy is much greater than the thermal energy of the molecules. Electrons collide in the main with neutrals rather than with each other or with ions. The energy spectrum of the ions is far from Maxwellian and depends on electric field. The electric field also determines the rate of electron impact ionization. Highly ionized plasma is in a state close to thermal equilibrium; that is, the electron gas and the gas of heavy particles have comparable temperatures, and the temperature determines the degree of ionization.

Chapter 4

56

In our consideration, we shall use the general notions of gas discharge physics described in the monographs by Meek and Craggs ( 1 953), Loeb ( 1 939), Kunhardt and Luessen ( 1 983), Korolev and Mesyats ( 1 998), Bazelyan and Raizer ( 1 997), Bortnik (1 988), and Raether ( 1 964) and from some original papers. In the initial phase of a spark discharge, weakly ionized plasma is generated. The motion of electrons in an electric field E consists of a chaotic motion with thermal velocity 'Vth and a drift motion along the electric field E with velocity Ve. The electron drift velocity is determined from the formula eE Ve = - = � eE,

(4. 1 )

mv

where �e i s the electron mobility and v i s the frequency of elastic collisions of electrons with molecules, which is determined from the relation (4.2) where n is the number of molecules in 1 cm3 , vth is the mean thermal velocity of an electron, and a is the scattering cross section. There is also the notion of the mean free path of an electron between collisions:

A=

Vth v

= _1_ _!__ ncr p -

-

'

(4.3)

where p is the gas pressure. The drift velocity of electrons in not very strong fields is low compared to their chaotic velocity ( Ve « 'Vth) and depends on the ratio Eln or Elp. This is a manifestation of the similarity law, which holds for weakly ionized plasmas. For the required range of Eln, the mobility �e is determined as an average value of vefE. For instance, for air at atmospheric pressure, room temperature, and E 20 kV/cm (n = 2.5 1 · 1 0 19 cm-3 , Eln 0.79· 1 0- 15 V·cm2) we have Ve 1 07 crnls and �e = 500 cm2 /(V·s). In physics of gas discharges, instead of the gas density n, the pressure p = nkT, where k is Boltzmann's constant, is often used. This is convenient and reasonable if the gas is cold and its temperature T can be considered fixed. For convenience, we give the relations between the units of measurement for Eln or Elp. For T 293 K we have Elp [V/(cm·Torr)] = 1 .32Eip [kV/(cm·atm)] = 3 .3· 1 0 1 6£/n [V·cm2 ] 0.33E/n [Td], where one townsend (Td) equals 1 0 17 V·cm2 • The mobility of ions is lower than that of electrons by a factor of several hundreds; therefore, ions, as a rule, make a small contribution to the electric current except when the electron density ne is much lower than the ion =

=

=

=

=

THE PULSED DISCHARGE IN GAS

57

density ni. For ne - ni, the current density j and the conductivity by the relations

cr are given (4.4)

cr = e�ene = e

2 ne

= 2.82 · 10-4 ne [cm1-3 ] (Q · cmt1 .

Since v oc n, the mv v[s- ] conductivity of a weakly ionized gas, cr, is proportional to the degree of its ionization, defined as neln. Generalization of experimental data on electron velocities yields the following approximation: where

(4.5) where n is a numerical exponent determined empirically. The drift velocity of positive ions is described by the relation (4.6) The values of the parameters c � > c2, and n are listed in Table 4. 1 [4]. Table 4. 1.

Gas

N2 02

C02 CN4 SF6

Elp, V/cm·Torr 120-3000 300-4000 1 00-8000 200-2000 1 50-2000 500-5000 1 20-1 000 300-5000 1 5-200 200-1 500

n

c2 .

3.3

0.5

1 1.1

3.75

0.5

1 .58

0.59

0.58

0.76

1 .6 7.1

0.6 0.3

CJ.

1 06

1 04

1 .46 1 .7 3.2

The principal mechanism of the production of electrons and ions in gas discharges is electron impact ionization of molecules and atoms. The number of ionization events Ne per cubic centimeter per second is determined as (4.7) where vi is the ionization frequency, i.e., the number of ionizing acts executed by an electron in a second. The ionization frequency is the main characteristic

Chapter 4

58

of the process rate. It is proportional to the gas density and is determined by the electron energy spectrum. The spectrum, in turn, depends on the ratio Eln. If the ionization frequency is a constant and there is no annihilation, the number of electrons increases in time in an avalanchelike manner by the law Ne = N0 exp ( vt) , where N0 is the number of electrons at t = 0. In an electric field, an electron avalanche develops not only in time, but also in space. All electrons move in a group with the same drift velocity, which is established very quickly, approximately during one collision. Therefore, it is reasonable to characterize the ionization process by an ionization coefficient a, the number of ionizing acts executed by an electron as it moves for one centimeter along the field E. Obviously, we have

a-

V· I

(4.8)

.

In a de field, according to (4. 7), the number of electrons increases along the direction of motion x by the law

Ne = No exp (ax).

(4.9)

For theoretical calculations and estimates, the semi-empirical Townsend formula

( i)

a = Ap exp -

(4. 1 0)

=

is often used. Here, A and B are constants which are chosen based on experimental data (Fig. 4. 1 ) (Bazelyan and Raizer, 1 997). For air we have A = 1 5 (cm·Torrt 1 and B 365 V/(cm·Torr) for 1 00 < E/p < 800 V/(cm·Torr). I Q- 1 1 8 � 6 a

I Q- 1 6 8 a 6 �

M'

�

� �

4

�

�=-

2

�

;>

:>

1 0- 1 2

s::-

tS

8

9 10 1 1 12 13 Eln · 1 0- 1 6 [V·cm2]

4 2

1 0- 1 7 0

200 400 600 Eln · 1 0- 1 7 [V·cm2]

800

Figure 4.1. Frequencies of ionization, v;, and electron attachment, v11, in air (a) and coefficients of electron impact ionization and attachment in elegas (SF6) (b) as functions ofE!n

THE PULSED DISCHARGE IN GAS

59

Besides formula (4 . 1 0), other interpolation formulas can also be used to find the dependence of alp on Elp. For instance, for air

(

)

2 1 a = 1 . · 10-4 E E for 44 < < 1 76 32.2 7 p cm · Torr p

( ) a = 5 9 ( )3 2 p

a = 0.21 E 11 2 3.6 5 p p p

·

E / p

1 cm · Torr

1 cm · Torr

E p

V cm · Torr

for 200 < - < 1000 for 1 10 <

E < 530 p

,

V cm · Torr

,

v

_ _ _ _

cm · Torr

(4. 1 1) Overcoming a potential difference of 1 V in a uniform electric field E and having an established energy spectrum, each electron brings forth, on average, alE electrons (ion pairs). To bring forth one ion pair, this electron should acquire, on average, an energy � eEia. This quantity, being a function of Elp, has a minimum. For the approximation (4.10) , we have �min = eeBIA , where e is the natural logarithm base and e is the electron charge. The minimum corresponds to Elp B. Even under these, most favorable for ionization, conditions, with Elp 365 Vl(cm·Torr), an electron, to bring forth one ion pair, expends an energy �min (Stoletov ' s constant), which is 66 eV for air. This is several times greater than the ionization potentials for N2 and 02 molecules (15.6 and 12 .2 eV, respectively), testifying to great energy losses for electron excitation of molecules. At high electron energies (> 10- 1 5 eV), the electron levels are excited in the main. Ionization events are always accompanied by excitation events; the excited molecules are even greater in numbers than the ions. This is of great importance for a spark breakdown, since there is a high probability that some excited molecules and atoms will emit photons. Photons participate in the generation of the initial electrons that give rise to avalanche ionization. When electron energies are some tens of electron-volts, the inelastic energy losses are much greater than elastic. In this case, elastic collisions are of minor importance compared to inelastic ones, and electrons are scattered in elastic collisions predominantly in the forward direction. Under these conditions, an electron will be gradually accelerated notwithstanding inelastic losses. This is called the electron runaway effect. In nitrogen this effect takes place for Elp � 365 Vl(cm·Torr). In a dense gas, an electron can be accelerated to energies over 1 keV. Electrons not only are born due to the ionization of atoms and molecules, but also annihilate when they recombine with ions or attach to gas molecules. In the course of the recombination of electrons with positive ions, if it is not

= ==

Chapter 4

60

complicated by other simultaneous processes such as ionization, the electron density of a neutral plasma with ne n; decreases with time by the law

noe dne = -�n1 , ne = , dt 1 + �noef

=

noe

=

ne(O) ,

(4. 12)

where � is the coefficient of electron-ion recombination. Electron attachment is one of the most important processes of electron annihilation in electronegative gases. In cold air in the absence of an electric field, electrons attach to oxygen molecules in triple collisions:

(4. 13) In an electric field, where electrons acquire several electron-volts of energy, reactions of dissociative attachment proceed which call for, in contrast to reactions (4. 1 3), an energy to be expended for the decay of molecules:

(4. 14) At low humidity, the electron attachment to oxygen plays the major part. The cross section for reaction (4. 14) increases with gas temperature, and the threshold energy for this reaction is lower than 3.6 eV. This is because vibrationally excited molecules are involved in the reaction and their energy also goes for the decay of molecules. As with ionization, electron attachment in a de field occurs on the background of their drift. The attachment coefficient 11 , which is similar to the ionization coefficient a, defines the number of attachment events experienced by an electron as it moves for 1 em along the field. The similarity law that is valid for ionization processes is also valid for dissociative attachment: 11/n j{Ein). The electron multiplication in an avalanche is described by the equation dneldx = (a - 11 )ne and is determined by the effective coefficient aeff = a - 11 . For air, the ionization frequency and the ionization coefficient a more strongly depend on E/n than the attachment frequency and attachment coefficient 11 , since ionization demands an energy several times greater than that needed for dissociative attachment. Therefore, the curves a/n and 11/n in Fig. 4. 1, b intersect (Bazelyan and Raizer, 1 997). According to the calculations based on the kinetic equation for air, they intersect at Elp � 41 V/(cm·Torr). For lower values of Elp we have a > 11, and the electron avalanche fails to develop. For another technologically important gas, SF 6 (elegas), the curves of a and 11 intersect at Elp � 1 1 7.5 V/(cm·Torr). Correspondingly, the threshold for breakdown is high, and this, along with other acceptable properties of SF 6, is the reason for its use as a high-strength gas insulator and as a fill gas in nanosecond spark gaps. =

THE PULSED DISCHARGE IN GAS 2.

TYPES OF DISCHARGE

2.1

The Townsend discharge. Paschen's law

61

Let us consider discharges o f different types, proceeding from the proportion between the gap spacing d and the critical length of electron avalanche, Xcr. at which the discharge of a single avalanche substantially distorts the electric field applied to the gap. Three types of discharge are distinguished: Townsend, streamer, and avalanche discharges. The distinguishing feature of a Townsend discharge is that the space charge of a single avalanche does not distort the electric field in the gap since Xcr > d, where Xcr is the critical length of the avalanche at which the field of the ion space charge is equal to the external field. For this case, we have (In Ne cr )Ia > d, where Necr is the number of electrons in the avalanche at x = Xcr· If Xcr < d, the dominant role in the development of the discharge is played by the primary avalanche, which changes into a streamer and then into a discharge channel (streamer discharge). For a streamer discharge to exist, it is also necessary that the avalanche emit a sufficient number of photons or runaway electrons capable of ionizing gas molecules near the avalanche head. The photons are emitted by excited gas molecules, whose average lifetime fexc is generally 1 o-9-1 o-s s. Therefore, if the time it takes an avalanche to develop to its critical size, fer• is shorter than fexc, the development of a streamer from the primary avalanche will be hindered. The criterion for a streamer discharge to exist is (In Necr )Ia � d. Finally, there is a type of discharge for which Xcr « d. This is the discharge with a high overvoltage for which (In Ne cr )Ia « d, and it is called the multiavalanche discharge because in such a discharge many avalanches of critical size are formed over the gap width. The secondary electron emission from the cathode is caused not only by positive ions, mentioned above, but also by photons and metastable atoms. In addition, photons give rise to photoionization of the gas. The secondary electrons generate new avalanches and new secondary electrons. If the voltage applied to a spark gap is high enough, the process of current rise ends with an electrical discharge, which is characterized by a drop in gap voltage resulting from the formation of conducting plasma between the cathode and the anode. A major problem in the gas discharge physics is to understand how a highly conducting medium is formed between cathode and anode. For a Townsend discharge, it is supposed that the principal role is played by the secondary electron emission from the cathode that is followed by generation of successive avalanches (Meek and Craggs, 1 953; Loeb, 1 939). If it is assumed that secondary electrons appear as a result of the

Chapter 4

62

bombardment of the cathode by positive ions and the electric field in the gap is uniform, the current I of the electrons that arrive at the anode will be determined by the relation

I=

Ioead 1 - y(ead - 1) '

(4. 1 5)

where d is the gap spacing; I0 is the electron current from the cathode, produced by some external source, y is the number of secondary electrons per positive ion produced at the cathode, and e is the natural logarithm base. For the secondary electron emission initiated by photons incident on the cathode, we obtain an expression similar to (4. 1 5) (Loeb, 1 939). Therefore, it is conventional to characterize various types of secondary emission by a unified coefficient y, which is determined by the cathode material and surface condition and by the gas type and pressure. According to the Townsend theory, the condition under which the denominator in expression (4. 1 5) becomes zero is the criterion for discharge initiation. Since y « 1 , (4. 1 5) takes the form (4. 1 6) If yead < 1 , the discharge is non-self-sustained. In this case, the discharge current I will cease if the initial current I0 is decreased to zero. If yead � 1 , the number of ions generated by one avalanche resulting from a single initiating electron, ead, is such that one secondary electron may appear owing to which the discharge will further develop. Thus, the discharge will be self­ sustained. In terms of the Townsend mechanism, condition (4. 1 6) is a criterion for discharge initiation. Increasing the electric field in a gas gap eventually results in yead > 1 . In this case, the ionization will be cumulative in character because of the generation of successive avalanches, and the discharge formative time will increase with yead. Condition (4. 1 6) makes it possible to determine the breakdown voltage of a discharge gap if the relations alp F1 (Eip) and y = F2(Eip) are known. Assume that y = const and the dependence of alp on Elp is expressed by formula (4. 1 0). In this case, for the de breakdown voltage, in view of y « 1 , we get

=

V,

de _ -

Bpd In Apd + In In y

The function Vdc(pd) has a minimum at

(4. 1 7)

THE PULSED DISCHARGE IN GAS

(pd)min = -e In -1 . A

y

63 (4. 1 8)

For the minimum value of Vdc we then have Be 1 Vdc min = ln . A -y

(4. 1 9)

Formula (4. 1 7) is a representation of the similarity law since Vdc = f(pd) . The dependence of y on Elp in (4. 1 7) can be neglected because y is under a double logarithm. This dependence is pronounced only in the region of the Vdc minimum, since in formulas (4. 1 8) and (4. 1 9) y is under a single logarithm. The quantity y is a generalized characteristic of the secondary­ emission properties of a cathode surface; therefore, it can be said that the properties of a cathode show up only in the region adjacent to the minimum of the function Vdc (pd) . This type of the relationship Vdc = f(pd) had been found experimentally before the appearance of the Townsend theory. This relationship is called the Paschen law that reads: if for a uniform field the product of discharge gap spacing by gas pressure remains constant, the breakdown voltage is a constant as well. Paschen ' s curves for several gases are given in Fig. 4.2. If the initial phase of a discharge is due to a great number of successive electron avalanches with the number of electrons in each Ne < Necr , this mechanism results in spatial passage of the current during the discharge formation phase. In particular, a glow discharge forms at low gas pressures.

1 02 �-W�������=-��= w- 1 wo w-4 w-3 w-2 pd [cm ·atm ] Figure 4.2. Breakdown voltage versus pd for different gases

Chapter 4

64 1000

d = 60 5(}.1/ Y40 mm

I /j./' r /30 25 20

'/ /.v/ / / I' // VL /_ I/v / v v

800 700

j// v v v/ v 1 // 1/ / / 5 mm / /

J'/v v

600

� 500 "

.,;: 400

1 00 0

V IO mm

t / I / 3 mm

300 200

15

V/

{/ I

t_V

y

mm 4

12 8 pd [cm ·atm ]

Figure 4.3. The right branch of the function Vdc electrode separations

=

16

20

j(pd) for elegas, plotted for different

As shown by Meek and Craggs (1 953), the similarity law for V(pd) can be violated. This takes place for the points on Paschen's curves that correspond to high electric fields [(0.3-0.5)· 1 06 V/cm]. For instance, this refers to the left branch of Paschen ' s curve corresponding to low pressures (near vacuum). This violation is due to the field emission (FE) current from cathode microprotrusions at the tips of which the electric field is enhanced many times. The FE electrons ionize the gas, and the resulting ions move toward the cathode. As this takes place, the FE is enhanced by the ion space charge and thus the FE current density further increases. Eventually, this leads to explosive electron emission and the formation of ectons and a cathode spot, as this occurs in a vacuum discharge. Paschen's curve also has deviations in its right branch corresponding to high pressures. This is associated with the electric field enhancement at the cathode microprotrusions resulting in a field emission current and in a violation of the similarity law (Meek and Craggs, 1 953). Figure 4.3 presents Vdc as a function ofpd for elegas (SF6) in a uniform field at different gap spacings (d = 1-60 mm) (Bortnik, 1 988).

2.2

The streamer discharge

The principal difference between the streamer and Townsend discharge mechanisms lies in the fact that the space charge of an avalanche can transform the avalanche into a plasma streamer. The electrons in the avalanche

THE PULSED DISCHARGE IN GAS

65

not only produce impact ionization, but also excite the gas molecules and atoms. The excited molecules or atoms, as they go to the normal state, emit photons that ionize the gas, generating photoelectrons. The electron avalanche arriving at the anode leaves at its surface positive ions whose charge creates an additional field E'. The photoelectrons appearing near the anode move toward the positive space charge region in the field E' + E, where E is the field due to the applied voltage V. If E' reaches a value of the order of E, the photoelectrons, while moving toward the positive space charge region, have time to initiate new avalanches. These avalanches neutralize the ion charge at the anode thus creating conducting plasma. The new positive ions resulting from the action of photoelectron avalanches behave as described above, and a plasma column, called a positive streamer, rapidly propagates toward the cathode. Raether ( 1 964) and Meek and Craggs ( 1 953) have formulated a condition for the formation of a streamer: E' = kE, where k is a number of the order of unity. During the formation and propagation of a streamer, the contribution to the generation of daughter avalanches is not only from photons, but also from runaway electrons, which appear in the primary avalanche plasma at rather high Elp. When the number of electrons in the avalanche reaches Necr , the avalanche space charge becomes high enough for its internal electric field to be comparable to the (counterdirected) external field. As this takes place, the field inside the avalanche appears to be enhanced. The velocity of propagation of a streamer is generally an order of magnitude greater than that of an avalanche. Therefore, it can roughly be assumed that the discharge formative time is

(4.20) As established in numerous experiments, Ncr � 1 08 for many gases under nearly atmospheric pressures (Raether, 1 964); hence, In Ner � 20. Formula (4.20) for atmospheric pressure air and E = 50 and 80 kV/cm yields td 1 0-8 and 2 · 1 o-9 s, respectively. From formula (4.20) it follows that for the discharge formative time td a similarity law is valid: ptd = j{Eip) . Figure 4.4 shows this relationship for a number of gases, obtained by F elsenthal and Proud ( 1 965). The decisive role in the Townsend-to-streamer discharge transition is played by the overvoltage factor Kover· Allen and Phillips ( 1 963) have shown that there exists a curve that divides the manifold of the values of the product of air pressure and gap spacing, pd, and coefficient Kover into two regions (Fig. 4.5). If the discharge conditions correspond to the region above this curve, the discharge occurs by the streamer mechanism; otherwise the Townsend mechanism comes into effect.

=

66

Chapter 4 1 04 r-------,

28 r-------, 24 20

N2 Oz Ar He 1 Q l '------'---'--'-' I Q-7 I Q-8 w-9 1 0-6 1 Q-S ptct [Torr ·s ]

Figure 4.4. The similarity law for the break­ down formative time plotted for different gases

850

1 45 0 2050 pd [Torr·cm]

2650

Figure 4. 5. The curve separating the regions corresponding to the streamer and the Townsend mechanism of a discharge in air

The electron density in a streamer channel, ne, approximately equals their density in an avalanche with a critical number of carriers:

ne =

3Necr 4 nr

3.

(4.2 1 )

=

Measurements for various gases give the avalanche radius r = 0.01 -0. 1 em. Assuming that Necr 1 08 , we obtain n = 1 0 10- 1 0 13 cm-3 • This means that even for r = 0. 1 em and n = 1 0 13 cm-3 , the resistance of the streamer channel under typical experimental conditions is over some tens of kiloohms. We take into account that the wave impedance of the coaxial cables by which a voltage pulse arrives at the discharge gap is Z0 � 50-75 Q. This implies that the decrease in gap voltage will be due the increase in channel conductivity in the subsequent phases of the discharge. This problem will be discussed in detail below. It should be noted that there exists two types of streamer: cathode-directed and anode-directed. The streamer considered above is anode-directed since the avalanche reaches its critical size inside the gap (Xcr < d) and, therefore, the streamer grows toward the anode. However, if the gap overvoltage is not too large, such that Xcr � d, the space charge field in the region adjacent to the anode will be high; then the streamer will grow toward the cathode. This will be a cathode-directed streamer. 2.3

The multiavalanche pulsed discharge

For highly overvolted gas gaps, the discharge formative time td lies in the range of nanosecond and subnanosecond times. In this range, a pulsed discharge has the feature that the spark development time is comparable to

THE PULSED DISCHARGE IN GAS

67

the time of growth of avalanches to their critical sizes and the time of de-excitation of excited molecules. This affects the spatial structure of the discharge, the statistical delay time, the duration of the process, etc. This type of discharge, which takes place at overvoltages Kover � 1 .5, is used in the switches and peakers of nanosecond high-power pulse generators. The criterion for such a discharge to be initiated is Xer « d. In this case, the development of a pulsed discharge in gas is strongly influenced by the current (or number) of initiating electrons, I0, and by the uniformity of their distribution over the cathode surface. In evaluating the effect of I0 on the discharge process, it is convenient to compare the average time between the appearances of two electrons from the cathode, e/I0, with the time it takes the avalanche to develop to its critical size, fer· If fer < e/I0, it can be assumed that the discharge is initiated by a single electron, and for this case we have I0 < eaveiNeer · As the discharge current is increased, the secondary processes become less and less important. If fer » e!Io, i.e., I0 » eaveiNecr. and the current I0 is uniformly distributed over the cathode, high currents are achieved, even before the onset of secondary processes, due to a great number of simultaneously developing avalanches. In this case, the formation of a discharge channel can be avoided and, if the gas pressure is much greater than atmospheric pressure, a discharge operating throughout the gas gap can be realized. Such a multiavalanche discharge was first investigated by Mesyats ( 1 966) who gave it the name a nanosecond multielectron discharge (Korolev and Mesyats, 1 998; Mesyats et al. , 1 968). The major information about the processes occurring in a discharge on the nanosecond scale is generally obtained from the spark current and voltage waveforms. By analogy with conventional pulsed discharges in gases, the terms delay time and discharge formative time are used, and by the onset of a discharge is meant the instant the current in the gap starts rapidly rising, while the voltage across the gap starts decreasing. However, it should be borne in mind that, in general, the formation of a nanosecond pulsed discharge does not stop as the current starts rising. When performing experiments, it is more convenient to measure separately the time in which the current reaches a few amperes and the time in which the current increases from a few amperes to its rated value. Mesyats ( 1 966) have found the relationship td(E) for multielectron­ initiated and single-electron-initiated discharges. To illuminate the cathode with ultraviolet light, a hole was made in the anode, which was covered with a grid. Between the grid and the spark illuminating the cathode, a diaphragm and a quartz glass sheet were placed; the latter was necessary to filter short waves and prevent photoionization of the gas. The current of initiating electrons was controlled by varying the size of the diaphragm. This

Chapter 4

68

experiment has shown that if the number of initiating electrons is of the order of 1 04 or greater, there is no j itter in discharge delay times. The relationship td(E) for air at atmospheric pressure turned out to be described by formula (4.20) (Fig. 4.6) derived for a streamer discharge, although the experimental conditions were far from being typical of streamers. Mesyats ( 1 966) explained this effect by the fact that a discharge of this type develops due to a great number of avalanches appearing at a time. 60 .-------� 40 20 1 01 6 4 2 1 0° 40

80

1 20 E [kV/cm]

1 60

Figure 4.6. Air breakdown formative time versus electric field for multielectron (1) and single-electron initiation of breakdown (2)

=

In view of the fact that the discharge current l(t) and the gap voltage by Kirchhoff s equation, we can write down the system of equations

V(t) E(t)d are related

eve (4.22) l(t) = Neo -expavet d d[Eo - E(t)] (4.23) l(t) = ' Zo where Eo is the initial electric field, Z0 is the wave impedance of the coaxial cable through which the voltage pulse is transferred to the gap, and d is the gap spacing. This system of equations is reduced to the equation

(

)

dE = 1 � Eave . dt - - E0

(4.24)

The discharge formative time is determined experimentally from oscillograms as the time from the application of voltage to the instant the current reaches /d = 0. 1 Va1Z0, where Va is the amplitude of the voltage

THE PULSED DISCHARGE IN GAS

69

pulse. Since during the time td the current Id « VIZ0 , then the quantities a and Ve can be considered invariable. In this case, from (4.24) it follows that (4.25) lf we put id = 10 A, d = 0. 1 em, Neo = 1 04, and Ve :::::: 1 07 crnls, the quantity under the logarithm sign in (4.25) will be 1 08, i.e., approximately equal to Necr for a streamer discharge. This explains the coincidence of the measurements of td(E) for a streamer discharge (Fletcher, 1 949) and those for a multielectron-initiated discharge (Mesyats, 1 966). The relationship td(E) for air at atmospheric pressure is presented in Fig. 4.6 (Mesyats, 1 966). According to (4.25), the discharge formative time obeys the similarity law ptd = f( Eip) This is confirmed experimentally for a variety of gases (Korolev and Mesyats, 1 998; Felsenthal and Proud, 1 965). For a multielectron-initiated discharge, the phase of the discharge voltage drop and current rise, similar to the discharge formation phase, is associated with ionization multiplication of electrons and is spatial in character (Fig. 4. 7). Figure 4. 7 also shows an oscillogram of the voltage across an air gap at atmospheric pressure with an initial electric field of 76 kV/cm (Bychkov et al. , 1 97 1 ). The cathode was illuminated with an intense ultraviolet flash 1 0 ns prior to the pulse arrival at the gap. From Fig. 4.7 it can be seen that the luminescence took place throughout the gap; that is, the discharge was spatial in character. This property of high-pressure discharges discovered by Mesyats and co-workers (Mesyats, 1 966; Mesyats et al., 1 968) is now widely used to produce subnanosecond high-power pulses and to pump high-power electric-discharge gas lasers. .

1

2

3

L=� ]___.__ 0

5

I

10

1 5 t [ns]

Figure 4. 7. Voltage waveform and photographs of the luminosity of a multielectron-initiated discharge in air (p 760 Torr, d = 0.3 em, Ea = 67 kV/em) =

70

Chapter 4 IO bii :I: 8

0.7

�

0.5 ;;::.

E E

-o 0 -

.....

!::).,

0.6 �

6

-

4

....

0.4

�

2 0 50

0.3

pts I30 90 I IO EaiP [V/(cm mm Hg)]

70

0.2 I SO

·

Figure 4.8. Quantities pts and y115 versus Elp for different gap spacings: I, 2, and 4 mm. The solid and dashed curves represent theoretical and experimental data, respectively. The experimental data are obtained for air at p I atm =

The voltage waveform in Fig. 4. 7 indicates that initially the rate of voltage drop is small; then it peaks, and then decreases abruptly. From Eqs. (4.22) and (4.23) one can find the maximum rate of voltage drop, (dV/dt) max • and the switching time fs = Va l(dV/dt)max • where Va is the amplitude of the voltage pulse. Obviously, the dependence of this time on gas pressure and electric field obeys the similarity law pts = f(Ea lp) since ts - 1/ave. Figure 4.8 presents the calculated and experimentally obtained values of pts versus Ea iP for air (Mesyats, 1 966). To characterize the phase of slow voltage drop, the voltage value can be used at which the drop rate will be one fifth of its maximum value. We denote this value by V115 and introduce the notation yu5 Vu51Va. The quantity Yus as a function of EaiP is also given in Fig. 4.8.

=

2.4

Single-electron-initiated discharges

Let us now consider a multiavalanche discharge initiated by a small number of electrons, such that the average time between the appearances of two electrons is comparable to or longer than the time it takes an avalanche to develop to its maximum size. In this case, the discharge acquires some new properties. To analyze this type of discharge, we consider the features of a single avalanche developing in a strong electric field. As shown above, as an avalanche develops, the electric field produced by the space charge of positive ions increases. It can easily be shown that the critical number of electrons decreases with increasing external field by the law Necr - a- 1 (Mesyats et a/. , 1 972b) . As the number of electrons approaches its critical

THE PULSED DISCHARGE IN GAS

71

value, the exponential growth of electrons in the avalanche will slow down (due to the decrease in impact ionization rate). Experimentally, the same effect, which can be referred to as self-deceleration of an electron avalanche, was been established for avalanches in nitrogen and in ether vapors, and it was revealed that as an avalanche developed, the effective coefficient a first decreased to almost half its initial value and then increased again (Raether, 1 964). The same effect was observed for avalanches in air at atmospheric pressure in an electric field E � 1 05 V/cm. It was shown that the increase in a was due to the ejection of electrons from the head of the avalanche and their acceleration in the anode-avalanche gap (Mesyats et a/. , 1 972b ). Along with the slowdown of the exponential increase in number of electrons, there is slowdown of the increase in number of excited gas molecules; hence, the number of photons leaving the avalanche will decrease. In an avalanche with a critical number of electrons, the number of emitted photons is proportional to lla2 ve, i.e., it decreases at a very high rate with increasing external electric field. An important role can be played by the effect of fast "runaway" electrons whose energy acquired in the electric field is greater than that lost in collisions (Gurevich, 1 960). Due to the above effects, the discharge formation process in a high electric field is slower than that for a discharge initiated by a great number of initial electrons. Figure 4.6 (curve 2) presents the formative time of a discharge in air at atmospheric pressure, td, as a function of electric field E: the discharge was initiated by a few electrons. The time td was taken to be the least one in the statistical distribution of delay times. The intensity of illumination of the cathode was chosen so that the mean statistical delay time was comparable to td. Comparison of curves 1 and 2 suggests that the time td for a discharge initiated by a few electrons is substantially longer than that for a multielectron-initiated discharge. Investigations of the phase of rapid current rise and voltage drop in a nanosecond discharge initiated by a few electrons (Mesyats et a/. , 1 972b) have shown that this phase is satisfactorily described by formula (4.24) derived for multielectron-initiated discharges. This is accounted for by the fact that once a great number of avalanches have been developed in a gap during a secondary process, the gap voltage drops within the lifetime of one generation of avalanches. However, in contrast to the case of a multielectron-initiated discharge, there is no slow decrease in gap voltage after its rapid drop because of the formation of one or several channels in the gap (Bychkov et a/., 1 97 1 ). From Fig. 4.6 it follows that, for the same pulse duration, a discharge with a few initiating electrons provides a considerably higher pulsed electric strength of the gas gap than a multielectron-initiated discharge. However,

Chapter 4

72

to realize this, it is necessary to know the sources of initiating electrons. At high electric fields, E > 1 05 V/cm, this source is field emission from the cathode. 3.

THE SPARK CURRENT AND THE GAP VOLTAGE DROP

During the phase of discharge formation, the current in the gap is low. As the conductivity of the discharge plasma becomes high, the current in the spark gap starts rising, while the gap voltage starts decreasing. This discharge phase is referred to as the spark phase. During this phase, the spark resistance varies from a very high value, which is determined by the properties of the avalanche or streamer, to a value far below the load resistance. The time it takes a gap to change from an essentially nonconducting to a conducting state determines the shortest possible rise time of the pulse across the load. The nonconducting-to-conducting state transition of a gap can be characterized by the time dependence of gap voltage V or resistance R. The curve V5(t) is commonly referred to as a switching characteristic. The duration of the switching process is characterized by the time t5, which is measured between two fixed points on the switching characteristic (Fig. 4.9). One of them is generally taken at v; = 0.9V0 (V0 is the initial gap voltage), while the other at Ys" , which, depending on the character of the curve, can be assumed equal to 0.2 V0 or 0. 1 Vo.

Figure 4. 9. The switching characteristic of a spark gap

The main characteristic of the phase of voltage drop (spark phase) is the spark resistance as a function of current, gas type and pressure, gap spacing, and applied magnetic field. Such a unified relation does not exist and seems

THE PULSED DISCHARGE IN GAS

73

to be impossible at all, since different physical processes are dominant in different types of discharge, depending on the current and on the gas type and pressure. Let us first discuss the switching characteristic for a multiavalanche nanosecond volume discharge, as discussed in Section 2 of Charter 4. To describe the increasing conductivity, it is necessary to know an averaged ionization constant, which depends on the ratio of the electric field to the pressure and on the energy delivered to the discharge, and to solve a self-consistent problem of the increase in conductivity and the decrease in gap voltage. Obviously, it is very difficult to solve this problem in the general statement. However, there are some models of the gas-discharge plasma that, when used for a limited range of conditions, make it possible to calculate the switching characteristic of a gap by solving simultaneously an equation for the varying conductivity of the plasma column and Kirchhoff s equation for the electric circuit. An example is the above model of avalanche multiplication of electrons, which was first proposed to calculate the switching characteristics of nanosecond pulsed discharges at high overvoltages (Korolev and Mesyats, 1 998; Mesyats, 1 966). Calculations by the avalanche model (Korolev and Mesyats, 1 998) [(see formula (4.24)] for the abrupt voltage drop phase fit well to experimental results. For multielectron-initiated discharges and spatial current passage, the avalanche multiplication model can also be used to calculate voltage waveforms for the phase of slow voltage drop. Comparison of an experimental oscillogram and a calculated waveform is given in Fig. 4. 1 0. From curve 3 it follows that the rate of voltage drop for a single­ electron-initiated discharge at the late stage is greater than that for a multielectron-initiated discharge. 1 .0 r------., 0.8

� 0.6 ::.::

1

0.4 0.2 0

2

4

t [ns]

6

8

Figure 4. 1 0. Experimental (J) and calculated voltage waveforms (2) for a space discharge in nitrogen (p = 760 Torr, d = 0.44 em, E = 68.5 kV/cm) and an experimental voltage waveform for a single-electron-initiated discharge (3)

74

Chapter 4

Let us now consider the case where a discharge operates as a narrow channel. For a streamer discharge, the channel formation is a natural process because the nucleation of the channel begins as soon as first signs of a streamer appear. As the streamer bridges the cathode-anode gap, the discharge channel starts forming. We already mentioned that the plasma density in a streamer is too low to pass the total current of the spark; therefore, some other physical processes should be involved to increase the plasma density in the discharge column. Such a process is explosive electron emission (EEE), which occurs as the streamer plasma interacts with the cathode. Since the plasma density in a streamer is rather low and may reach only 1 0 13 cm-3 , the most probable mechanism for the initiation of EEE is the electrical breakdown of dielectric films on the cathode due to their charging by the ion flow from the streamer channel. This results in the appearance of a cathode spot and in intense heating of the channel plasma by the EEE current. There are several models for the resistance of a spark, which are operative in different ranges of channel currents. One of the earliest models is the Topler empirical model according to which

(4.26) where K is Topler' s constant characterizing the gas and d is the gap spacing. From (4.26) it follows that the resistance of a spark· is inversely proportional to the charge transferred through the discharge channel. A more substantiated expression of the spark resistance as a function of current and time was derived by Rompe and Weizel (1944) based on the energy balance for a spark channel:

(4.27) Here, d is the gap spacing, a is a constant depending on the gas type, and p is the gas pressure. The key assumption of the theory by Rompe and Weizel was the time independence of the coefficient. This was confirmed experimentally for times t ::;; 1 o-s s and currents of up to several kiloamperes for discharges in atmospheric air, nitrogen, and argon (Mesyats, 1 966; Mesyats, 1 974; Andreev and Vanyukov, 1 96 1 ; GrUnberg, R., 1 965). It was obtained that a = 0.8-1 (atm·cm2)/(s·V2) for air and nitrogen and 30 (atm·cm2)/(s·V2) for argon.

THE PULSED DISCHARGE IN GAS

75

Analysis of the transient processes in a discharge circuit taking into account formula (4.27) for the spark resistance shows that the discharge development is governed by the parameter 8 = 2 pd 2 /a V02 , which is the spark conductivity rise time. For the time e, the similarity criterion Sp - (Eipt2 is applicable. If a discharge operates at a de voltage, V0 Vdc, then pd const (Paschen ' s law) and, hence, 8 lip; that is, increasing gas pressure decreases the spark conductivity rise time. This conclusion is in good agreement with the well-known experimental results (Mesyats, 1 974). From Paschen ' s curve it follows that for p const, as the gap spacing is decreased, the electric field E Void at which the gap is broken down increases, resulting in a decrease in time e since e - l !E 2 ' and this also agrees with the experimental results (Mesyats, 1 974). It can readily be shown that for millimeter gaps at a pressure of nitrogen, air, or other gas of the order of 10 atm and more we have e < 1 o-9 s . This property of a spark to reduce the switching time with increasing resistance is widely used in the technology of production of nanosecond high-power pulses. A spark channel, besides the resistive component of its impedance, also has an inductive component, which depends in the main on the channel length. The inductance of the channel additionally increases the pulse rise time. To moderate the effect of the inductance, multichannel switching is accomplished. The role of the inductance vanishes when a volume discharge is used. Formula (4.27) was obtained under the assumption that there exists a discharge channel, which starts forming once a streamer has bridged the cathode-anode gap. It was also assumed that there is no hydrodynamic expansion of the channel and the conductivity increases due to the ionization of the gas. Therefore, relation (4.27) can also be used to estimate the characteristics of multielectron-initiated multiavalanche discharges. As the degree of ionization of the discharge plasma increases, the mechanism for the spark development in the discharge zone changes over. The model of Rompe and Weizel proposes that the switching in gas is governed by the ionization process. This process is also considered dominant in the multiavalanche switching model (see Section 2 in Charter 4). However, the model of Rompe and Weizel is much simpler than the multiavalanche model. On the other hand, for some conditions, both models may give the same results. For instance, in terms of the multiavalanche model, we have pt5 - [ (a/p)vet and alp - (Eip)312 for Elp = 100-500 V/(cm·Torr) [see formula (4. 1 1)], and for Ve - (Eip)1 12 we then obtain pt5 - ( Eipt2 , which also results from the model of Rompe and Weizel. If the degree of ionization of the plasma in a spark channel is close to unity, the conductivity of the channel may increase in the main due to two

=

=

=

=

=

Chapter 4

76

factors. First, as the plasma is heated, its conductivity increases proportional to T 3 12 . Second, the hydrodynamic expansion of the channel becomes substantial (Drabkina, 1 95 1 ; Braginsky, 1 958) and, as a result, the cross­ sectional area of the discharge column increases, while its resistance decreases. In reality, this process shows up even for n 2::: 101 8 cm-3 and p 760 Torr. If the channel conductivity cr is a constant and the magnetic pressure is low compared to the gas-kinetic pressure, the relationship between discharge current and spark resistance has the form (Braginsky,

=

1 958)

Rs - d

( f� J 2 dtri 13

(4.28)

In a streamer breakdown, the channel diameter is an order of magnitude greater than that in breakdowns of overvolted gaps and in single-electron­ initiated discharges. Therefore, an increase in density even to n :::::: 10 1 8 cm-3 results in an insignificant decrease in voltage at short-circuit currents of several hundreds of amperes (Tholl et a!. , 1 970; Koppitz, 1 967). Here, the switching characteristic is described in terms of the hydrodynamic model of an expanding channel. In this case, not only the calculated and measured switching times coincide, but also the measured channel expansion velocity coincides with that calculated from the power delivered to the channel (Koppitz, 1 967). For very high short-circuit currents in the discharge circuit (I 2::: 1 0 kA), the conditions in the discharge channel by the onset of voltage drop are such that the conductivity of the channel increases in the main due to its hydrodynamic expansion. Therefore, the model of an expanding channel is generally used to calculate the switching characteristics of nanosecond high-current switches (Mesyats, 1 974). In the above models, the physical limitations are very stringent and, actually, the description of the process takes into account only one factor, which is dominant under given conditions (e.g., hydrodynamic expansion). Such a situation is possible in model tests with a specially created single channel (Tholl et a!. , 1 970; Koppitz, 1 967) rather than under the operating conditions of a spark gap over a wide range of currents. Measurements of switching characteristics in combination with observations of the dynamics of channel development by the laser shadow and interferometric methods with nanosecond time resolution (Korolev and Mesyats, 1 998) show that the conductivity increases due to several factors, which can hardly be considered independently. To calculate the rise time of a pulse generated in a circuit with a spark gap, the switching characteristic is sometimes represented as an exponential function:

THE PULSED DISCHARGE IN GAS fs

=

77

Voe -aot '

where the value of ao is to be found from experiment or from well-known models of a spark. For instance, the model of Rompe and Weizel gives

a0 0.038ap �

(!)

' ,

where E is the electric field at which breakdown occurs.

4.

THE DISCHARGE IN GAS WITH DIRECT INJECTION OF ELECTRONS

4.1

Principal equations

As shown above, free electrons present in a gas-discharge gap radically alter the physics of the discharge phenomena. The simplest way of producing free electrons in a gap is to initiate electron emission from the cathode due to the photoelectric effect, to illuminate the gap with ultraviolet radiation to cause photoionization, or to locally heat the cathode surface with a laser beam to cause thermoelectron emission. Mesyats et a/. ( 1 972a) proposed to inject electrons produced by an electron accelerator directly into the gas gap. The electron beam should pass through a thin metal foil cathode. In preliminary experiments (Koval ' chuk et a/. , 1 970), these authors were able to produce a discharge in nitrogen at a pressure of 1 5 atm, and this was a volume discharge having no channel. Various modes of such a discharge have been used for pumping high-power gas lasers, in nanosecond high­ power gas switches, in pulsed power plasmatrons, etc. The first comprehensive study of this type of discharge was carried out by Koval ' chuk et a/. ( 1 97 1). The charge voltage of the energy-storage line reached 1 000 kV, the maximum energy of the electron beam downstream of the foil was 200 keV, the beam current was varied from a few amperes to a kiloampere, and the beam current duration was about w-s s (Fig. 4. 1 1 , a). The discharge processes depend substantially on whether the voltage across the gas gap, V, is higher or lower than the de breakdown voltage Vdc · If V < Vdc, the discharge current in the gap is close in waveform to the beam current and increases linearly with the latter. As this takes place, if the electron supply into the gap is terminated, the discharge current ceases. In this case, the mode of a non-self-sustained discharge is realized, and the discharge operates throughout the volume into which electrons are injected (Fig. 4 . 1 1 , b).

78

Chapter 4 (a)

---y---­

(b)

(c)

(d)

Figure 4. 1 1. Typical current waveforms for injected electrons (a), a non-self-sustained discharge (b), a spark discharge (c), and an avalanche discharge (d)

If the voltage is increased to about the de breakdown voltage, the non­ self-sustained volume discharge will change into a channel discharge and the current will abruptly increase (Fig. 4. 1 1 , c). For V > Vdc (pulsed discharge) (Fig. 4. 1 1 , d), a spatial glow was observed during 1 0-7 s in a discharge in nitrogen at a pressure of -3 atm. In this case, the discharge operated due to avalanche multiplication of electrons as a multielectron-initiated pulsed discharge. The transition into a channel phase may occur in both self­ sustained and non-self-sustained discharges. A discharge in gas operating under the conditions of intense ionization of the gas by an injected electron beam differs from a discharge operating at low­ intensity ionization by the mechanism of conduction, which resembles that realized in a glow discharge. At high ionization rates (over 10 1 6 cm-3 ·s-1) and high pressures (104-1 06 Pa), the electric field is enhanced in a narrow near­ electrode region, remaining practically constant in the discharge column (Fig. 4. 12). In this case, the fall potentials in the near-cathode and near-anode regions are generally low compared to the total voltage applied to the gap. Thus, the gap conductance is governed by the discharge column, and, since the use of an electron beam ensures high ionization rates, high discharge current densities are realized. First pulsed discharge experiments were carried out with electron beams of duration 10-7 s and shorter (Koval'chuk et a/., 1 970; 197 1 ; Marcus, 1 972). A discharge sustained by an electron beam of duration 1 o-s s was realized by Fenstemacher et a/. (1972).

THE PULSED DISCHARGE IN GAS c

Ec

79 A

X

Figure 4. 12. Sketch of the field distribution between the electrodes

If w e res tri ct o urs elves to th e co nsid eratio n of o nl y th e vo lume dis cha rge phase and do no t consider th e pro blems o f dis charge s ta bi li ty, th e pri nci pal pro cess es o ccurri ng i n th e dis charge can be des cri bed by th e co nti nui ty eq uatio ns and Poisson's eq ua tio n fo r th e electri c fi eld. Fo r th e o ne­ di mensio nal cas e, we have

one - 0 (neve ) - avene - Pneni + \jl + q,. ot ax

(4.29 )

On; - o( n;V; ) . = avene - Pneni + \jl,

(4.30 )

ot

oE Ox

ax

= -e

( n; - ne ) so ;

(4.31) (4.32) (4.33)

Th ese eq uations sho uld be complemented wi th i ni tial and bo undary co ndi tio ns: (4.34 ) (4.35 )

J: E(x) dx

= V0.

(4.36 )

In Eqs. (4.29 )-(4.36), n; a nd ne a re th e io n a nd th e el ectro n densi ty, res pe cti vely; ve, v;, J.le, and J.l; are the respecti ve drift velo ci ti es and mo bi liti es o f ele ctro ns and io ns; E is th e el ectri c fi eld; V0 is the po tentia l di fference betwe en th e electro des; d is th e gap s pa ci ng; 'I' is th e rate o f io ni za tio n o f th e

Chapter 4

80

gas by the beam electrons; q is the rate of thermalization of fast electrons; is the coefficient of secondary electron emission from the cathode; a and � are the impact ionization and recombination coefficients, respectively; eo is the dielectric constant, and e is the electron charge. For rigorous account of the electron impact ionization of gas, one should complement Eqs. (4.29)-(4.36) with the kinetic equation, which describes the transfer of fast electrons in matter, and consider self-consistently two subsystems: the electrons and ions of the gas discharge, on the one hand, and the beam electrons, on the other hand. The self-consistency implies that the quantities 'l' and q depend on the fast electron flux, which is affected, in turn, by the field E, and, hence, by the quantity ni - ne. However, in this case, the problem becomes much more complicated and its solution looses in clearness. Therefore, we assume that \j1 and q are determined by the beam electrons and by the external field E. The ratios q/\jl and s/�, where s is the average energy going for the formation of one electron-ion pair and � is the average energy of the beam electrons, are of the same order of magnitude. The function \!l(x) is determined from the relation y

(4.37) where }b is the current density of the injected electron beam and D(x) is the distribution of the energy lost per electron along the gap. The distribution D(x) depends on the initial energy of the beam electrons and on the electric field in the gap. We assume that the ionization in the gap is uniform throughout the gap. Qualitatively, the field distribution between the electrodes is the same as that in the case of weak ionization (see Fig. 4 . 1 2). In region II of the discharge column, the field is constant, the space charges of electrons and ions neutralize one another, and the ionization is balanced by volume recombination. In the cathode (/) and anode (Ill) regions, the electric field is stronger than in the column due to the prevalence of the space charge of ions and electrons, respectively. We shall not consider in detail the phenomena taking place in regions I and Ill, since the most important phenomena occur in region II, that is, in the discharge column. 4.2

The discharge column

Let us first consider the case of uniform ionization of the gap. If there is no thermalization of electrons (q = 0) and the ionization is uniform, the electric field in the discharge column, i.e., in a region away from both the cathode and the anode, will be invariable and equal to E0• In this case, for

THE PULSED DISCHARGE IN GAS

81

practically important pressures and electrode separations, relations V0 » Vc + VA ; d » lc + IA , where Vo is the total voltage across the gap, are generally fulfilled. It follows that the conductance of a gas-discharge gap is mainly the conductance of the plasma column where ni = ne = n. The above considerations substantially simplify the determination of the discharge current-voltage characteristic, since in Eqs. (4.29) and (4.30) we may put B(nv)/Bx = 0 for both ions and electrons and define the electric field in the column as E0 = (V0 - Vc - VA )Id � V0/d. Then, for a non-self-sustained discharge (a = 0) we readily obtain n(t)

=( ) \II �

112 1 - exp [ -2(\11 �) 1 12 t J . 1 + exp [ -2(\II �Y 1 2 t]

(4.38)

From (4.38) it can be seen that in classifying discharges it is convenient to compare the discharge operative time and the duration of the fast electron beam current, tb. If tb « 112(\ll � t 11 2 , we have a nonstationary discharge or a discharge initiated by a beam of fast electrons. The role of the beam is to produce in the gap, within a short time tb. an initial electron and ion density n0 = \jlt, and subsequently there occurs recombination decay of the plasma by the law

(4.39) where n0 is the initial density of charged particles in the discharge column. For tb » 112(\ll � t 11 2 we have a discharge sustained by an electron beam or a quasi-stationary discharge in which the equilibrium electron and ion density is given by neq = (\jii�Y 1 2 and the characteristic time it takes the equilibrium density to be achieved by t = 112(\ll � t 11 2 • The usefulness of the above classification was substantiated in early experiments. For instance, for short tb the current-voltage characteristics are linear because j e\jlfbJleEo . Since Jle oc p-1 and \jl oc p, then for invariable Eo and tb the peak value of the non-self-sustained discharge current is independent of gas pressure (Fig. 4. 1 3) (Koval'chuk et a/. 1 970). As follows from (4.38), for a quasistationary mode with recombination electron losses, the discharge current density is related to the beam current density as j oc (jb Y 1 2 • As the electric field in a discharge initiated and sustained by an electron beam is increased, the electron density increases due to ionization. For short tb and E0 const, the time dependence of the electron density in the column (and, correspondingly, the current waveform) is described by the expression (Bychkov et a/. , 1 978)

=

=

,

82

Chapter 4 (4.40)

Finally, the limiting case of a discharge with ionization multiplication is realized at very high initial voltages across the gap (which are several times greater than the de breakdown voltage). In this case, even if the initial electrons (generated, e.g., by ultraviolet illumination) are few in number, there occurs avalanche electron multiplication, and a volume discharge with a high current density is formed. The discharge formative time and the duration of its volume phase are generally on the nanosecond scale; therefore, these volume discharges are sometimes called nanosecond discharges (Mesyats et a/. , 1 972; Bychkov et a/., 1978). 400 300 E

...... M

� 200

X -}

·-.

D-2 0-3

1 00

5

0

15 10 E [kV/cm]

20

25

Figure 4. 13. Current-voltage characteristic of a discharge, measured for jb p = 4· 1 03 (1), 7- 1 03 (2), and 1 0· 1 03 Pa (3)

=

I0

A/cm2 and

For high-pressure discharges, for all conditions discussed, there exists a certain time of steady operation during which the volume discharge does not go into a spark discharge and the energy delivery to the gas remains uniform. Nonuniform ionization of the gas over the gap length results in a nonuniform distribution of the electric field in the column, E(x). The determination of E(x) for the plane-parallel electrode geometry is described by Smith (1974) and Evdokimov et a/. (1 977). If the effect of thennalized electrons is ignored, E(x) can be found in implicit form from the relation (Evdokimov et a/. , 1 977)

e\jl(x) + a(E)j

=

Pf eJ.L;£2

.

(4.4 1)

Assuming for definiteness that the electron beam is injected into the gas gap on the cathode side, we obtain that the electric field near the cathode will

THE PULSED DISCHARGE IN GAS

83

be a minimum, Emin. because of the highest ionization rate 'I' in this region. Then, neglecting impact ionization for the near-cathode region, we write relation (4.41 ) as

'l' (x) a(E)J.!eEmin E�in . \ji(Xmin ) [B'I'(x)f' 2 - E2 (x) _

(4.42)

_

Figure 4. 1 4 (Evdokimov et a/. , 1 977) shows the field distribution in a gap filled with nitrogen at atmospheric pressure which is ionized by electrons of energy 1 50 keV that have passed through an aluminum foil of thickness 50 J..lm . In the region of weaker ionization, the electric field is enhanced and the specific power dissipated per unit volume increases.

15

,...... �

2::.

10 e �

2)

;;r

5

0

-

�

20

10 d [em]

-

Figure 4.14. Field distribution in a gap with uniform ionization for Emin 4 kV/cm: 1 - \jl(x),

2

E(x) with no account of impact ionization, and 3

E(x) with account of impact ionization =

One more reason for the field distortion in the discharge column may be the presence of thermalized beam electrons giving rise to the buildup of a negative space charge in the gap. This also increases the field in the discharge column region adjacent to the anode. Let us consider the effect of thermalized electrons on the field distribution at short times, t < 112('1'Bt 1 1 2 , for which the recombination losses can be ignored. Assuming additionally that the condition for plasma quasineutrality is roughly preserved (ni � ne). we get an equation for the charge density p:

: + ( eJl::t ) p = eq + [eJleEt (Z)] .

(4.43)

where q is the rate of appearance of thermalized electrons in a unit volume. The right side of (4.43) indicates that the space charge is generated by

84

Chapter 4

thermalized electrons due to the existence of a gradient of rate of generation of charge carriers. For a region where O\tf18x is negligibly small, Eq. (4.43) yields p = eqt

s; exp [ -at2 (1 - y) }ty,

a = ef..!.e\jll2so . t = (s0 1ef..!.et)11 2 the charge density p takes Pmax = eq 12a11 2 associated with the maximum field

where At

(4.44) a maximum value

(4.45) where o is the mean range of fast electrons in the gas. The increase in field within a short time after the beam injection is due to the accumulation of electrons, and its subsequent decrease results from an increase in plasma conductivity and in a more intense space charge runoff. For }b = 1 A/cm2 , dlo = 1 , f..l.e 5 · 1 02 cm21(V·s), and \jl = 1 02 1 cm31s, we have Emax = 4· 1 03 VI em. This estimate shows that the effect of thermalized electrons on the electric field is substantial at current densities of injected electrons of the order of 1 A/cm2 and higher.

=

4.3

Constriction of volume discharges

One of the most important physical processes occurring in a volume gas discharge is its constriction, i.e., the transition to a channel. Examples of volume discharges are the low-pressure glow discharge, the self-sustained pulsed volume discharge that may operate at both low and high ( 1 atm and higher) pressures, and, finally, the non-self-sustained discharge with intense external ionization (e.g., by an electron beam). In volume discharges, constriction begins at the cathode because of the appearance of an ecton due to field emission or breakdown of dielectric films present on the cathode surface (Fig. 4. 1 5). Bearing in mind that the mechanism of constriction is the same for all mentioned types of discharge, we consider this effect for the discharge controlled by an electron beam. Characteristic features of this type of discharge are the volumetric current passage and the presence of a cathode fall potential layer owing to which electrons are uniformly supplied to the discharge column. The value of the fall potential across the near-cathode region is generally from several hundreds of volts to some kilovolts and the size of the near-cathode region is such that the conditions are provided for the discharge to be self-sustained due to ionization and secondary cathode processes.

THE PULSED DISCHARGE IN GAS

85

,. 2 Y. J y ' � \ 5

I

��ol �I I

....... 200

0

2

3, 4

40

80

�

�

6

6

5

I

1 20 t [ns]

�

I

1 60

�

\

L�

200

•

Figure 4. 15. Waveform of the current flowing through a cathode spot and photographs of the spark gap, taken at different stages of discharge development (frames 3 and 4 were taken with different stop apertures)

Secondary electrons may appear at the cathode under bombardment with positive ions, due to the photoeffect, under bombardment with neutral atoms resulting from charge exchange, and due to other processes. These processes provide, as a rule, a uniform distribution of the secondary electron current density at the cathode and, hence, a uniformly structured cathode layer. As a certain current density is achieved in a discharge, there occurs a stepwise transition of the volume discharge to a channel one. This transition is accompanied by a redistribution of the current in the discharge column (column constriction) and a redistribution of the current at the cathode (its localization in the cathode spot region). There are two ideas on the mechanism of the transition of a volume discharge into a spark. One idea is that the constriction is due to instabilities appearing in the discharge column. For instance, if the distribution of the inj ected electron beam density is nonuniform over the gap length, conditions for the appearance of an electron avalanche with the number of electrons N ::::: Ncr may arise in the enhanced field region. This may even lead to the appearance of a streamer in which the plasma density is higher than that in the other space. Therefore, the gas is heated and displaced from the internal regions, and the neutral density decreases. The decrease in density intensifies the power dissipation at the discharge axis (Korolev and Mesyats, 1 998). However, there exists another approach based on experimental data on the instabilities originating in the near-electrode regions (as a rule, in the near-cathode region), leading to discharge constriction (Korolev and Mesyats, 1 998). These instabilities result in the instability of the discharge column. According to the concept developed in Chapter 3, one type of

Chapter 4

86

instability may appear in the cathode region if the electric field at the cathode is high enough to initiate FE from some regions of the cathode surface. The FE current is enhanced by the space charge of positive ions, resulting in an additional increase in current density, in the explosion of microprotrusions, and in the formation of ectons. The work on studying volume discharges in high-pressure gases was reviewed by Korolev and Mesyats ( 1 998), Bychkov et al. ( 1 978), Tzeng and Kunhardt ( 1 990), and other authors.

5.

RECOVERY OF THE ELECTRIC STRENGTH OF A SPARK GAP

When producing high-voltage pulses at high repetition rates, it is important to know how quickly the spark gap recovers its electric strength after a spark discharge. When the current already stops to flow through the spark, the spark channel still contains a column of hot and strongly ionized gas in which there occur diffusion and recombination that reduce the conductivity of the spark channel with time. However, a simultaneous increase in gap voltage due to the charging of the pulse-forming unit of the circuit hinders the recovery of the gap electric strength. If the recovery occurs more rapidly compared to the rise of the gap voltage, the pulse­ forming unit will be charged to the total voltage and the circuit will be capable of generating the next pulse. If the rising gap voltage reaches its breakdown value earlier than the pulse-forming unit is completely charged, a noncontrollable breakdown will occur. The repeated operation voltage at which a spark gap goes out of control is found by constructing j ointly the curve ofthe increasing gap voltage, Vg(t), and the recovery curve, Vr(t), and is determined by the ordinate of the point at which these curves intersect or touch one another. Much work was done to study the recovery of the electric strength of a gap after a spark discharge; its review is given in the monograph by Meek and Craggs ( 1 953). The recovery of the gap electric strength after a spark discharge in hydrogen, nitrogen, oxygen, air, inert gases, and gas mixtures was investigated in detail for voltages of up to 1 0 kV, pressures of up to 1 atm, and electrode separations of up to 20 mm (Fig. 4. 1 6) (Rubchinsky, 1 958). The pulsed discharge current reached a peak value of 1 000 A at a variable pulse duration. The rate of gap voltage rise was 0.5-1 kV/�s. The electric strength recovered most rapidly in hydrogen and most slowly in nitrogen. The difference in recovery rates for these gases was very large. For instance, 50% of the initial strength recovered within 1 60 �s in hydrogen and within 4000 �s in nitrogen. For various pure inert gases, the difference in recovery

THE PULSED DISCHARGE IN GAS

87

rates was not substantial. The dependence of the recovery rate on pressure was weakly pronounced for all gases. The slope of the characteristic Vr(t) was strongly affected by various adds to pure gases. For instance, the addition of 0. 1 % hydrogen to argon almost doubled the recovery rate. A similar effect was observed on adding oxygen to argon; the lower the rate of rise of the gap voltage, the more efficient was the action of the oxygen add. Adding nitrogen to argon hindered the recovery of the gap strength. Nitrogen turned out to be more sensitive to adds than inert gases. To recover 50% of the initial strength in pure nitrogen, it took 4000 J.!S, while in nitrogen with 1 % hydrogen the recovery time was only 1 300 J.!S.

� �

0.4

0

1 000

2000 3000 t [J.!S]

4000

5000

Figure 4. 16. Recovery characteristics for different gases. p = 760 mm Hg for air and 600 mm Hg for the other gases; electrode separation = 5 mm; 140 A, 3 J.!S discharge current pulse. Vdc is the de breakdown voltage of the gap

The recovery rate is strongly affected by the shape and polarity of the electrodes. If the anode is a needle, the electric strength in nitrogen is recovered more rapidly than in the case of plane-parallel electrodes or if the cathode is a needle. The electrode material affects the run of the v;.(t) curves not substantially. Investigations of the duration and amplitude of the pulsed current flowing through a spark gap have shown that an increase in pulse duration decreases the recovery rate more substantially than an increase in pulse amplitude. Most of the Vr(t) curves obtained by Smith ( 1 974) have two sections different in slope: steep and tapered. The initial, steep section is determined by the breakdown strength of the ion sheath formed at the cathode under the action of the gap voltage, while the tapered section is associated with the increase in gas density in the discharge column on cooling.

88

Chapter 4

A decrease in charge density increases both the thickness of the ion sheath and Vr. For the charge density becoming low, such that the sheath expands throughout the gap under the action of the applied voltage, this corresponds to the beginning of the second section of the Vr(t) curve. Since the gas cools more slowly than the charge density decreases, the second section is more tapered than the first one. Calculations have demonstrated qualitative agreement of the experimental and theoretical Vr(t) curves for all gases except nitrogen and argon. The effect of the adds of oxygen and hydrogen, which increase the steepness of Vr(t) for nitrogen and argon, can be accounted for by the tendency of hydrogen and oxygen to form negative ions. The recombination of negative ions with positive ones occurs more rapidly than the recombination of electrons with positive ions; therefore, adding hydrogen and oxygen to argon and nitrogen intensifies the decrease in charge density in the gap and promotes the recovery of its strength. Moreover, the add molecules may destroy metastable molecules of the main gas responsible for the reduction of the gap breakdown strength due to stepwise ionization. Besides the above methods, to speed up the recovery of the strength of a gap after a spark breakdown, gas or magnetic blasting can bt: employed, a multielectrode spark gap switch can be used, etc. Thus, the pulse repetition rate depends on the time it takes the gap to recover its breakdown strength. However, the relation Vr(t) is not a unique characteristic of the repetitive operation capability of a spark gap. It is also necessary to know the characteristic that describes the rising voltage across the gap, Vg( t), which should lie below Vr(t) and have no intersection or touch points with the latter. It is of primary importance for Vg(t) to have an initial gently sloping section. It is interesting that this is promoted by the low post­ discharge resistance of a spark gap, which remains almost equal to zero for some time after the discharge. The latter hinders the increase in gap voltage since the charge voltage is almost completely applied to the charging resistor (or inductor). The decrease in voltage rise rate for the initial portion of the characteristic Vg(t) is promoted by the charging of the pulse-forming capacitor or line through an inductor (especially for resonant charging) as distinct from the charging through a resistor (Rubchinsky, 1 958). Moreover, the charge passing through an inductor increases the efficiency of the generator, whereas a charging resistor does not. Because of the large recovery time of a spark gap, the pulse repetition rate in pulse generators with spark gap switches operating with pulse currents of up to 1 kA and voltages of some tens of kilovolts is about 103 Hz. The pulse repetition rate can be substantially increased by using multielectron-initiated discharges in overvolted gaps. As demonstrated in Section 4 of Charter 4, in this case, the discharge operates not in a channel

89

THE PULSED DISCHARGE IN GAS

but in the whole of the gap in which there are initial electrons and a high electric field. According to the data reported by Mesyats ( 1 974), for a discharge of this type operating in air at atmospheric pressure, a short-term mode with a frequency of up to 1 06 Hz is possible. Megahertz pulse repetition rates can also be achieved with hydrogen thyratrons. More information on the problem of deionization of the plasma in gas­ discharge switches can be found in the review by Buttram and Sampayan ( 1 990).

REFERENCES Allen, K. R. and Phillips, L., 1 963, Mechanism of Spark Breakdown, Electrical Rev. 173:779-783. Andreev, S. I. and Vanyukov, M. P., 1 96 1 , Investigations of the Electrical Processes in Spark Discharges ofNanosecond Duration, Zh. Tekh. Fiz. 31:96 1 -964. Bazelyan, E. M. and Raizer, Yu. P., 1 997, Spark Discharge. CRC Press, Boca Raton. Bychkov, Yu. 1 ., Gavri1yuk, P. A., Korolev, Yu. D., and Mesyats, G. A. 1971, Investigation of Development of Discharge in Nanosecond Range under Atmospheric Conditions. In Proc. X Conf. on Phenomena in Ionized Gases, Oxford, p. 168. Bychkov, Yu. 1., Korolev, Yu. D., and Mesyats, G. A. 1978, Pulsed Discharges in Gas under Intense Ionization with Electrons, Usp.Fiz. Nauk. 126:45 1-477. Bortnik, I. M., 1 988, Physical Properties and Electric Strength of SF6 Gas (in Russian). Energoatomizdat, Moscow. Braginsky, S. I., 1 958, On the Theory of the Spark Channel, Zh. Eksp. Teor. Fiz. 34: 1 548- 1 557. Buttram, M. T. and Sampayan, S., 1 990, Repetitive Spark Gap Switches. In Gas Discharge Closing Switches (G. Schaefer, M. Kristiansen, and A. Guenther, eds.), Plenum Press, New York, pp. 289-324. Drabkina, S. 1., 195 1 , On the Theory of the Development of the Channel of a Spark Discharge, Zh. Eksp. Tear. Fiz. 21 :473-483. Evdokimov, 0. B., Mesyats, G. A., and Ponomarev, V. B., 1977, The Volume Discharge in Gas Triggered by an Electron Beam under the Conditions of Nonuniform Ionization, Fiz. Plazmy. 3:357-364. Felsenthal, P. and Proud, J. M., 1965, Nanosecond Pulse Breakdown in Gases, Phys. Rev. A. 139:1 796- 1 804. Fenstemacher, C. A., Nutter, M. J., Leland, W. T., and Boyer, K., 1 972, Electron-Beam­ Controlled Electrical Discharge as a Method of Pumping Large Volumes of C02-Laser Media at High Pressure, Appl. Phys. Lett. 20:56-60. Fletcher, R. C., 1 949, Impulse Breakdown in the sec Range of Air and Atmospheric Pressure, Phys. Rev. 76: 1 50 1 - 1 5 1 1 . GrUnberg, R., 1 965, Gesetzmal3igkeiten von Funkenentladungen im Nanosekundenbereich, Z. fur Naturforsch. A . 20:202-2 12. Gurevich, A. V., 1 960, On the Theory of the Effect of Runaway Electrons, Zh. Eksp. Teor. Fiz. 39: 1 296. Koppitz, J., 1 967, Die radiale und axiale Entwicklung des Leuchtens im Funkenkanal, untersucht mit einer Wischkamera, Z. for Naturforsch. A. 22: 1 089- 1 097.

IQ-9

90

Chapter 4

Korolev, Yu. D. and Mesyats, G. A., 1 998, Physics of Pulsed Breakdown in Gases. URO-Press, Ekaterinburg. Koval'chuk, B. M., Kremnev, V. V., and Mesyats, G. A., 1 970, Avalanche Discharges in Gas and Generation of Nanosecond and Subnanosecond High-Current Pulses, Dokl. AN SSSR. 191:76-78. Koval'chuk, B. M., Kremnev, V. V., Mesyats, G. A., and Potalitsyn, Yu. F., 1 97 1 , Discharge in High Pressure Gas Initiated by Fast Electron Beam. In Proc. X Conf on Phenomena in Ionized Gases, Oxford, UK, p. 175. Kunhardt, E. E. and Luessen, L. N., eds., 1983, Electrical Breakdown and Discharges in Gases. Plenum Press, New York-London. Loeb, L. B., 1 939, Fundamental Processes of Electrical Discharge in Gases. Wiley, New York; Chapman & Hall, London. Marcus, S., 1 972, Excitation of a Longe-Pulse C02-Laser with a Short-Pulse Longitudinal Beam, Appl. Phys. Lett. 2 1: 1 8-19. Meek, J. M. and Craggs, J. D., 1953, Electrical Breakdown of Gases. Clarendon Press, Oxford. Mesyats, G. A., 1 966, Doctoral Thesis Study of the Generation of High-Power Pulses of Nanosecond Duration. Tomsk Polytechnic Institute. Mesyats, G. A., Bychkov, and Yu. I., Iskol'dsky, A. M., 1 968, The Formative Time of Discharges in Short Air Gaps on the Nanosecond Time Scale, Zh. Tekh. Fiz. 38: 1 2 8 1 - 1 287. Mesyats, G. A., Koval'chuk, B. M., and Potalitsyn, Yu. F., 1972a, USSR Patent No. 356 824 (November 23, 1 972). Mesyats, G. A., Bychkov, Yu. I., and Kremnev, V. V., 1 972b, The Nanosecond Pulsed Electrical Discharge in Gas, Usp. Fiz. Nauk. 107:20 1-228. Mesyats, G. A., 1 974, Generation of High-Power Nanosecond Pulses (in Russian). Sov. Radio, Moscow. Raether, H., 1 964, Electron Avalanches and Breakdown in Gases. Butterworths, London. Rompe, R. and Weizel, W., 1944, Uber das Toeplersche Funkengesetz, Z. for Physik. 122:636. Rubchinsky, A. V., 1 958, Investigations of Electrical Discharges in Gases. In Trans. All­ Union Electrical Engineering Institute (in Russian). Gosenergoizdat, Moscow, p. 54. Smith, R. C., 1 974, Use of Electron Backscattering for Smoothing the Discharge in Electron­ Beam-Controlled Lasers, Appl. Phys. Lett. 25:292-295. Tholl, H., Sander, I., and Martinen, H., 1 970, Eine automatische Apparatur zUr Ortlich und zeitlich aufgelosten Spektroskopie an Funkenentladungen, Z. for Naturforsch. A. 25:4 1 2-420. Tzeng, Y. and Kunhardt, E. E., 1990, Electron Beam Triggering of Gas Filled Gaps. In Gas Discharge Closing Switches (G. Schaefer, M. Kristiansen, and A. Guenther, eds.), Plenum Press, New York, pp. 125- 1 44.

Chapter 5 ELECTRICAL DISCHARGES IN LIQUIDS

1.

BACKGROUND

The ideas of the physics of electrical discharges in liquids have gone an intricate way and have always kept pace with the development of the physics of discharges in gas and vacuum. Since the start of the 20th century, there have been two essentially different viewpoints on the phenomenon of electrical discharge in liquid (EDL). According to one of them, an EDL is a discharge in gas which occurs in gas bubbles that either are initially present in the liquid and on the electrodes or are formed under the action of voltage (electrolysis, boiling, degassing of the electrode surfaces, etc.). The proponents of the other viewpoint treat an EDL as a consequence of the avalanche multiplication of free charge carriers in the liquid itself and use a model which is, in fact, a version of the gas discharge model as applied to the liquid phase. They believe that in strong fields, electrons may be accelerated in liquid and ionize molecules and atoms. The electric strength of a liquid is related, through the mean free path of electrons and the cross section for interaction, to the molecular structure of the liquid. This EDL mechanism is called pure electrical. McFarlane, as early as at the close of the 1 9th century, noted that during a long-term application of voltage, four processes occur in the EDL: the formation of filaments from weighed particles, the motion of the liquid, the formation and motion of gas bubbles, and, finally, a spark discharge. This viewpoint was the basis for the creation of a number of non-electronic theories of the breakdown in liquids, such as thermal, gas-thermal, polarization, etc. (Ushakov, 1 975), and was prevailing up to the mid 40s of the 1 9th century.

92

Chapter 5

At the same time, some superficial analogies in the phenomena accompanying, in particular, the development of a discharge in liquid or gas and the resemblance of the relations characterizing the electric strength of liquids and gases formed the basis for a theory of breakdowns in liquids, similar to the Townsend theory for gases. In later studies, it has been shown that at a pulsed voltage the impurities present in a liquid, its temperature, and the pressure of the gas over the liquid have a lesser effect upon the breakdown than in the case of prolonged application of voltage. These facts and the short breakdown delay times (� 1 o-8 s) measured for liquids by Walther and Inge ( 1 934) pointed to the electronic rather than ionic character of a pulsed EDL and was interpreted as a proof for the ionization mechanism of breakdown. However, measurements of the electron and ion mobilities in liquids (Ushakov, 1 975) show that these quantities are very small [�1 0-4 cm2/(Y. s) for ions and �10-3 cm2/(V·s) for electrons] and too low for impact ionization of liquid molecules and atoms to take place. Therefore, the mechanism for breakdown of liquids should be treated, in our opinion, based on the phenomena that start in gas bubbles due to ionization. Recall that the average electric field in a gap is � 106 VIem, while at the electrodes it is no less than 1 08 V/cm. Therefore, it can be stated that the initial injection of electrons and ions into the liquid and the formation of gas bubbles due to high energy densities at the anode and cathode surfaces are quite possible. The mechanism of a discharge in liquid can be understood only based on a detailed description of all phases of the discharge in their time and space sequence. Komelkov (1 945) described a discharge in liquid based on the data of high-speed photography and simultaneous oscillography of the voltage and current waveforms. Discharges in transformer oil and distilled water in needle-plane and needle-needle gaps with d = 12-20 em were photographed using a Bois camera with mechanical sweeping. It was established that the discharge resembled the leader process in long air gaps. It was followed by a bright flash, which was compared by the author of this work to the main (reverse) discharge in a long air gap; after this flash, an arc developed. The ionization zone was � 1 em in size, and the effective rate of growth of the leader channel was 1 . 7 · 1 05 and 6· 1 04 cm/s, respectively, for the positive and the negative leader in transformer oil. This experiment gave no answer to the question of the reason for the appearance of the primary plasma at the electrode upon breakdown. However, it has been demonstrated that there exists a self-growing channel with its ionization zone localized in its head ionization. It has been noted the leader starts developing, as a rule, at the anode; therefore, the electron emission from the cathode is not the dominant process in an EDL.

ELECTRICAL DISCHARGES IN LIQUIDS

93

Later, similar investigations were performed by Liao and Anderson According to their data, a discharge of this type goes through not three, as pointed out by Komelkov (1945), but four stages: the "initiating" streamer, the pilot streamer, the stepwise streamer, the reverse discharge, and the arc. The subsequent studies of the mechanism of an EDL that were performed with the help of electron-optical image converters gave no data that would change the idea of the general pattern of the process. Ushakov (1975) summarized all data on the pulsed EDL available in the literature and complemented them with the results of some important studies.

(1 953).

2.

THE PULSED ELECTRIC STRENGTH OF LIQUID DIELECTRICS

The experiments on investigating the properties of water as an insulator under the action of 1 0-8-s voltage pulses, performed by Mesyats and Vorob ' ev ( 1962), have shown that the electric strength of water is not lower than that of transformer oil and increases with gap spacing (Fig. 5 . 1 ), remaining within the limits (2-3)- 1 06 V/cm. A similar relationship was revealed for transformer oil (see Fig. 5.1). Investigations of the electric strength of water in nonuniform (Rudenko and Tsvetkov, 1 965) and uniform electric fields (Mesyats and Vorob'ev, 1 962) showed that this quantity increases with decreasing pulse duration. For instance, the electric strength of water in a centimeter gap in a uniform electric field for tp 1 0-8 s is 2 · 1 06 VIem, while for tp 3 J..LS and an identical gap it is only 3 · 1 05 V/cm (Ushakov, 1 975). This relationship is the same in character for transformer oil, glycerin, and castor oil.

=

=

'? 4 r-----...----+-__,.,---+---1 �

� 3 f-----+"<:----"-..!--1 �

2 f-----+---....::>o...d---�..,-----1

} �---�---�---� o w w-1 w-2 w-3 d [em] Figure 5. 1. Breakdown electric field Ebr as a function of d for transformer oil (J) and distilled water (2). Uniform field; tp = I 0 ns

94

Chapter 5

For liquids, including water, a strong dependence of the electric strength on the degree of uniformity of the electric field at the electrodes (sharp edges, microprotrusions, etc.) is typical. In this case, the polarity effect is observed to be abnormally strong in asymmetric nonuniform fields. For pulse durations over 1 JlS, the factor by which the breakdown voltage for a negative needle exceeds that of a positive needle is -4 and decreases to -1 .5 for fp 1 0-s s (Ushakov, 1 975). The above data suggest that for a pulse duration of a few nanoseconds, the electric strength, even for technical-grade liquids is over 1 MV/cm, and for fp = 4 ns and d 1 .25 mm in a uniform field it reaches 4 MV/cm. The data on the nanosecond electric strength of liquids for fp 3-100 ns are described satisfactorily by an equation ofthe form (Ushakov, 1 975)

=

=

=

lg Ebr = A - B lg t ,

(5.1)

·

where

Here, Ebr is measured in megavolts per centimeter, t in nanoseconds, and d in centimeters. The values of the coefficients k�. k2, k3 , and k4 for the four test liquids and three typical discharge gaps are listed in Table 5 . 1 . Table 5. 1. Liquid

Gap type

kl

kz

k3

k4

transfonner oil

S-S -N + P +N - P

0.50 0.41 0.37

0.32 0.49 0.32

-0.41 -0.35 -0.35

0.029 0.0 1 0 0.042

distilled water

S-S -N + P +N - II

0.28 0.65

0.82 0.46

-0.36 -0.22

0.220 0.060

glycerin

S-S -N + P +N - P

0.25 0.67 0.53

0.50 0.32 0.35

-0.45 -0. 1 1 -0.24

0.080 0.320 0.043

castor oil

S-S -N + P +N - P

0.38 0.2 1 0.23

0.35 0.37 0.39

-0.41 -0.44 -0.33

0.023 0. 1 1 0 0.077

Here, the symbol S denotes a sphere, N a needle, and P a plane. The sign "+" or "-" ofN and P implies that the electrode is anode or cathode.

ELECTRICAL DISCHARGES IN LIQUIDS 3.

95

THE ELECTRICAL DISCHARGE IN WATER

In view of the exceptional interest in water, which is used as an insulator in lines and as an electrical-discharge medium in switches, we now consider in more detail the physical pattern of an electrical discharge in water. At high electric fields, the conductivity of water substantially increases (Briere, 1 964), and at the prebreakdown stage, it can pass currents of tens of amperes and even some kiloamperes. In this case, an important question is whether a vapor-gas phase can be formed in a gap at the stage preceding the formation of a discharge and ahead of the developing discharge channel. Investigations (Ushakov, 1 975) show that for a water of conductivity cr > 1 0-6 n- 1 ·m- 1 exposed to voltage for t > 10-6 s, the electrothermal ("bubble") discharge mechanism is realized. In the region of the transition from the ionization to the electrothermal breakdown mechanism, the gas formation due to electrolysis (electrochemical discharge) is substantial. If the electrothermal or electrochemical mechanism of a discharge in water in a uniform field is realized, the discharge is initiated at that electrode where the gas generation is more intense (Ushakov, 1 975). In this case, the delay in the appearance of luminosity is largely determined by the formation of a gas bubble (or film) on the electrode and its growth to some critical size (Alfimov et a!. , 1 970). In the range of microsecond pulse durations, the discharge occurs as a leader process developing in two stages (Ushakov, 1 975). The first stage is the growth of constricted channels of diameter ( 1-5)· 1 o-6 m, called primary channels, from the electrode into the gap with a velocity of 1 03-105 rnls. For an electrode potential of 1 05 V, the electric field at the head of a primary 0 channel reaches 1 0 1 V/m. The development of a primary channel from the positive or negative electrode is due to self-ionization or impact ionization in the liquid, respectively. At the stage of nucleation of a primary channel, the electric field necessary for the development of ionization in the liquid (about 10 1 0 V/m) is created at electrode microprotrusions. Primary channels consist of weakly ionized plasma and have high resistance. The longitudinal gradients of potential in a primary channel are (1 .5-2)· 1 06 V/m. As the temperature at the base of a primary channel reaches its critical value, the second stage begins; namely, the ionization wave starts propagating through the ionization channel and the latter transforms into a highly conducting channel. The pressure in the channel increases to several thousands of atmospheres, the channel expands, with a velocity of (1-5)· 1 03 rnls, to (5-1 0)- 1 0-6 m. Simultaneously, the current through the channel increases by three orders of magnitude and becomes brighter due to impact and thermal ionization. The primary channel perturbations starting at its origin propagate at a velocity of (1-3 )· 1 05 rnls toward its head. This is the final event of the

96

Chapter 5

first stage of the jerky development of the highly conducting leader channel with longitudinal potential gradients of (2-5)- 105 V/m. Subsequently, a primary channel develops from the head of the leader channel and transforms into a leader channel similar to that described above. The rate of development of a primary channel, the time intervals between the jerks of a leader, and, hence, the effective velocity of propagation of the leader channel, depend on the properties of the liquid and on the parameters of the voltage pulse (Ushakov, 1 975; Alfimov et a!. , 1 970). For voltage exposure times from 1 o-6 s to some nanoseconds, the results of experiments on pulsed breakdown of liquids also suggest the influence of the gas medium. These results are as follows (Ushakov, 1 975): a) The electric strength increases with hydrostatic pressure for both non­ degassed and degassed liquids. b) The electric strength decreases with increasing temperature. c) For E close to Ebro even in carefully cleaned liquids, the energy density near electrode microprotrusions reaches 1 00 J/cm3 , and this may cause local boiling within some fractions of a microsecond. d) Using high-speed shadow photography, local optical structures other than plasmas have been detected. An experiment was performed (Ushakov, 1 975) to study the discharge in water on the nanosecond time scale (Figs. 5.2-5.4). The pulse generator used generated voltage pulses of amplitude up to 1 MV and rise time 2 ns with the pulse duration varied in the range 1 o-8-1 o-6 s. The water conductivity was cr � 1 0-7 n- ' ·cm- 1 • The gap spacing was 0.03-0. 1 2 em for hemisphere­ hemisphere steel electrodes of diameter 0.8 em, 0.07-0.8 em for needle­ plane electrodes, and 0. 1 5-0.5 em for blade-plane electrodes. Molybdenum and tungsten needles were used. The blade length was 1 .5 em. For diagnostics, an electron-optical image converter with exposure times of 10-9-1 0-8 s was used. For a needle of negative polarity (-N, +P), luminosity appeared, within a few nanoseconds, at the cathode and moved with a velocity of (2-5} 106 crnls toward the anode (with the average electric field being 0.8 MV/cm). As the cathode luminosity covered 60% of the gap spacing, another luminosity appeared at the anode and moved with a velocity of -107 cm/s toward the cathode, and this was accompanied by a current of 1 -5 A. As these two luminosities came together, the switching process began. The discharge from a positive needle had some characteristic features. Luminosity first appeared at the anode. Its motion velocity was high, no less than 1 07 crnls (E = 0.4 MV/cm), and the current was -30 A. At the opposite electrode (cathode), no luminosity appeared. The switching process in the (+N, -P) gap began as the anode luminosity touched the plane. As the needle was replaced by a blade, the characteristic manifestations of the polarity

ELECTRICAL DISCHARGES IN LIQUIDS

97

effect persisted. When the blade was at a negative potential , an increase in E increased the number of simultaneously developing channels (to 3 -7) and the current accompanying their development (to 25-7 5 A). For a blade of positive polarity, an almost homogeneous luminosity throughout the blade length was observed at the stage of discharge initiation. Subsequently this luminosity became discrete, consisting of 10-15 separate blobs carrying a current of up to 3 00 A. With a blade of positive polarity, two or three discharge channels were formed, while with one of negative polarity only one discharge channel developed. As the average electric field was increased to 0.7 MV/cm, 15 channels developed on the positive blade and three on the negative one.

Figure 5.2. Stages of a discharge developing in water in a nonuniform field with a negative needle cathode. E = 1 .2 MV/em; d = 1 .5 mm; interframe interval = 1 0 ns

Figure 5.3. Stages of a discharge developing in water with a negative needle anode. F = 0.35 MV/cm; d = 3.2 mm; interframe interval = 1 0 ns

Figure 5.4. A discharge in a uniform electric field. E = 3.5 MV/cm, d = 0.7 mm; interframe interval = 2 ns

98

Chapter 5

For a discharge in a uniform field of 1 .5-3 MV/cm, 6-9 ns prior to the onset of switching, luminosity started propagating from the anode to the cathode with a velocity of � 1 07 cm/s (Fig. 5.4). As this luminosity touched the cathode surface, it started growing into a discharge channel, and the switching process began. Considerable progress in the study of the mechanism of electrical discharges in liquids was achieved due to the use of laser technology. Investigations of the prebreak:down phenomena in liquids were carried out with a ruby laser used as an illumination source in a scheme of high-speed schlieren photography (Alfimov et al., 1 970; Ovchinnikov and Yanshin, 1 985; Abramyan et al. , 1 97 1). The nanosecond time resolution made it possible to observe an anode-initiated discharge in a uniform field and to reveal some important features of its initiation and development. In particular, it was established that the electrical discharge had an intricate character and went through several successive stages with different mechanisms and development rates. The fine structure of the discharge at the initial stage was revealed. The results of the experiments (Alfimov et al. , 1 970; Abramyan et al. , 1 97 1 ) have demonstrated an exceptional importance of the time and space resolution of the recording equipment in studying electrical discharges in liquids. The use of laser illumination in combination with conventional optical methods (schlieren photography, interferometry, etc.) allows one to achieve high time and space resolution simultaneously, which is especially important in studying prebreak:down phenomena in liquids. The optical methods based on measuring the refraction index (density) of the medium make it possible to reveal the earlier stages that precede the occurrence of intense ionization processes (the luminosity stage of an electrical discharge).

4.

THE ROLE OF THE ELECTRODE SURFACE

In liquids, as well as in other dielectric media, a decrease in field uniformity decreases Ebr· In this respect, liquids feature a stronger dependence of the electric strength on electrode micro- and macrogeometry than gases. This can be accounted for by the fact that pulsed coronas, whose space charge might screen electrodes and distort the field distribution specified by the electrode geometry, fail to develop in liquids and by the high density of liquids owing to which local fields operating in small volumes are capable of initiating a discharge. An important component of the discharge operation time td - the time delay to the discharge initiation ti - is determined for a given liquid by the micro- and macrogeometry of the electrode and by the rate of rise of gap voltage. Obviously, the effect of the electrode geometry on the electric

ELECTRICAL DISCHARGES IN LIQUIDS

99

strength of a discharge gap should be most substantial in those cases where ti makes up a significant portion of the total discharge operation time. The effect of the electrode micro- and macrogeometry on the electric strength of the liquid should be more pronounced for smaller gaps, more uniform electric fields, and higher voltage rise rates (overvoltages). Experimental data support these statements. It has been established (Vitkovitsky, 1 987) that the breakdown voltage of needle-plane gaps (d = 3-9.7 em) in oil for pulses of rise time 1 .2 !J.S decreases on average by 25-40% as the tip radius of the needle electrode is decreased by more than two orders of magnitude (from 2.5 to 0.01 mm). The measurements performed by Ushakov (1975) have shown that for rectangular pulses of duration 50-60 ns with electrode separations of the order of 1 mm, an increase in tip radius from a few micrometers to several hundreds of micrometers increases Vbr by a factor of 1 .5-2.

The electrode microgeometry, whose effect on Ebr shows up in short gaps with uniform and weakly nonuniform fields, is determined by the surface condition of the electrodes and by the crystalline structure of the electrode metal. It is well known that a way of reducing the number of sites of local field enhancement on electrodes made of polycrystalline metals is their aging by discharges. This operation (sometimes called conditioning) is widely used in vacuum breakdown experiments and in some electrovacuum devices. In some experiments (Lewis, 1 959; Felsenthal, 1 966; Ward and Lewis, 1 963), aging of electrodes was employed in measuring the electric strength of liquids. The exposure of electrodes to discharges prior to measurements is aimed at increasing Ebr and decreasing the spread in Ebr and td. Different experimenters recommend substantially different aging modes. For instance, the recommended number of aging discharges ranges from 5 to 1 00. Analysis of the experimental data and the aging mechanism itself point to the fact that the conditioning effect depends on a number of factors: the electrode material, area, and surface condition, the voltage exposure time, the amount and rate of release of energy in the spark channel, and the properties of the liquid. Electrode aging has a favorable effect not for all liquids. An increase and stabilization of the discharge time (for E = const) in purified water were observed after 1 5 -20 discharges (Ushakov, 1 975). In this experiment, sphere-sphere (0.8 em diameter) electrode systems and Rogowski electrodes (2.6 em diameter) were used; the electrodes were made of stainless steel. In the course of aging, the liquid was partially renewed after each breakdown. It can be supposed that no conditioning was observed in oil because not only electrode microprotrusions were destroyed and molten off by the aging discharges, but also hydrocarbon decomposition products deposited on the electrode surfaces, preventing the stabilization of

100

Chapter 5

the properties of the electrode surface. The foregoing shows that aging of electrodes is an inefficient way of increasing and stabilizing the parameter Ebr for liquids. In some cases, the most efficient method for reducing the effect of the electrode microgeometry and increasing Ebr of liquids is to cover electrodes with a thin layer of high-strength solid dielectric. It was observed (Ushakov, 1 97 5) that the breakdown voltage of transformer oil and the flashover voltage of solid dielectrics in a system of coaxial cylinders exposed to microsecond pulses increased by 20-25% if the electrodes were coated with a bakelite lacquer layer of thickness 1 20-1 50 fJm. An increase in breakdown voltage of transformer oil in gaps with a weakly nonuniform field on application of microsecond pulses to electrodes coated with dielectric films was also observed by Standring and Hughes (1962). It should be taken into account that the electric strength of insulating gaps with coated electrodes, which represent a type of combined insulation, depends on the redistribution of the field over the layers of the solid and liquid dielectrics and on the proportion between their Ebr values for a given pulse duration. The feature of highly polar liquids, in particular water, as components of a combined insulation is that they have higher conductivity and permittivity compared to solid dielectrics. These factors are responsible for the overloading of solid dielectric layers operating in a sequential combination with highly polar liquids. Ushakov (1975) pointed out that the coating of electrodes with dielectric films increased to some extent the pulsed electric strength of the insulating gap in water; however, this increase was unstable and not in any case this was the consequence of a poor quality of the coating. In analyzing the effect of barriers on the breakdown voltage of insulating gaps in liquids, it should be borne in mind that the dominant factor in the "barrier effect" in liquid is that the barrier behaves as a mechanical obstacle hindering the development of the discharge channel. By the barrier effect is meant the increase in breakdown voltage of a discharge gap due to thin dielectric obstacles mounted in the gap. Since in liquids, in contrast to gases, the ionization zone is extremely small, the barrier is charged to low voltages and its blocking action (by the opposite field) is insignificant; therefore, the barrier effect in liquids is much less pronounced than in gases. The condition for breakdown of an insulating gap in liquid is that the barrier should be broken down under the action of the field localized at the head of the primary discharge channel. The highest electric strength of a gap with a barrier can be achieved by choosing the liquid-to-solid dielectric constant ratio as small as possible and by using high-strength materials for the barrier. For instance, with a celluloid barrier in transformer oil, Ebr increases by 24-30%, while in purified water it increases only by 8-19%. The use of

ELECTRICAL DISCHARGES IN LIQUIDS

101

high-strength Mylar film in combination with water in a pulse-forming line (Smith et a!. , 1 97 1 ) has made it possible to increase the working gradients of the insulation and its resistance with the dielectric permittivity retained high. As the pulse duration is decreased to several nanoseconds, the use of a sequential combination of liquid and solid dielectrics becomes ineffective since under these conditions solid and liquid dielectrics have comparable electric strengths (A. Vorob'ev and G. Vorob'ev, 1 966). The electric strength of a liquid insulator decreases with increasing the volume of the dielectric and/or the electrode area for a given degree of field uniformity. An increase in electrode area increases the number of weak points that favor the occurrence of breakdown. These weak points are (solid, liquid, and gaseous) impurity particles in the liquid bulk and geometric irregularities, remainders of polishing agents (abrasive, chromium oxide, etc.), products of oxidation of the electrode metal, adsorbed gases and moisture) on the electrode surface. The available experimental data on the electrode area effect are controversial. The dependence of Ebr on electrode 0 area S is very weak: Ebr oc s - · 1 (Martin et a/., 1 996). Therefore, this effect is not always detectable. In this situation, some inferences can be drawn from experiments performed with different types of voltage pulses, other conditions being comparable. Ushakov ( 1 975) investigated the effect of the electrode area on the electric strength of transformer oil for microsecond pulses and rectangular nanosecond pulses Ctr = 2 ns, fp = 3 5 ns). The working gaps were formed by four pairs of stainless-steel Rogowski electrodes of different area. The maximum electrode diameter was chosen so that the interelectrode capacitance would not distort the leading edge of the nanosecond pulse. The electrode areas were 1 . 1 3 , 1 .88, 3 . 1 4, and 5.24 cm2 • The electrode surfaces were carefully polished and a constant time of oxidation of the electrode in air was provided. Preliminary statistical processing of the measurements for electrodes of different area performed to reveal whether they belong to the same or to different categories showed that under these experimental conditions the area effect was observed for microsecond pulses and was absent for nanosecond pulses. The experimental results demonstrate that the electrode area effect depends on the time of voltage action. For a prolonged action of voltage, bridges of foreign inclusions may form where conditions are favorable for breakdown and flashover. Under pulsed voltages, such that impurity microparticles can be considered immobile, an increase in voltage application time enhances the field distortion by impurity particles as they are polarized and, therefore, decreases Ebr of the liquid. In a nanosecond breakdown, the major contribution to the area effect should be from weak points on the electrode (anode in a uniform field) surface. However, due to the fact that the discharge is initiated near individual microprotrusions,

1 02

Chapter 5

which are present in great numbers on large-area electrodes, comparatively small changes in S change the number of initiating centers only slightly and have no effect on the breakdown. If the electrode area is varied over wide limits, the electrode area effect should be expected on the nanosecond scale as well. Data on the effect of the electrode area on the pulsed electric strength of gaps are given in Chapter 7. 5.

THE ROLE OF THE STATE OF THE LIQUID

An important problem concerns the state of the liquid, namely, its degree of contamination, hydrostatic pressure, and temperature. Weighed solid particles, in high concentrations, have a significant effect on the value of Ebr (Ushakov, 1 975). The natural moistening of insulating oils does not change their pulsed electric strength at voltage action times of the order of 1 o-s s even if the de breakdown voltage changes three times. It is well known (Skanavi, 1 958) that as an oil with 0.03% moisture content is subject to prolonged action of voltage, its Ebr decreases to one tenth. This implies that the decrease in oil strength by a factor of -3 .5, as in the experiment under consideration, is achieved if the moisture content makes up no more than 0.01%. These small variations in impurity concentration fail to change appreciably the pulsed electric strength of oil. At high moisture concentrations in transformer oil corresponding to emulsions of "water-in-oil" (� 30-40%) and "oil-in-water" (� 30-40%) type, the pulsed electric strength of the system decreases with increasing moisture concentration. The decrease in electric strength reaches 40-50% for a pulse duration of -1 o-s s and there is almost no decrease for fp � 1 0-8 s. The data on the effect of impurities on pulsed electric strength suggest that the requirements to the purity of the insulating liquids used in pulsed power systems can be moderated. The liquid must be renewed and purified only in the case where it is intensely contaminated with decomposition products as a result of sparking (e.g., in switches) or with particles of the material under treatment (in electric-pulse technologies). An increase in hydrostatic pressure to 1 50-200 atm, realized in experiments on breakdown of liquids (Kalyatsky and Krivko, 1 964; Alfimov et al. , 1 970) and achievable in systems with liquid insulation, does not change the properties of the liquids because of their practical incompressibility. Therefore, the increase in electric strength of liquids with pressure (Fig. 5.5) should be associated with the gas present in the liquid and at the electrodes prior to the application of an electric field and resulting from boiling and electrolysis under the action of the conduction current. An

ELECTRICAL DISCHARGES IN LIQUIDS

1 03

increase in pressure may change the conditions of gas formation, the point of equilibrium between the dissolved molecular gas and the gas in the form of bubbles, and the conditions under which ionization in gaseous inclusions takes place. It should be borne in mind that the leader channel in a liquid is an ionized gas-vapor structure with an insignificant excessive pressure. An increase in hydrostatic pressure may vary the electrical parameters of the leader channel and, as a consequence, the characteristics of the discharge in the liquid even if the breakdown is due to ionization. Studies of the gas formation in liquids gave clear relations of the excessive pressure effect with the pulse duration, conductivity, temperature, and degree of degassing of liquids, which are confirmed experimentally. Increasing hydrostatic pressure can be recommended as a way of increasing the working gradients of insulators of high-voltage devices for a) high-conductivity liquids (water, glycerin); b) large-area electrodes, and c) long-term action ofvoltage (> 0.5-1 J.l.S). 0.5 0.4

s � 6 �

�

0.3 0.2 0.1

v--

L

-

I

5

0

10 p [atm]

15

20

Figure 5.5. Breakdown electric field Ebr for water (a = 5 · 10·-7 n-1 -cm-1) pressure. Uniform field; t = 0.2 J.!S; d 0.8- 1 .2 em

as

a function of

=

Attention should be given to the effect of the temperature of an insulating liquid on Ebr· Increasing temperature favors the gas formation in a liquid because of a) the decrease in temperature increment que to the energy release as a result of the passage of a current necessary for boiling; b) the increase in conductivity of the liquid, and c) the decrease in gas solvability in the liquid. These effects favor the development of an electrothermal breakdown in a liquid and reduce its electric strength. Kalyatsky and Krivko ( 1964) investigated the time-voltage characteristics of water at 5, 20, 60, and 98°C

1 04

Chapter 5

=

and transformer oil at 5, 20, 60, and 1 40°C. The experiment was carried out with an (+N, -P) electrode system (d 1 em) at pulse durations of 0.3- 1 0 J..LS . As the pulse duration fp was decreased, the temperature effect on Ebr decreases and for fp < 0 . 5 J..LS it was not detected at all. The temperature effect on Ebr for transformer oil was observed at higher temperatures than for water. Thus, an occasional increase in temperature of an insulating liquid cannot reduce substantially the pulsed electric strength of the liquid for fp � 1 J..LS unless the boiling point is achieved. Other liquids, in particular, glycerin (s = 40) can also be used for insulation in lines. Mesyats et a/. ( 1970) described several types of nanosecond generators and electron accelerators (� 1 06 V) using glycerin. Among them were a single-pulse generator with a helical coaxial line, a single-pulse generator for powering a pulsed electron accelerator, and a repetitively pulsed accelerator operating at a frequency of 1 00 Hz. The conductivity of water, cr, is one of its important parameters that determine the mechanism of pulsed breakdown and, hence, the electric strength (Ebr). However, the character of the dependence of the electric strength of water on cr is most actively debatable in the literature. Alfimov et a/. ( 1 970), Torijama and Shinohara ( 1 937) and other researchers mentioned an increase in pulsed breakdown voltage of water with increasing cr, while Ushakov ( 1 975) reported, on the contrary, on a decrease in Ebr with increasing cr. An intricate effect of cr on the development of pulsed breakdown was noted by Henry ( 1 948). The contradictions in experimental data were accounted for by the complicated character of the dependences of Vbr and Ebr on cr and by the flaws of the measurement technique (first of all, the strong distortion of the pulse due to the high internal resistance of the generators used). Ushakov ( 1 975) investigated the effect of cr on the electric strength of water and water solutions of NaCl in uniform and highly nonuniform fields in the range of conductivities 1 0-4- 1 0-8 o 1 ·m- 1 for rectangular pulses with tr 1 o-s s, fp 2.6 · 1 o-7 s and the generator wave resistance equal to 4 Q and for oblique waves with tr (0.5-50)· 1 o-6 s. The data presented in Fig. 5.6 show that the dependences of Vbr and Ebr on cr, in the nanosecond and microsecond ranges of voltage application times, have a complicated character, which is determined by the shape of the field and by the polarity of the voltage pulse . Contrary to the wide-spread opinion, reducing the electric strength of water by superfine cleaning does not increase the electric strength of insulating structures with a uniform or a weakly nonuniform field. The optimum value of cr should be determined taking into account the required value of Ebr and the resistance of the water­ insulated unit as well as the expenditures for the production and preservation of water with a small cr in the unit.

=

=

=

-

ELECTRICAL DISCHARGES IN LIQUIDS 1 .3

c.

�

1.1 0.9

.. 0.7 b

�

�

.,....-

�

- .......

1 05

""'r:-...1

0.5 0.3 0.1 1 0-6

__.......

1 0-5

--- -l.

1 0-3 1 0-2 0"1-v - 1 0-2 rn- 1 . m- 1 ] 1 0-4

1 0-1

Figure 5. 6. Breakdown electric field Ebr for water and water solution of NaCl in a uniform field as a function of low-voltage conductivity a1.v. 1 - rectangular pulse; tp = 7 - 1 0-8 s, d = 2 · 1 0-4 m; 2 - oblique wave; A = 1 .47· 1 09 V/s, d = 25-10-4 m

The specific low-voltage conductivity of water can be reduced by thorough purification to 1 0-9 n- 1 -m-1 • The conductivity of water abruptly increases on application of a strong electric field because of the Wien effect, the increase of the dissociation constant, and the appearance of an electron current component due to electron emission from the cathode and ionization. We shall return to some aspects of discharges in liquids, in particular, to the solid dielectric flashover in liquid, when considering liquid spark gaps and liquid-filled lines. A review of the studies on discharges in liquids as applied to fast switching of currents in pulsed power generators is given by Vitkovitsky ( 1 987).

REFERENCES Abramyan, E. A., Komilov, V. A., Lagunov, V. M., Ponomarenko, A. G., and Soloukhin, R. I., 1 97 1 , Megavolt Energy Condenser, Dokl. AN SSSR. 201:56-59. Alfimov, A. P., Vorob'ev, V. V., Klimkin, V. V., Ponomarenk:o, A. G., and Soloukhin, R. 1., 1 970, The Development ofan Electrical Discharge in Water, Dokl. AN SSSR. 194 (5). Briere, G. B., 1 964, Electrical Conduction in Purified Polar Liquids, Brit. J. Appl. Phys. 15:4 13-4 1 7. Felsenthal, P., 1 966, Nanosecond Breakdown in Liquid Dielectrics, J. Appl. Phys. 37:37 1 3-3 7 1 5 . Henry, H . F . , 1 948, Velocity o f the Anode Spark i n Copper Surface Solutions under Application oflmpulsive Potential, J. Appl. Phys. 19:988. Kalyatsky, I. I. and Krivko, V. V., 1 964, Investigation of the Pulsed Electric Strength of Transformer Oil and Water at High Pressures and Temperatures. In Breakdown of Dielectrics and Semiconductors (in Russian), Energia, Moscow, pp. 249-25 1 .

1 06

Chapter 5

Komelkov, V. S., 1 945, Mechanism of the Pulsed Breakdown of Liquids, Dokl. AN SSSR. 47:269-272. Lewis, T. J., 1 959, The Electric Strength and High-Field Conductivity of Dielectric Liquids. In Progress in Dielectrics, Vol. 1 . (J. B. Birks and J. H. Schulman, eds.), Heywood, London, pp. 97- 140. Liao, T. W. and Anderson, J. G., 1 953, Propagation Mechanism of Impulse Corona and Breakdown in Oil, Trans. AlEE, Pt I, Communication and Electronics. 72:64 1-647, disc. pp. 647-648. Martin, T. H., Guenther, A. H., and Kristiansen, M., eds., 1 996, J. C. Martin on Pulsed Power. Plenum Press, New York. Mesyats, G. A. and Vorob'ev, G. A., 1 962, On the Possibility of Using Liquid Spark Gaps in Nanosecond High-Voltage Pulse Circuits, Izv. Vyssh. Uchebn. Zaved. , Fiz. 3:2 1-23. Mesyats, G. A., Nasibov, A. S., and Kremnev V. V., 1 970, Formation of Nanosecond High Voltage Pulses (in Russian). Energia, Moscow. Ovchinnikov, I. T. and Yanshin, E. V., 1 985, Measurements of the Prebreakdown Conductivity of Water. In Pulsed Discharges in Dielectrics (in Russian, G. A. Mesyats, ed.), Nauka, Novosibirsk. Rudenko, N. S. and Tsvetkov, V. I., 1 965, Investigation of the Electric Strength of Some Liquid Dielectrics under the Action ofNanosecond Voltage Pulses, Zh. Tekh. Fiz. 35 ( 1 0). Skanavi, G. I., 1 958, Physics ofDielectrics (Strong Fields) (in Russian). GIFML, Moscow. Smith, J., Champney, P., Hatch, L., Nielsen, K., and Shope, S., 1971, High Current Pulsed Electron Beam Generator, IEEE Trans. Nucl. Sci. 18:491 -493. Standring, W. G. and Hughes, R. C., 1962, Impulse Breakdown Characteristics of Solid and Liquid Dielectrics in Combination, Proc. fEE. A. 109:473-478. Torijama, 1., and Shinohara, V., 1 937, Electric Breakdown Field Intensity of Water and Aqueous Solutions, Phys. Rev. 51 (8). Ushakov, V. Ya., 1 975, Pulsed Electrical Breakdown of Liquids (in Russian). Tomsk State University Publishers, Tomsk. Vitkovitsky, I., 1 987, High Power Switching. Van Nostrand Reinhold Company, New York. Vorob'ev, A. A. and Vorob'ev, G. A., 1 966, Electrical Breakdown and Destruction of Solid Dielectrics. Vyssh. Shkola, Moscow. Walther, A. F. and Inge, L. D., 1934, Electrical Breakdown of Liquid Dielectrics, Zh. Tekh. Fiz. 4:1 669-1 887. Ward, B. W. and Lewis, T. J., 1 963, The Influence of Static Stress and Electrode Surface Layers on the Electric Strength of n-Hexane, Brit. J. App/. Phys. 14:368-373.

PART 3 . PROPERTIES OF COAXIAL LINES

Chapter 6 SOLID-INSULATED COAXIAL LINES

1.

PRINCIPAL CHARACTERISTICS

Coaxial lines and cables with polyethylene and fluoroplastic insulation, coaxial lines with liquid insulation (transformer oil, glycerin, water), and coaxial vacuum lines are widely used for the formation, transformation, and transmission of high-voltage pulses. The operating voltage of these lines may reach 1 05- 1 07 V. When using coaxial lines for pulse formation and transformation, it is necessary to know the characteristics that determine the reliability of the lines and the limits of their use. These characteristics are the electric strength of a cable in repetitive operation and the frequency band. Below we use the name "coaxial lines" for both coaxial lines and cables. The main formulas for the calculation of the parameters of coaxial lines are given in the monograph by Belorussov and Grodnev ( 1 959) . Here, we give only those necessary for the calculation of the parameters of high­ voltage lines. The inductance L of a coaxial line with copper conductors is determined by the formula

(

)

D2 1 3 .33 1 1 L_ HIm, + + - 0 . 2 1n � Dz , J..l �

.J7

(6. 1 )

where D2 and D 1 are the diameters (in mm) of the outer and the inner conductor, respectively, and f is the frequency of the signal propagating through the line. If the signal frequency is high, the second summand in (6. 1 ) can be neglected. The capacitance of a coaxial line is determined by the formula (Belorussov and Grodnev, 1 959)

Chapter 6

1 10

C=

8 nF/m' 1 8 ln (D2/� ) '

(6.2)

where 8 is the dielectric permittivity. For a coaxial line with an insulation combined in length (air-insulated cable with bearing disks) we have 8=

81Jii + 8z Vz ' Vi + Vz

(6.3)

where the quantities with indices " 1 " and "2" refer to the first and the second dielectric, respectively, and V1 and V2 are the volumes occupied by the respective insulators. For an insulation combined in the radial direction, we have (6.4)

where the indices " 1 " and "2" refer, respectively, to the inner and the outer dielectric and Dr is the diameter of the interface between the media. For the wave impedance Z0 , from (6. 1 ) and (6.2) we obtain (6.5)

The velocity of propagation of an electromagnetic wave along a coaxial line is determined by the formula v=

c

.J;.

,

m/s,

(6.6)

where c is the velocity of light in vacuum. Let us now consider the problems of choosing the design dimensions of a coaxial line at which the highest possible electric strength is achieved. The electric field Ex at a point located at a distance rx from the cable axis (�/2 < rx < D2/2) is given by (Belorussov and Grodnev, 1 959)

Ex =

v rx ln (Dzl� )

'

(6.7)

=

where V is the voltage applied to the cable. Obviously, for rx = D 1 12 the quantity Ex has the highest value, while for rx D2/2 it has the lowest value. If V and D2 are given, from (6.7) it can be obtained that for D 1 D2/2.72 the value of Ex will be a minimum.

=

SOLID-INSULA TED COAXIAL LINES

Ill

To the condition D2/D 1 = 2. 72 there corresponds a coaxial line with a wave impedance 60/ Jf. . It should be noted that in this case the coaxial line will not be under the best conditions for wave damping (D2/D 1 = 3.6 for copper wires) (Belorussov and Grodnev, 1 959). When designing coaxial lines intended for transmission of nanosecond pulses, it should be borne in mind that these lines, because of wave damping, have some limitations in frequency. Moreover, lines with a discrete insulation (e.g., insulating and centering disks placed at a certain distance in an air-insulated cable) have limitations associated with the nonuniformity of these lines. The critical wavelength /..0 , such that signals of shorter wavelength cannot be transmitted through the line, is determined as

A.0 = 2(a + I1Jf.),

(6.8)

where a is the distance between the disks (in em), 11 is the disk thickness (in em), and s is the permittivity of the dielectric. If the wavelength is comparable to the transverse dimensions of a coaxial line, waves of higher (TE 1 1 and Hu) types appear in the line. For these waves, the theory based on the telegraph equations is not valid. In this connection, the pulse transmitted by the line is distorted. The frequency at which higher types of wave appear and can be transmitted through a coaxial line is called critical. The critical frequency of a coaxial line is given by the following formulas: (6.9)

for type TE 1 1 waves and (6 . 1 0)

for type H 1 1 waves.

2.

PULSE DISTORTION

When a pulse passes through a coaxial line, the pulse shape is distorted due to three main reasons: the losses in the metal, the dielectric losses in the insulation, and the losses associated with ionization processes.

Chapter 6

1 12

The modern technology of production of solid-insulated coaxial cables ensures a small volume of air inclusions. Therefore, the effect of ionization processes on the deformation of high-voltage pulses can be neglected. Kalyatsky et al. ( 1 965) investigated the distortion of high-voltage pulses of amplitude up to 70 kV in their transmission through a type RC- 1 03 cable (type of Russian rf cable) of length 530 m. It has been shown experimentally that the presence of a corona affects the damping and distortion of high­ voltage pulses only slightly and the deformation of high-voltage pulses in solid-insulated coaxial cables with high field gradients (up to 50 kV/mm) can be calculated by the method used for low field gradients. In this case, the experimentally obtained damping appears to be greater than the calculated one by 3-8%. Additional investigations have shown that this difference is due to the pulsed corona occurring in the air gap between the solid insulation and the cable braid. At frequencies of up to 50 MHz, the dielectric losses in the insulation of polyethylene-insulated cables make up no more than 3-5% of the losses in the metal and can be neglected. With increasing frequency, the losses in the dielectric increase more rapidly than in the metal and become prevailing at frequencies over 1 .5-3 GHz (Morugin and Glebovich, 1 964). Taking into account the losses in the metal only, one can describe the deformation of a rectangular pulse ("single step") the expression (Zhekulin, 1 94 1 ) (6. 1 1 )

h (l, t) = erfc (Z) = 1 - (Z) ,

where h (/, t) is the transient characteristic of the cable; (Z) is the probability integral (Kramp's function); Z = _!!L .' 2

Jj;

eo �(

)

1 1 1 � =v J.!P - + - ; 47t Lo RI R2 -

td = ! .)Lo Co

is the delay time of the cable; Lo = 2 · 1 0-7 1n (R2 /R1 ) (Him) is the inductance per unit length of the cable; C0 = e · I 0-9 1 1 8 ln (R2 /RJ ) ] (F/m) is the capacitance per unit length of the cable; e is the relative dielectric permittivity of the insulation; R 1 and R2 are the respective radii of the inner and outer conductors of the cable (mm); J.! and p are, respectively, the magnetic permeability and the resistivity of the conductor material (for copper J.! 47t· 1 0-7 Him); I is the cable length, and p = 1 .75· 1 0-2 fl·mm2/m. The probability integral

=

<1> (Z)

=

(

1 s:

2 e-x dx

SOLID-INSULA TED COAXIAL LINES

1 13

cannot be expressed in terms of elementary functions. However, its values can be found in tables. When calculating the deformation of nanosecond pulses, if there is a need to take into account the losses in the dielectric, one should calculate the transient characteristic of the cable by the formula (Zhekulin, 1 94 1 )

h (l, t ) = � 1t

Joo0 P(ro) sin rot1 dro , (l)

(6. 1 2)

J

where P ( ro) = e-a/ cos (ro/ LoCo - Bl) is the frequency characteristic of the cable, which is the real part of the transmission coefficient;

a = � {Co + Go {I; 2

vr;;

vc;;

2

is the damping coefficient of the cable (in the high-frequency range); � = bt. 2roLo/C0 is the active resistance of the cable per unit length (Q/m), and G0 = ro C0 tg8 is the conductivity of the insulation per unit length of the cable (.Q- 1 ·m- 1 ). For frequencies above several hundreds of kilohertz, the frequency dependence of tg8 for polyethylene-insulated cables can be expressed by the formula (Morugin and Glebovich, 1 964)

J

tg 8 = where a 1

JOO

a1 , 1 + moo

=

B = ro

1 .2· 1 0-8 s 1 12/rad1 12 ; m

=

(6. 13) 2· 1 0- 1 1 s/rad, and

Co Go {I; )2 2LoCo + (-� vr;;{Co-vc;; Lo

2

2

is the phase coefficient. The calculation of the transient characteristic by formula (6. 1 2) can be performed either analytically or with the use of numerical methods. To some approximation, the transient function of a coaxial cable, with due regard for the losses in the dielectric, can be presented (Morugin and Glebovich, 1 964) by formula (6. 1 1 ); the argument Z is calculated by Z=

0.347 a b/ = 2 robt1 2 robt1 '

J

J

(6. 14)

where rob is the boundary frequency of the bandwidth of the cable and ab is the coefficient of damping at the boundary frequency. The boundary

Chapter 6

1 14

frequency rob is equal to the frequency at which the transmission factor k = e - rl (where y = a + j�) decreases by 3 dB with respect to its value at low frequencies. In accordance with the above definition, rob can be calculated by the formula (6. 1 5) Since this transcendent equation is difficult to solve, we give plots of the boundary frequency of the cable bandwidth for the most widespread types of cables (Fig. 6. 1 ) (Morugin and Glebovich, 1 964). �

.... � ... ��

f---

r--

��� -......; �S::t::

RC-50-1 1 - 1 3 f--- RC- 1 00-7-1 3 f--- RC-75-4-1 5 I f--f--- RC-75-4- 1 8 f--RC-50-2- 1 3 / 1 01

.)-...t-. ..'-' ...

�� / "' �""' I' ' "

"�

f---

I

2

3

5

10 I [m]

� ...... ........

20

30

50

Figure 6. 1. Bandwidth boundary frequency as a function of cable length measured for several cable types taking into account the losses in the dielectric and conductor

1 .0 0.8

-..::

0.6 0.4 0.2

0

0.04

t [ns]

0.08

0. 1 2

Figure 6.2. Transient characteristics of the RC-50-1 1 - 1 3 cable for different lengths

1 15

SOLID-INSULA TED COAXIAL LINES

Figure 6.2 presents the transient characteristics of type RC-50- 1 1 - 1 3 cable of length 1 , 5, 1 0, and 30 m (Morugin and Glebovich, 1 964), where is the ratio of the input voltage to the output one V1 • If one needs to calculate the deformation of a pulse whose waveform is other than rectangular, the Duhamel integral should be used. In this case, the output voltage is given by

A(t)

V2

V2(t) V2(t) = f�Jil'('t)h(t-'t)d't, (6. 1 6) where 't is the running time and Jlj'('t) is the derivative of the input voltage.

3.

NONUNIFORMITIES

In coaxial lines used as pulse-forming and transmission units of nanosecond high-voltage pulse generators, nonuniformities of two types may appear. These are nonuniformities associated with the electric layout of the generator individual units and circuits (when additional elements are connected to the line, when lines with different wave impedances are connected to one another, when lines are branching, etc.) and nonuniformities associated with design and wiring (abrupt changes in wire dimensions, inclusion of support insulators, breaks of lines, etc.). To estimate the effect of a nonuniformity of the first type on the waveform, an equivalent circuit is generally used which consists of a two­ terminal network and a generator. The generator consists of a source of voltage 2 Ylnc. where Ylnc is the voltage of an incident wave of arbitrary shape (Vorob ' ev and Mesyats, 1 963), and a transmission line of wave impedance Z0• The resistance of the two-terminal network consists of the input resistance of the remaining portion of the line, Z0, and the input resistance of the added element, Z0 1 • The type of the two-terminal network depends on the way by which the nonuniformity is involved. For instance, if a circuit element of resistance Z01 (uniform line or active resistance) is connected into a braking of a line with wave impedance Z0, the resistances Z01 and Z0 are series-connected. If an arbitrary element of resistance Z0 1 is connected at the end of a line, this resistance will serve as the resistance of a two-terminal network. In this case, for a short circuit we have Z0 1 0, while for an open end of the line Z01 = oo . It should be borne in mind that an equivalent circuit is applicable only for the time interval between the arrival of a wave at the nonuniformity and the point in time at which the waves refracted and reflected from the nonuniformity return from the end and the beginning of the line. To take into consideration the reflected waves, one can use the superposition method.

=

Chapter 6

1 16

When analyzing nonuniformities in transmission lines and their effect on the pulse shape, one can use the results obtained in microwave technology. In doing this, it is necessary to know the highest frequency fm in the pulse spectrum that is to be transferred so that the relevant amplitude and phase change not substantially. Forfm we can take the upper boundary frequency of the frequency characteristic, which corresponds to the point where the amplitude decreases by a factor of 1 I J2 compared to the amplitude at medium frequencies. The relationship between fm and pulse rise time tr, which is determined between the 1 0% and 90% levels of the amplitude, is given by (Lewis and Wells, 1 954) fm � 0.4/tr .

(6. 1 7)

In the general case, the effect of a second-type nonuniformity on the voltage waveform (Lewis and Wells, 1 954) is taken into account by replacing the nonuniformity with a four-terminal Pi or T network whose parameters depend on the nonuniformity characteristics and on the line dimensions. The simplest nonuniformities of interest to us can be replaced by a capacitor connected in parallel with the line. Let us consider a stepwise change in the radius of a coaxial cable conductor as a nonuniformity of frequent occurrence. In practice, three different cases may take place: a) only the inner conductor diameter changes (Fig. 6.3, a); b) only the outer conductor diameter changes (Fig. 6.3, b); c) both diameters change simultaneously (Fig. 6.3, c). In all cases, the nonuniformity is taken into account by including a capacitance (Fig. 6.3, d) C = FD,

(6. 1 8)

where D is the diameter of the outer conductor (for the second case, we may take D = (� + D2 )/2 ). The coefficient F as a function of the diameter ratio is given in Fig. 6.4 (Meinke and Gundlach, 1 956). The curve d1 /D = 0 corresponds to the break of the inner conductor. For the third case, the capacitance C (Fig. 6.3, c) is determined based on the results of the two previous cases. In doing this, it is first assumed that only the inner conductor has a step and then that the outer one has a step, too. The equivalent capacitance is found by adding the capacitances associated with the first and second assumptions. It should be borne in mind that the data given here can be used for the wavelength A. > 5D', where D' is the largest diameter of the line. The curves for the determination ofF, given in Fig. 6.4, are intended for designing air lines. For a cable filled with a dielectric, the capacitance C should be multiplied by the dielectric permittivity s. If a dielectric fills only a line with the inner

1 17

SOLID-INSULA TED COAXIAL LINES

conductor of smaller diameter, the value of the capacitance C estimated with the help of the plots in Fig. 6.4 should be multiplied by e. If a dielectric fills a line with a larger diameter of the inner conductor, we can roughly assume that the value of C found for the air line remains unchanged. For lines with the outer conductor of variable diameter, one can assume that as a line of larger diameter is filled with a dielectric, the value of C increases e times, while for a line of smaller diameter C remains unchanged. If only some part of a coaxial line with invariable dimensions is filled with a dielectric, this is tantamount to stating that the wave impedance experiences a jump.

I!

���

(a)

D

Zo2

(!

n2

(c)

d,

DI

.I

(d)

--

. ...!

Zo1

I

Zo2 d2

D2

Ll

Zo2

Figure 6.3. Second-type line nonuniformities (a, b, and c) and their equivalent circuit (d)

(b) 0.5

(a) 0.4

0.4

0.3 t:-..

t:-..

0.2 0.1

0

0.3 0.2 0.1

0.2

0.4

0.6

d2/D

0.8

1 .0

0

0.2

0.4

0.6

0.8

1 .0

d/D2

Figure 6.4. Plots for the calculation of the capacitance C, corresponding to the nonuniformities shown in Fig. 6.3, a and b

Chapter 6

118

In some cases, stepwise changes in line dimensions may occur with the wave impedance remaining unchanged. In this case, the condition d1 /D 1 = d2/D2 should be fulfilled. The nonuniformity at the joint is taken into account by introducing a capacitance C in the equivalent circuit. The effect of this capacitance can be substantially moderated by shifting the inner conductor for a distance /::,. = D2/ 1 0 from the position of the nonuniformity (shown by the dashed line in Fig. 6.3). This shift is the same as if we included a series-connected inductance to compensate the effect of the capacitance C. At high voltages, the electric strength of such a joint is small because of the presence of sharp comers. The best way of increasing electric strength is to use a smooth conical reducer between two lines. It is appropriate to choose the length of this reducer from the relation

l � 2Dz.

(6. 1 9)

A conical reducer is often used in discharge devices, pulse peakers, and the like. A detailed procedure for designing such a reducer is given elsewhere (Vorob'ev and Mesyats, 1 963). Methods for eliminating nonuniformities resulting from the presence of dielectric support elements were described by Lewis and Wells ( 1 954).

PULSED ELECTRIC STRENGTH OF SOLID

4.

INSULATORS

Investigations of the mechanism of breakdown of solid dielectrics under the action of rectangular voltage pulses of nanosecond rise time were performed at Tomsk Polytechnic University (TPU) (A. A. Vorob'ev and G. A. Vorob'ev, 1 966). We shall discuss only those publications where the dependence of the breakdown delay time on electric field is given for practical insulating materials. The electric strength was studied for a number of polar and nonpolar polymers in uniform and nonuniform electric fields at voltage exposure times � 3 · 1 0-8 s (Korolev and Torbin, 1 970). The applied voltage pulse had amplitude of up to 500 kV and a rise time of 3 ns. The peak voltage decreased by 7% within 30 ns. The test materials were organic glass, polystyrene, polyethylene, polyvinylchloride, and fluoroplastic-4. For the breakdown experiment in a nonuniform field, the thickness of the samples was 1 .5-3 mm Breakdown was initiated in the point-plane geometry. A needle with a tip radius of 65 J.!m was pressed in a dielectric for a depth of 3 mm A uniform field in a sample was created using the sphere-plane electrode geometry. The spherical electrode was a polished steel ball of .

.

1 19

SOLID-INSULA TED COAXIAL LINES

diameter 14 mm pressed, in the heated condition, in the dielectric. The gap spacing was 0.5 mm A piece of copper foil attached to the dielectric surface with Vaseline oil served as the plane electrode. Samples were immersed in transformer oil. It was revealed that the electric strength of organic glass and polyvinylchloride in a point-plane field was much lower than that of nonpolar polymers (Fig. 6.5), while in a uniform field, the electric strength of polar polymers was considerably higher than that of nonpolar polymers. .

3

3 2 'E 0 >

'E 2

� 6

6 �

>

�

0

20

10

30

0

10

t [ns]

20

30

t [ns]

Figure 6.5. Average breakdown field as a function of voltage application time for polystyrene (1), polyethylene (2), organic glass (3), fluoroplastic-4 (4), and polyvinylchloride (5) for a point of negative (a) and positive polarity (b)

The electric strength as a function of the time of voltage application was found for polystyrene, fluoroplastic-4, organic glass, and muscovite at pulse durations varied from 5 · 1 0-9 to 3 · 1 0-6 s (Mesyats et al., 1 970). Hemispherical and plane electrodes were prepared by vaporizing tin in vacuum. The thickness of samples at the places where breakdown occurred is given in Table 6. 1 . Also given is the spread in electric strength values about an average value for a pulse of duration about 5 · 1 0-9 s. Film materials are superior in electric strength to sheet materials. Table 6. 1. Dielectric material

Thickness, em

Spread, MV/cm

Organic glass

0.035

1 .50

Polystyrene

0.050

1 .25

Fluoroplastic-4

0.080

0.92

Fluoroplastic-4 (film)

0.032

1.18

Polystyrene (film)

0.021

1 .45

1 20

Chapter 6

The insulating material most widely used for radio-frequency and pulse cables is polyethylene, which, in plane samples, shows a considerable electric strength (300-600 kV/mm). For short pieces of cables exposed to single pulses, the maximum breakdown electric field is of the same order of magnitude. However, it decreases to 1 0-20 kV/mm for multipulse exposure and strongly depends on the technology of application of the insulation, the presence of semiconductor layers, the diameter of the core conductor, etc. Examination of polyethylene has shown that the main factor responsible for the reduction in electric strength of the cable insulation is that the insulator contains variously sized air and gas inclusions in which, at high voltages, electrical discharges occur, leading to quick destruction of the insulator and to breakdowns of the cable. In this case, the insulator is first destroyed near the air inclusions and thereafter discharge channels grow into the bulk of the insulator. For a breakdown to be complete, a certain number of pulses are required, and this number depends on the number of air inclusions and their size, the pulse amplitude and shape, and some other factors. Reliable data on the electric strength of coaxial cables exposed to voltages corresponding to the operating modes of nanosecond high-voltage generators are not available. It is possible to obtain only rough estimates of the lifetime of cables operated in these modes. The most correct information is obtained from the so-called "lifetime curve" of a cable, which represents an experimentally obtained relation between the number of pulses leading to breakdown and the amplitude of these pulses. A typical "lifetime curve" of type IC-2 (pulse) cable obtained for its 10.6-m long pieces exposed to voltage pulses of rise time 0.8 ms and duration 3 JlS (Mesyats et a/. , 1 970) is given in Fig. 6.6. The question of how the lifetime curve will change on changing the pulse waveform yet remains open. It can be expected that the effect will be not very pronounced (Mesyats et a/. , 1970). A considerable increase in lifetime is anticipated only for bipolar pulses. As established experimentally, for tp = 1 00 ns, V = 50 kV, and f = 50 Hz, the average lifetime of type RC- 1 06 cable, reaching in some cases 1 000 h, is largely determined by the cable quality (Mesyats et a/. , 1 970). To determine experimentally the lifetime curve of a cable is time- and material-consuming. Therefore, of interest is a method (Delektorsky, 1963) in which it suffices to determine experimentally two or three points of the lifetime curve, and the rest of the points are obtained analytically. For rough evaluation of the number of unipolar pulses that can be held off by the polyethylene insulation of a cable, the following empirical formula can be used (Howard, 1 95 1 ):

SOLID-INSULATED COAXIAL LINES N = 7.2 · 1 01 0

( � )8.4 2 c

121

,

(6.20)

where Vc is the amplitude value of the initial voltage at which a corona appears and Va is the amplitude of the pulsed voltage applied to the cable. For instance, for an RC- 1 06 cable operated with unipolar pulses of amplitude Va = 50 kV, we have the number of pulses

N

�

7.2 - 1 01 0

( � r, -s

2

d .6 - 1 06

The most efficient way of increasing the voltage at which ionization begins is to use semiconductor layers on the inner conductor and beneath the screen. The necessary condition for the semiconductor layers to work well is their good adhesion to the insulation layer. When choosing the value of the resistivity of the semiconductor layer, the requirement must be met for the air inclusion at the boundary of the conductor to be reliably shunted. 500 400

> 300 c.

� 200 " "'

1 00 0

1

2

3

4 lg N

5

6

7

Figure 6. 6. "Lifetime curve" for a 1 0.6-m long piece of iC-2 cable

The use of superconductor layers has made it possible to produce a series of type CPV high-voltage cables with polyethylene insulation (CPV- 1120, CPV- 1150, CPV- 1/75, CPV- 11300). Experiments performed at TPU have demonstrated that a piece of CPV- 1 /300 cable of length up to several tens of meters is capable of holding off 6-1 0 hundred pulses of amplitude 250 kV and 1 00-200 hundred pulses of amplitude 1 80 kV. The type IC-4 cable with semiconductor layers, commercially produced in Russia, is designed for prolonged operation under unipolar pulses of amplitude 75 kV. In the United States, a series of special pulse cables with polyethylene insulation and

1 22

Chapter 6

semiconductor layers is produced. These cables are rated to voltages ranging from 20 to 1 00 kV and have lifetimes no less than 1 06 pulses (for the maximum electric field in the insulation 20-25 kV/mm). Of considerable promise for the use with nanosecond high-voltage generators are coaxial lines with liquid insulators. They have a number of advantages over polymer-insulated cables, such as higher reliability, better conditions for cooling, self-healing of the liquid insulation after breakdown, and less intense damping (Mesyats et al. , 1 970). The high reliability of this type of coaxial system is ensured by the fact that the solid insulator occupies a small volume and therefore can be carefully examined and tested. The properties of liquid-insulated lines are considered in the following chapter.

REFERENCES Belorussov, N. I. and Grodnev, I. I., 1 959, Radio-Frequency Cables (in Russian). Gosenergoizdat, Moscow-Leningrad. Delektorsky, G. P., 1 963, Mechanism for Breakdown of Polyethylene-Insulated High-Voltage Cables on Application of Voltage Pulses, Vestnik Elektropromyshlennosti. 1:55-57. Howard, P. R., 1 95 1 , The Effect of Electric Stress on the Life of Cables Incorporating a Polythene Dielectric, Proc. lEE. 98:365-370. Kalyatsky, I. I., Dulzon, A. A., and Zhelezchikov, B. P., 1 965, Distortion of Monopolar High­ Voltage Pulses in Coaxial Cables, Izv. SO AN SSSR, Tekh. Nauki. 10: 1 5 1 -1 54. Korolev, V. S. and Torbin, N. M., 1 970, Electric Strength of Some Polymers under the Action of Short Voltage Pulses. In Electrophysics Apparatus and Electrical Insulation (in Russian). Energia, Moscow. Lewis, I. A. D. and Wells, F. H., 1 954, Millimicrosecond Pulse Techniques. Pergamon Press, London. Meinke, H. and Gundlach, F. W., eds., 1956, Taschenbuch der Hoch.frequenztechnik. Springer, Berlin. Mesyats, G. A., Nasibov, A. S., and Kremnev, V. V., 1 970, Formation ofNanosecond High­ Voltage Pulses (in Russian). Energia, Moscow. Morugin, L. A. and Glebovich, G. V., 1964, Nanosecond Pulse Power Technology (in Russian). Sov. Radio, Moscow. Vorob'ev, A. A. and Vorob'ev, G. A., 1966, Electrical Breakdown and Destruction of Solid Dielectrics (in Russian). Vyssh. Shkola, Moscow. Vorob'ev, G. A. and Mesyats, G. A., 1 963, Techniques for the Formation of Nanosecond High-Voltage Pulses (in Russian). dosatomizdat, Moscow. Zhekulin, L. A., 1 94 1 , Propagation of Electromagnetic Signals through Coaxial Cables, Izv. AN SSSR, Tekh. Nauki. 3: 1 1 -24.

Chapter 7 LIQUID-INSULATED LINES

1.

GENERAL CONSIDERATIONS

As the methods for production of nanosecond high-power pulses were developed, a need aroused in pulse generators with currents of 105-1 06 A, voltages of 1 06-1 07 V, and pulse durations of 1 o-8-1 0-7 s. Generally used as energy stores in generators of this type are capacitors and coaxial or strip lines filled with liquid dielectric (as a rule, transformer oil or water). The nanosecond high-power pulse generators commonly use lines of two types (corresponding to their purposes): energy-storage lines and transmission lines. The former operate with pulse transformers charged by Marx generators or they are charged by a pulse of rise time � 1 o-6 s. The latter are intended to transfer energy by pulses of duration 10-8-1 o-7 s. Therefore, it is important to know how oil and water behave under exposure to microsecond and nanosecond electric fields. Distilled water was first used as a dielectric for an energy-storage capacitor in experiments with electrically exploded wires (Chace and Moore, 1 959). Early low-inductance nanosecond generators capable of producing high pulsed electron currents and intense electric fields were developed at the Institute of Nuclear Physics (Novosibirsk) (Lagunov and Fedorov, 1 9 7 8). Recall that, according to formula (6.5), the wave impedance of a coaxial line is given by Z0 = (60/ .J;.) ln (D2 /Dt ) [Q], where s is the relative dielectric permittivity and D2 and D1 are the respective diameters of the outer and inner conductors. For a strip line, we have z0

=

3 77 d .j;, b

[Q]

'

(7 . 1 )

Chapter 7

1 24

where b is the strip width and d is the distance between two strips. The general case is d « b. If a conventional long line is discharged into a matched load, the current carried by the load is

l= _I_ 2Z0 '

(7.2 )

where V is the charge voltage of the line. Substituting in (7 .2) the wave impedance for a strip line, we get the current supplied by the generator per unit width of the strip: (7.3) Here, E is the electric field in the line insulation. For a coaxial line, the reduced current is given by

_!__ D1

=

4. 1 5 · 1 0-3 E.ft

.

(7.4)

From formulas (7.3) and (7.4) it follows that the highest reduced current that can be received by a line from a generator combined with an energy­ storage line is determined by the permittivity of the insulation and its electric strength. To produce high currents, it is necessary to use dielectrics with large values of the quantity E.ft . In fact, this quantity determines the specific stored energy 6E2 12 . Water has 6 = 80 and high pulsed electric strength. Water purification methods, such as deionization with ion­ exchange resins, filtering, and degassing have been well developed in the technologies of water purification at thermal and atomic power plants, in semiconductor industry, etc. By its specific energy storage capability, water is superior to all dielectrics and is compared with Mylar. Water recovers its electric strength after breakdown and ensures a high rate of current rise in a discharge. This makes it possible to use water spark gaps as switches and peakers in pulsed power systems. The basic challenge in using water for insulation is its high conductivity, quickening the self-discharging of water-filled capacitors. It can readily be shown that the time constant for self-discharging is given by the formula

6 ts-d ' 367t · 1 01 1 cr

(7.5)

----

-

where cr is the conductivity of water cn- 1 cm- 1 ). To charge a water-filled energy store, its charging time should be much shorter than fs-d· For water with cr = 1 0-6 n- 1 -cm- I , the charging time of the line should be -1 0-6 s, while with cr = 1 0-5 n- 1 cm- 1 this time should be 1 0-7 s. -

-

LIQUID-INSULA TED LINES

2.

1 25

TYPES OF LIQUID-INSULATED LINE

Figures 7. 1 and 7.2 present two most practical types of energy-storage lines in strip and coaxial versions. These are a single and a double (Blumlein) line. In a single line with a load whose resistance R1oad equals the wave impedance of the line, R1oad = Z0, the voltage across the load is half the charge voltage, while for a double line these voltages are identical. Table 7 . 1 lists the insulating properties o f water and oil and the general properties of coaxial lines filled with these dielectrics, described by Smith ( 1 976). Owing to the fact that both liquids are readily available and low-cost, they serve as fillers in almost all big pulse-forming lines erected by now. They are significantly different in dielectric permittivity, and this makes it possible to realize a wide range of wave impedances. (a)

Vo�

�

Single line ----��----

-- )�� --------- --

Matched load voltage

Vo� x�...:-�-----

=

Double line

(b)

�

--"T

V0!2

{ - -------�---------------1� Rload

Matched load voltage =

Vo

Figure 7. 1. Two principal types of strip pulse-forming line (a) Input

:�

put

___.(�

(Vo) �(o= = �:Ll (Vo) :�:=======;::::� = --'"-----------T'"""-' _ _

Output

Switch

Output

(V&'2) (Vo)

Figure 7.2. Two types of coaxial pulse-forming line: a simple coaxial line (the output voltage is half the charge voltage and the output current equals the current through the switch) (a) and a triple coaxial Blumlein line (the output voltage equals the charge voltage and the output current is half the current through the switch) (b)

The formulas for the wave impedance of a coaxial line given in Table 7 . 1 suggest that oil and water are convenient to use in lines operating with impedances of several tens of ohms and $; 1 0 n, respectively. The coaxial geometry is most often used since round-cross-section conductors simplify the design and, in addition, the use of a closed outer conductor filled with dielectric makes the design efficient and ensures electromagnetic screening.

Chapter 7

1 26 Table 7. 1. Insulating properties ofwater and oil Permittivity Wave impedance of coaxial line Practical electric field at positive electrode, kV/cm Energy density, J/1 Surface current density, kA/m Polarity effect

Oil 2.3 40ln(D21Dt) 200-300 4-9 80-120 - 1 .5 : 1

Water 80 6.7ln(D2/D 1) 1 00- 1 50 35-80 240-360 2:1

Also given in Table 7.1 are the electric fields admitted for use in pulsed power systems with charging times of � 1 !JS. These fields compare in value, being somewhat higher for oil. However, because of the difference in permittivity between water and oil, the energy stored per unit volume and the current tapped off a unit width of a conductor are greater for water-filled lines. Thus, water provides for a more compact design. It should be noted that the data on electric fields refer to electrodes of positive polarity; at electrodes of negative polarity, higher electric fields are admissible for both liquids. This phenomenon is known as the "polarity effect", and it is most pronounced for water. Since discharges are initiated at electrodes, the breakdown electric field could formally be almost doubled by creating proper conditions (by applying coatings on the electrode surfaces, degassing the electrodes, choosing proper electrode shapes, etc.) and by increasing the pressure in the liquid. However, this improvement is unattainable in actual pulse generators (Martin, 1 996). Figure 7.2 shows two versions of coaxial pulse-forming line: a conventional coaxial line with a series-connected switch and a triple coaxial line being a variety of the Blumlein double line. In accordance with the above characteristics, a conventional · coaxial line is better suited for the production of high currents, while a double line is adequate for the generation of high voltages. Thus, in practice, a conventional coaxial line is considered a low-resistance system and, hence, is insulated with water, while a double line, which is thought to be a high-resistance system, is filled with oil. This trend is based on the fact that a conventional coaxial line is simpler in design if the fill liquid (such as water) shows a pronounced polarity effect. Using this effect allows one to produce near-limiting electric fields (and, hence, energy densities) throughout the generator volume. In a Blumlein line, the polarity effect is of minor importance. Each system can be operated with a resistance transformer - a pulse­ forming line section with controllable impedance between the generator and the load. This type of transformer can be used if the current in the pulse­ forming circuit or the voltage across the latter are too high and need to be reduced. Moreover, with this type of transformer, a pulse-forming line will have wave impedance approaching the optimum value for the fill dielectric.

LIQUID-INSULA TED LINES 3.

127

PHYSICAL PROPERTIES OF LIQUID­ INSULATED LINES

As we mentioned in Chapter 5, the mechanism of electrical discharges in liquids is not clearly understood. Therefore, to estimate the electric strength of liquids, empirical formulas are often used where the electric field is taken to be equal to 50% of the breakdown electric field. Most of the experimental data on the pulsed electric strength of liquid dielectrics available in the literature have been obtained in the fields of coaxial cylinders, since insulating liquids are most often used in coaxial energy storage and transmission lines. For large-area (� 1 04 cm2) coaxial electrodes subject to the action of voltage during a time ranging from some tens of fractions of a microsecond to a few microseconds, the breakdown electric field Ebr (in MVIcm) can be determined by the formula (Martin, 1 996)

1 1 3S1 11 0 ' Ebr = K I teff

(7.6)

E+br = 0 29 I tlt3as eff o.o9 '

(7.7)

where ferr (in JlS) is the effective voltage action time (the time during which the electric field in the discharge gap is over 0.63Ebr; S (in cm2) is the effective area of the electrodes, and K is a coefficient, which equals 0.5 for transformer oil irrespective of the polarity of the inner electrode. For the breakdown of water with the inner electrode of positive or negative polarity, we have, respectively, K+ = 0.3 or K - = 0.6. For glycerin and castor oil, we have K = 0.7. To estimate Ebr for water, Frazier ( 1 975) took into consideration that the electric field in a coaxial system is nonuniform. For purified water, he has proposed the following formulas: ·

Ei;r = 0.581t!�aS 0·09•

[

T

(7.8) 2

Here, a = 1 + 0. 1 2 ( Emax 1Eav ) - 1 is a coefficient taking into account the degree of nonuniformity of the electric field; Emax is the maximum electric field (at the inner cylinder), and Eav is the average electric field in the gap. Obviously, we have Eav = 2VI(D2 - Dt ) , where V is the voltage between the electrodes of the coaxial system and D2 and D1 are the respective diameters of the outer and inner cylinders. The above equations take no account of the effect of the gap spacing on Ebn although it is clearly observed for both small (:s; 1 mm) and large (� 1 em) gaps. For a uniform field and pulse durations of 1 0-8-1 0-7 s, this effect can be taken into account with the use of an empirical formula for Ebr (MVIcm) (Mesyats and Vorob ' ev, 1 962; Ushakov, 1 975): Ebr = Kd1 14,

Chapter 7

1 28

where d is the gap spacing (em); K = 1 . 1 for water and 1 .7 for oil. Investigations of Ebr in relation to the ratio D2/D1 for a coaxial system have shown that the function has a maximum at D2/D1 = 3.5-4 (Ushak:ov, 1 975). More general physical properties of liquid dielectrics in high electric fields are described in Chapter 5 .

FLASHOVER OF BASE INSULATORS

4.

Any high-voltage system with a liquid used for the main insulator or working medium incorporates bearing and insulating components made of solid dielectrics. In this case, one should bear in mind the possibility of a surface discharge occurring over the interface between the solid dielectric and the liquid (dielectric flashover). The conditions of occurrence of a surface discharge determine in many respects the electric strength of the entire insulating structure and its overall dimensions and reliable operation. The insulators themselves can also be broken down. A redistribution of the field at the liquid-solid dielectric interface leads, as a rule, to a considerable decrease in the electric strength of the insulating gap with a solid dielectric, Efl, compared to Ebr that characterizes breakdown in the bulk of a liquid dielectric. For systems with a combined insulation, the most critical area is the interface between the solid and the liquid dielectric. Ushak:ov ( 1 975) described an experiment on investigating the electric strength of the interface between transformer oil and a solid dielectric under the action of an oblique voltage pulse with dV/dt of about 2000 kV/J..t.s in the field of coaxial cylinders. It was found that the cylinder diameter ratio corresponding to the highest dV/dt, D21Dt . lied in the range 2.8-3 .3 and was almost independent of the insulator shape and material. For disk-type insulators used at an optimum D2/D1 ratio, the following relations were proposed to calculate the electric strength: - for the flashover of polyethylene insulators:

Emax = 1 05.7 - 1 .75Dt ;

(7.9)

- for the flashover of organic-glass insulators:

Emax

=

95.6 - 1 .53Dt ,

(7. 1 0)

where Emax is the maximum electric field (kV/mm) that takes place near the inner cylinder and D 1 is the diameter (in mm) of the inner cylinder.

LIQUID-INSULATED LINES

1 29

For the negative polarity of the inner electrode, Ebr at the interface is greater than for the positive one by an average of 20% for polyethylene insulators and by 30% for organic-glass insulators with an optimum electrode diameter ratio. This difference increases with decreasing d. The spread in Efl is 4-1 5%, being almost independent of the polarity of the voltage pulse. The voltage-time characteristic of the flashover of solid dielectrics immersed in transformer oil in the field of coaxial cylinders was investigated by Ushakov (1975). It has been found that Ebr is 360-400 kV/cm at t = 0.4 f.l.S and falls to 220-230 kV/cm at t = 4 f.l.S. Ushakov ( 1 975) also investigated the flashover of variously shaped polyethylene and organic-glass insulators immersed in distilled water in a system of coaxial cylinders, which occurred during the rise time of a positive-polarity oblique voltage pulse with a rise rate of 2000 kV/f.!s. The disk-shaped insulators showed higher Vfl. For the flashover voltage Vfl the following relationships have been obtained: Vfl = 0.85 Vbr ( Vbr being the breakdown voltage of water) for organic glass insulators and Vfl � 0.72 Vbr for polyethylene insulators. An experiment on investigating the effect of the shape of a polyethylene insulator on the voltage of its flashover in purified water with 1 cr = 10--6 o ·cm 1 in the field of coaxial cylinders was described by Ushakov (1975). It was observed that disk-type insulators showed the highest flashover voltage. The spread in experimental data was 3-4%, being almost independent of the insulator shape. The disk-shaped insulators made of caprolon and organic glass showed somewhat higher flashover voltages than those made of polyethylene. The flashover of insulators in distilled water in a uniform field was also described by Ushakov (1975). The results of measurements of Efl in a Rogowski electrode system with the electrode separation varied from 1 to 5 em were given. Cylindrical insulators were made of organic glass, caprolon, and three types of compound; they were placed at the center of the electrodes, in the region where the electric field was uniform. The duration of the applied voltage pulse was about 1 .5 f.l.S and its rise rate was 500 kV/f.l.S. The experimenters arrived at the conclusion that the insulators (except those made of caprolon) had almost no effect on the electric strength of the liquid­ dielectric gap. It was noted that there were almost no damage to the insulator surface, and this testified that the discharge occurred in the liquid dielectric. As the electrode separation was increased, the electric strength of the solid­ dielectric gap decreased roughly as Efl oc d -1 14 • For the flashover that occurred in the Rogowski electrode system as d was varied from 1 to 7 em, the relationship Efl oc d -1 13 has been established. -

-

130

Chapter 7

The effect of the insulator shape and that of the method of controlling the electric field in purified water with cr = 5 · 1 0-7 n-' · cm- 1 was investigated for oblique-shaped voltage pulses of duration 1 JlS (Stekolnikov et al., 1 962). The field configuration in the gap was chosen so that ( 1) the field was weaker at the anode due to its enhancement in the cathode region and (2) the maximum field was shifted from the electrodes into the discharge gap or to the liquid-solid dielectric interface or into the bulk of the solid dielectric. Neither of the two conditions, when fulfilled, gave improved results. The flashover voltage in this case decreased by 5-1 5% compared to Vfl for cylindrical insulators. The nns spread in Vfl was about 3%. A slight increase in Vfl was achieved for the electric field maximum shifted into the solid dielectric bulk. The shifting of the field away from the anode was most efficient. It was established (Ushakov, 1 975) that the roughness of the insulator surface subject to flashover in water has a very weak effect on Efl: an increase in size of irregularities by more than an order of magnitude (from 1 0 to 200 Jlm) resulted in a decrease in Efl only by 6-7%; the defects present in the solid dielectric near the surface subject to flashover (foreign inclusions, cracks, and the like) reduced Efl by 1 0-30%; the air bubbles on the insulator surface decreased the flashover voltage by a factor of 1 .5-3 even if they did not fonn a continuous bridge between the discharge gap electrodes; the flashover voltage depended in the main on the wettability of the insulator surface. It was also shown that the electric strength of the water-solid dielectric interface depends on time as Efl - t-114 • These data can be generalized by an empirical equation allowing one to calculate Efl for cylindrical insulators in a unifonn field: (7. 1 1 ) Here, K is a coefficient, which depends mainly on the material of the solid dielectric. For polyethylene and caprolon insulators, we have K = 0.2 and 0.22, respectively. The electric field strength is measured in megavolts per centimeters, time in microseconds, and gap spacing in centimeters. An investigation of the flashover of insulators in transfonner oil under the action of an oblique-angled voltage pulse was also described by Ushakov (1 975). For a pulse of duration 1 .5 JlS, the flashover voltage for a cylindrical insulator in a unifonn field was 3 1 0 kVIem. The flashover of insulators made of pressboard, polycarbonate, polyphenil, Pennaly, and Perplex in transfonner and silicon oils, Aroclor, and in their mixtures in a unifonn field was investigated with oblique voltage pulses of duration 1 0-20 JlS. The solid insulators were shaped as disks of thickness 0.5 em and diameter 1 .2 em. It has been shown that Ebr substantially depends on the degree of pollution of the liquid and on the liquid-to-solid pennittivity ratio, B!iq/8501• High values of

LIQUID-INSULA TED LINES

131

took place for e1iq/8501 > 1 . The rms spread in the measurements was 5-1 8%. The voltage-time characteristic of the flashover of polyethylene insulators in transformer oil was investigated with rectangular voltage pulses of duration up to 20 J..I.S . Measurements were performed for specimens of height 1 .5 em in the field of Rogowski electrodes. It has been revealed that the dependence Efl = f{t) for a gap with a solid dielectric is pronounced only for t < 1 0 J..I.S . For a solid dielectric in transformer oil, Et1 is almost independent of the dielectric material (insulators made of caprolon, organic glass, polyethylene, fluoroplastic, and polyvinyl chloride plastic were tested). When a solid dielectric in a liquid is exposed to nanosecond high-voltage pulses, the electric strength of the liquid increases so much that the solid dielectric itself becomes the weak point (A. A. Vorob'ev and G. A. Vorob'ev, 1 966) since electrical discharges occur in the latter. In this case, to work out the principles of design and choice of insulators, tests were performed with a coaxial transmission line filled with transformer oil and containing variously shaped centering washers made of fluoroplastic, polyethylene, and organic glass (Fig. 7.3). The outer-to-inner cylinder diameter ratio was 2.5. Since the electric field measurements were performed only for two limiting field configurations (uniform and asymmetric, highly nonuniform), the insulation of a nanosecond line was designed based on the data obtained for the (+N -P) system: The calculations of the breakdown fields and average flashover fields for the insulating materials of the coaxial line that were performed by empirical formulas (Ushakov, 1 975) for d = 0.6 em and t = 30 ns showed that fluoroplastic-4 had the lowest value of Ebr (0.28 MV/cm). Therefore, the test electric field strength was chosen based on Ebr for fluoroplastic-4.

Et1

Figure 7.3. Section of an experimental coaxial line (J) and variously shaped dielectric washers (2)

Initially, 1 .5 · 1 05 pulses of amplitude 1 40 kV were applied; no breakdown or flashover was observed in the line. As the amplitude was increased to 1 5 5 kV, breakdown of the fluoroplastic washers occurred after several hundreds of pulses, while the washers made of organic glass and polyethylene were broken down only after several tens of thousands of pulses. It is noteworthy that conical and stepped washers were broken down

1 32

Chapter 7

the most. This is due to the fact that solid dielectrics are close in strength to transformer oil, and the presence of a normal field component inherent in the test shapes of washers enhances the field in the solid dielectric. The experience gained in operating nanosecond high-voltage generators and the tests performed support the principal inferences from analyses and experimental investigations of the mechanisms underlying the electric strength of insulators. These data suggest, in particular, that in designing insulating structures of nanosecond pulse systems where liquids are used for the main insulation and solid dielectrics play the part of the construction material, the operating field strength should be chosen based on the relevant data on the electric strength of the insulation. In insulating structures, one must avoid a successive arrangement (with respect to E ) of solid and liquid insulators. A great deal of useful information about discharges over the surface of solid dielectrics in liquids can be found in the reviews by J. C. Martin (Martin et a/., 1 996), Ushakov (1 975), and Sharbaugh et a/.

(1 978).

REFERENCES Chace, W. G. and Moore, H. K., eds., 1959, Exploding Wires, Vol. I. Plenum Press, New York. Frazier, G. B., 1 975, "OWL-II", Pulse Electron Beams Generator, J. Vac. Sci. & Techn.

12: 1 1 83-1 1 87.

Lagunov, V. M. and Fedorov, V. M., 1 978, Use of Water Insulation in Current Pulse Generators and Electron Accelerators at Novosibirsk Institute of Nuclear Physics, Fiz. Plazmy. 3:703-714. Martin, T. H., Guenther, A. H., and Kristiansen, M., eds., 1 996, J. C. Martin on Pulsed Power. Plenum Press, New York. Mesyats, G. A. and Vorob'ev, G. A., 1 962, On the Possibility of Using Liquid Spark Gaps in Nanosecond High-Holtage Pulse Systems, Izv. Vyssh. Uchebn. Zaved. , Fiz. 3:21-23. Sharbaugh, A. H., Devins, J. C., and Rzad, S. J., 1 978, Progress in the Field of Electric Breakdown in Dielectric Liquids, IEEE Trans. Electr. Insul. 13:249-276. Smith, I., 1976, Liquid Dielectric Pulse Line Technology. In Energy Storage, Compression, and Switching: Proc. ofthe 1st Intern. Conference on Energy Storage, Compression and Switching (Nov. 5-7, 1974) (W.H. Bostick, ed.), Plenum Press, New York-London, pp. 15-23. Stekolnikov, I. S., Brago, E. N., and Bazelyan, E. M., 1962, Reduction ofDischarge Voltages in Long Gaps with an Oblique Wave, Zh. Tekh. Fiz. 32:993-1000. Ushakov, V. Ya., 1 975, Pulsed Electrical Breakdown of Liquids (in Russian). Tomsk State University Publishers, Tomsk. Vorob'ev, A. A. and Vorob'ev, G. A., 1 966, Electrical Breakdown and Destruction of Solid Dielectrics (in Russian). Vyssh. Shkola, Moscow.

Chapter 8 VACUUM LINES WITH MAGNETIC SELF-INSULATION

1.

PHYSICS OF MAGNETIC INSULATION

If a voltage wave propagates through a vacuum coaxial or strip line and creates an electric field capable of initiating explosive electron emission (EEE), a vacuum breakdown will occur in this line. The explosively emitted electrons come against the opposite electrode and heat it, which results in the appearance of anode plasma and ions. The cathode and anode plasmas as well as electrons and ions moving in opposite directions disturb the normal operation of the vacuum line and this eventually leads to a vacuum discharge in the line. However, if the self magnetic field of the current wave is strong enough, the explosively emitted electrons will be returned to the cathode and the discharge process will be slowed down. This in fact means that there will be no vacuum discharge during the pulse. This effect has been termed magnetic self-insulation. It was discovered by Bernstein and Smith ( 1 973). Earlier Baksht and Mesyats ( 1 970) established that the delay time of a vacuum discharge increases with external magnetic field. Magnetically insulated vacuum lines (MIVL' s) are used to transfer electromagnetic energy to a load and as inductive energy stores. In the second case, they simultaneously store energy and transfer it to a load. Let us consider a coaxial vacuum line, denoting the inner and outer electrode diameters by D 1 and D2 • In this case, the electric field at the surface of the inner electrode is given by (8. 1 )

1 34

Chapter S

where V � IZ0 (I being the current and Z0 the wave impedance of the line). From (8. 1 ) it follows that the electric field at the surface of the inner electrode increases with current. It can be shown that at a power density of 1 0 1 0 W/cm2 and more, for a wave propagating in a vacuum transmission line, the electric field exceeds the threshold value at which there occurs explosive electron emission from the negative electrode. The magnetic field at the surface of the inner electrode, which is characterized by IID�. will also be high. Thus, we should consider the problem of an electromagnetic pulse and an electron flow propagating together through a line. When considering the efficiency of energy transfer, an important problem arises which concerns the destiny of the electrons that, after acceleration in the electrode gap, can arrive at the anode and cause considerable losses of the pulse electromagnetic energy and generation of plasma at the anode. The counter motion of electrons (Fig. 8. 1 , a) in an electrode gap occurs on condition that (8.2) where V is the potential difference between the inner and the outer conductor of the line.

cl> = V

(a) I D2 /tccccccccccccccccccccc

(b)

ci> = V

--

n2 / t t t t t t t t t t t t t t t t t t t t t t

I

r r*T ::���������� D1 >;;;;;;;;;;;;;;;;;;;;;; ci> = 0 dcl>ldr = 0

Figure 8. 1. Trajectory of electrons in a vacuum transmission line: a - kinetic model, b Brillouin model. - potential. r* and rT - e-beam boundaries ci>

Relation (8.2) is the magnetic insulation criterion for one particle. Since the effect of magnetic insulation results from an increase in the intensity of the self magnetic field of a wave propagating through a vacuum transmission line, it is referred to as magnetic self-insulation of a vacuum transmission line. To exactly calculate the current I necessary for self-insulation of a transmission line at a given voltage V and of other parameters of the electron flow occurring in the line, it is necessary to solve the kinetic equation for electrons. Conventionally, an electron moves in a cycloid. However, numerical simulations of the formation of the electron flow in a line show that the trajectories of electrons away from the beginning of the line are straight lines rather than cycloids (Fig. 8. 1 , b). Therefore, to consider magnetic self-insulation, the magnetohydrodynamic (MHD) approximation

VACUUM LINES WITH MA GNETIC SELF-INSULATION

135

is used that was proposed by Brillouin (195 1 ) to analyze the operation of magnetrons. In this approximation, the motion of electrons is treated merely as their drift in crossed electric and magnetic fields. Danilov ( 1 963, 1 966) considered two-dimensional configurations taking into account the external magnetic fields. The kinetic model of magnetic insulation was developed by Voronin and Lebedev ( 1 973), Lovelace and Ott (1 974), Korolev ( 1 990), and Ron et a/. ( 1 973). In a quasistationary approximation, for a line of length I < ctr (c being the velocity of light and tr the rise time of the electromagnetic wave propagating through the line), the electrodes of the line can be considered as the plates of an ordinary capacitor in which, due to the passage of a current, a magnetic field is created. In this case, the electrons resulting from the EEE at the cathode form a layer, which, provided that there is magnetic self-insulation, occupies some part of the electrode gap. The self-insulation criterion for the electron layer is that the effective Larmor radius of an electron becomes smaller than the electrode gap spacing. With no account of the variation of the magnetic field due to the diamagnetism of electrons, the self-insulation criterion is given by relation (8.2). The Brillouin approximation gives a rather adequate interpretation of experimental results (Korolev, 1 990). For a given potential V applied between the electrodes of a coaxial line there exists some minimum current Imin( V) at which the line becomes magnetically self-insulated. Assuming that the electron layer is adjacent to the cathode, we have

-[

Imin -

8.5

]

(

3

G"-;) ,

-1 In • + ln (D2 /� ) Y• Y vY*

(8.3)

Umin being measured in kiloamperes), where the relativistic factor is determined by the expression

(

y = Y• + (y; - 1)312 ln Y• + �y; - 1

).

(8.4)

where y = 1 (v5Ic2 ) with v0 being the velocity of electrons at the line and y. = 1 - (v5.1c2 ) with Vo• being the velocity of electrons at the electron layer boundary. The event that an electron flow fills up a vacuum gap is associated with the so-called parapotential current Ipp( V), which, for a coaxial line, is given by -

[

85

]

(

· y- - I y 1n y + ...;Gl IPP = ln (D2 /� )

)

'

(8.5)

where Ipp is measured in kiloamperes. As this current is achieved, the equilibrium of the electron layer is no longer violated.

1 36

Chapter S

If we consider the evolution of quasistationary equilibrium in a vacuum transmission line after EEE and formation of ectons at the cathode, we see that, because of the appearance of electrons in the vacuum gap, the electromagnetic field is partially displaced and the energy of the equilibrium state decreases. As this takes place, the experimentally realized equilibrium corresponds to a minimum of the total energy of the system minus the rest energy of the electrons (Gordeev et al., 1 975). This state is not substantially different from the equilibrium state with a minimum current. As electrons enter the vacuum gap, the conventional inductance and capacitance per unit length cease to completely characterize the state of the line because of the appearance, in addition to the electrical and magnetic energies, the kinetic energy of electrons, which also depends on line voltage and current. The above considerations refer to the main equilibrium region, where, ideally, there is no leakage and the magnetic self-insulation is complete. However, the latter is achieved due to an increase in magnetic intensity, which is provided by an extra current passing in the line in contrast to a conventional vacuum line. In a vacuum line with one end open, the entire current flows as a leakage current in a region whose size is about several electrode gaps at high potentials across the line and can be substantially greater at low potentials. If a resistor whose resistance corresponds to the impedance of the line with electrons is connected to one end of the line, the leakage current can be completely switched into the load, thus eliminating losses. However, in experiments with vacuum transmission lines, their critical characteristic is the current in a line with one end open. From the energy viewpoint, this situation should correspond to a minimum of energy. However, in this case, the current only slightly exceeds the minimum current in the line that ensures insulation. In view of this and because of a simpler expression for the minimum current, in what follows we shall compare such limiting currents in a line with the minimum current.

THE QUASISTATIONARY MODE

2. An

investigation of the operation of a line for the case 1/ctr « 1 was described by Gordeev et a!. ( 1 975). Typical oscillograms of the voltages and currents are given in Fig. 8.2. The time lag between the line current and voltage ( 1 0-1 5 ns) was necessary for ectons to occur at the negative electrode. The onset of electron emission corresponded to the break in the voltage waveform and to the appearance of x rays from the lateral wall of the outer tube of the coaxial system. The electron current toward the anode lagged by 5-1 0 ns relative to the line current. The additional time shift arose since the development of electron emission from the face cathode requires a

VACUUM LINES WITH MA GNETIC SELF-INSULATION

137

longer time than that from the side surface of the inner electrode because of the higher current density at the cathode. For rather small cathode-anode gaps, as the electron emission processes were completed, the diode current coincided, to within 1 0%, with the line current. As the cathode-anode gap spacing was increased, the line current decreased and the voltage across the line increased with Ipp and V tending to their limiting values.

:>' 450 0 :::...

0

� .�

20

�

0

�

§."

�

19

Figure 8.2. Oscillograms of voltage V, currents at the line input, Inne , and output, !output. and leakage current (dashed curve)

The origin of the limiting voltage and current values can readily be understood proceeding from the following considerations: As the gap spacing d, and, hence, the impedance of the acceleration gap, is increased, the voltage should increase and the current should decrease, since the resistance of the line in relation to the leakage electron currents that appear between the line electrodes because of their large area, is much lower than the resistance of the generator. Therefore, a small excess of the line voltage above its limiting value suffices for the appearance of a leakage current toward the outer electrode, which restricts further increase in voltage. As a result, a self-consistent mode is established in the line, such that both the current and the voltage reach their limiting values. Let us consider in more detail the nature of the leakage current toward the opposite electrode of a line. The dynamics of the establishment of magnetic self-insulation was investigated with the help of Faraday cups placed on the outer coaxial tube (Baranchikov et al., 1 978). The leakage currents toward the outer electrode appeared within the rise time of the line current pulse with Ipp < Imin· The leakage current ceased or decreased by an order of magnitude when the line current became 1 0-20% greater than Imin·

1 38

Chapter 8

In the experiment, the leakage was observed at low voltages during the current drop (Fig. 8.2). To explain this effect, we shall consider the distribution of the leakage current near the end face in the limiting mode. Once the cathode has acquired an emissive power necessary to pass Imin, the current, according to the estimates obtained with the help of the Child­ Langmuir law, closes at the end of the line over a length equal to about the electrode gap spacing. Decreasing voltage increases the width of the leakage region at the end of the line. For y � 2, the width of the leakage region, L\, is of the order of the electrode gap spacing, L\ � (r2 - r 1 ), and for (y - 1) « 1 , the leakage region may be considerably grater than the electrode gap, L\ � 9nd/8(y - 1) » d, and be comparable to the length of the line (Korolev, 1 990; Gordeev, 1 990). The duration of the first leakage current pulse is determined by the processes initiating explosive electron emission and by the inductance of the line. The leakage currents have the highest values early in the pulse and then decrease quicker than the difference between the line and the anode current. This testifies to a displacement of the leakage currents toward the load with increasing current and magnetic field in the line. (A diode with explosive electron emission is usually used as a load.) This conclusion is confirmed by direct measurements of the density distribution of the electron leakages along the line (Baranchikov, 1 978; Aranchuk et a/, 1 989). The dynamics of the distribution of leakage currents at the end of the line was additionally measured with x-ray gages by scanning the lateral surface of the outer electrode with a resolution of 4 mm. Early in the current pulse, the characteristic length over which the electron flow was concentrated, was 2-3 em, which was equal to 4-6 electrode gaps. Once plasma had appeared at the internal surface of the outer electrode, ion currents were detected at the negative electrode of the line. The electron current density increased at the stage of growth of the ion current, and this was judged from the observation that the electron leakage region halved in size while the total current varied only slightly. Generally, the electron layer occupies not the whole of the electrode gap. The current !nne - Ic is transferred by electrons in the coaxial gap. The cathode current is given by the relation (Gordeev, 1 990)

fc = fnne fY*

(8.6)

For a line operating in the limiting mode, we have

fc flmin = 1/y � 1 for low voltages [ (y - 1) « 1] fc //min � y- l /3

(8.7) and

(8.8)

VACUUM LINES WITH MAGNETIC SELF-INSULATION

1 39

for high voltages. Thus, at large y most of the current is transferred by electrons accelerated in the electrode gap. Once magnetic insulation has been established, electrons fill the whole of the electrode gap. Numerical calculations that have been carried out for a line with r2/r 1 = 2. 7/1 . 1 (em) operating in the limiting mode at a voltage of 4 1 0 kV confirm the conclusion that the motion of particles far from an end face of a line occurs in an electron layer adjoining the inner electrode (Fig. 8.3). However, this layer is wider than that predicted by hydrodynamic calculations. Thus, according to the hydrodynamic theory, for the above values of current and voltage, the layer width is 0. 7 em (dashed line), while the numerical calculations yield 1 .0 em. This discrepancy can be accounted for by the initial spread in particle velocities. The leakage electron current depends on the gap spacing d. For d > d0 (d0 being the gap spacing that corresponds to the peak power dissipated in the load), the amplitude of the leakage current pulses increased during the current rise time and fall time, and the plateau between the pulses was more pronounced. This can be explained by the fact that for d > d0, as mentioned, V and Yline tend to their limiting values depending on the wave impedance of the line.

0

8

16

z

[em]

Figure 8.3. Trajectory of electrons in the steady-state insulation mode ( V = 4 1 0 kV, d = 2 em)

The efficiency of the energy transfer through a cylindrical line in a steady-stated mode for a quasi-stationary case with /line > /min is close to 1 00%. The energy flux density achieved in lines of length up to 1 m on the MITE system and on one module of the Angara-5 system is over 1 01 1 W/cm2 at an electric field E :$ 2 MV/cm2• The effect of magnetic insulation allows one to obtain high electric fields in a gap. The maximum electric field in the electrode gap of a coaxial line, with the electrode layer taken into consideration, is determined by the expression

E. = -30/minDr (Y• - 1)112 / y . , where the current /min is measured in kiloamperes. In experiments, the electric field in cylindrical lines of length about 1 m is over 5 MV/cm2 (Baranchikov et al. , 1 978; Smith et a/. , 1 976). The features of the operation of conical lines with magnetic insulation are described by Korolev ( 1990).

1 40 3.

Chapter 8 THE WAVE MODE

A key process in long coaxial lines is the establishment of the mode of magnetic self-insulation on application of a pulsed voltage V. As this takes place, the front of an electromagnetic wave propagates in the line during the time tr > lie. Baranchikov et al. ( 1 977a), based on nonlinear telegraph equations with the assumption that magnetic insulation is established behind the front, have obtained a simple expression for the wave velocity: (8.9) The velocity v of the electromagnetic wave propagating in a coaxial line appears to be much lower than the velocity of light c because of the inertia of the electrons that appear in the coaxial gap due to explosive electron emission and move in electromagnetic fields. This is accompanied by energy losses near the wave front, which are associated with the displacement current and electron leakages. The wave mode of magnetic self-insulation was first investigated in experiments on the MS system with coaxial lines of length 4.5 m at a pulse amplitude of 500 kV (Baranchikov et al., 1 977b). Subsequently, experiments were performed (Voronin et al. , 1 979; DiCapua and Pellinen, 1979; Van Devender, 1 979; DiCapua et al. , 1 977) in which, alongside with coaxial lines, plane (double or three-strip) lines were used. A magnetically insulated vacuum line operated into a diode or resistive load. The use of the latter eliminated the nonlinearity of the current-voltage characteristic of the load, providing for a simpler interpretation of results. For strip lines, the problem of providing a fixed gap along the line is solved much easier by introducing various supporting tools that can be combined with diagnostic gages. The length of the lines in these experiments reached 1 1 m with the parameter ctr II < 1 . Pulses of both positive and negative polarity of amplitude up to 3 MV were applied to the electrodes of a line; in this case, the electric field was over 2 MV/cm. The lines were equipped with a conventional set of diagnostic gages. In addition, for measuring currents and voltages in different sections along the axis of a line, magnetic loops (or Rogowski coils) and resistive voltage dividers were placed, respectively. The principal features of the wave mode of magnetic self-insulation have been revealed on the MS accelerator in experiments with coaxial lines of length I = 3.5 and 4.5 m (Baranchikov et al. , 1 978, 1 977b). The parameter ctrll was 2.6-3.4. For ease of mounting, the lines were erected vertically at the output of the accelerator. The radii of the outer and inner electrodes of the coaxial lines were 2.6 and 1 .0 em, respectively. The i.l.ne load was a

VACUUM LINES WITH MAGNETIC SELF-INSULATION

141

diode whose acceleration gap was varied from zero to 1 em. A 500-kV pulse of negative polarity and 40 ns FWHM was applied to the line input. To diminish the delay time of explosive electron emission, in some experiments a dielectric insert of length 4 em was placed at the line input; in other experiments, the initial segment of the inner electrode of length 20 em was covered with Aquadag. The development time of explosive electron emission was determined by the time shift between the current at the line input and the leakage current onto the lateral surface of the outer electrode, measured by a Faraday cup in the beginning of the line. The leakage current resulting from the intense electron emission at the Faraday cup (Fig. 8.4) appeared 1 0 ns after the arrival of the pulse. > 500 =::...

0

� .5

...:::;"

19

..

0

�

�

17

� "

0

50

t [ns]

1 00

Figure 8.4. Oscillograms of the voltage V and currents at the line input, /line , and output, Ioutput , for I 4.5 m and r2/r1 = 2.6/2.0 (em) and of leakage currents (dashed curves) measured at 0.4 and 3.9 m from the beginning of the line =

As a current pulse propagated along the line, its waveform varied. The wave front became more abrupt. This effect had been predicted and termed the magnetron effect by Kataev ( 1 963) who studied shock electromagnetic waves in lines. The current measured by a Faraday cup at the end of the line had a characteristic spike preceding the main front. It should be noted that the signals from the x-ray gages that detected the radiation from the anode practically followed the waveform of the current measured by the Faraday cup placed at the end of the line. The current and the intensity of x rays from the surface of the outer electrode measured at the output of the line suggested that there existed a vacuum forerunner of small amplitude, which was followed by the wave front. The velocity of propagation of the forerunner was equal to the velocity of light. The interval between the onset

142

Chapter 8

of explosive electron emission, determined by breaks in oscillograms of the voltage at the line input, and the pedestal of the main current pulse measured by the Faraday cup placed at the line end determined the velocity of propagation of the magnetic self-insulation wave. The velocity of propagation of the leading edge of the main pulse over the base l = 4.5 m was much lower than the velocity of light and for a medium amplitude of the voltage pulse at the line input of 460 kV it was 0.45 ± 0.05c. The same values were obtained by the delay of the signals from the x-ray gages that detected the radiation from the line lateral surface and by the occurrence of maximum leakage currents measured by the Faraday cups located along the line. The velocity of the wave front increased with the amplitude of the voltage pulse. In experiments performed on the PULSERAD-1 500 machine ( V = 3 MV, Z0 = 50 n, fp = 50 ns) (DiCapua and Pellinen, 1 979), the velocity of the magnetic self-insulation wave, determined from oscillograms of currents measured at different places of a coaxial line with r2/r 1 = 1 1 .43/5.72 (em) and length 1 0 m at a voltage of 1 .8 MV, made up 0.70 ± 0.06 of the velocity of light. As follows from these experiments, a minimum current is established behind the wave front, which corresponds to the configuration of the electron layer adjoining the inner electrode of the line. Figure 8.5 presents the results of experiments carried out at I. V. Kurchatov Institute of Atomic Energy on strip and coaxial lines with diode and resistive loads (Aranchuk et al. , 1 989; Airapetov et al. , 1 98 1 ; Ware et al., 1 985). The polarity of the inner electrode of length up to 1 0.7 m was either positive or negative and the voltage was 3 MV. Also given in Fig. 8.5 are theoretical expressions for currents i = 2ellmc 2 g [ g = (ln r /1it 1 for the cylindrical case and 2 g = (2rcdlbt 1 , where d and b are, respectively, the gap spacing and the line width, for the plane case] obtained in the one-body approximation, i = (y 2 - 1)1 1 2 , and in the MHD approximation corresponding to a minimum current /min and a parapotential current /PP = y ln iy + (y 2 - 1)1 1 2 are given as well. The measured velocities of propagation o fthe wave front fit well to the formula obtained on the assumption that a minimum current is established behind the wave front and that there exists an electric layer adjoining the negative electrode (Gordeev, 1 990)

]

c

YY• - 1

(8. 1 0)

From oscillograms of the leakage currents and the line input and output currents (see Fig. 8.4), it follows that after the onset of explosive electron emission the wave front in the line becomes steeper. In the experiments on

VACUUM LINES WITH MAGNETIC SELF-INSULATION

1 43

the MS system, the rise time of the output current was 7-1 0 ns, which made up one-third of the input current. At small amplitudes, as follows from formula (8.9), the velocity of forward areas at the front of a magnetic self­ insulation wave is low, and these areas will be caught up with the areas of the wave front with a higher voltage. This process results in an increased steepness of the wave profile at the front and in the generation of shock waves. o-1 0 -2 A -3

12 9 6 3 01

2

3

y

4

5

6

Figure 8.5. Limiting current i versus voltage y = 1 + eV!mc2: a - one-body approximation,

i = (y2 - 1 )1 12 ; b - curve corresponding to the minimum current Im;n; c - curve corresponding to the parapotential current Ipp y ln(y + (y2 - 1 ) 112); 1 - data of Aranchuk et a!. ( 1989), 2 Airapetov et al. ( 198 1 ) 3 - Woodall and Stinnett ( 1 985) =

,

The width of the wave front calculated by the measured velocity and duration of the main leakage pulse is 1 - 1 . 5 m, which is 3-4 times less than the length of the line (Baranchikov et al., 1 978). The reliability of this estimate of the front width is testified by the fact that the measured amplitude of the leakage current density, 3-4 A/cm2, is in agreement with the value calculated from the leakage current at the main front and the surface of the section of the outer electrode equal to the length of the front: j1eak = I1eak.l2rtrvtr . As reported by DiCapua and Pellinen ( 1 979), as a wave propagated through a line, the duration of the wave front decreased to less than 4 ns over a base of 1 0 m. This corresponded to the front width equal to 0.6 m, which was substantially smaller than the length of the line. The rate of current rise reached 1 0 1 2-1 0 1 3 A/s. Prior to the onset of explosive electron emission, a vacuum forerunner, an ordinary electromagnetic wave, propagates through the line ahead of the front of the magnetic self-insulation wave. The structure of the wave front strongly depends on the emissive power of the cathode material. For example, for the inner electrode coated with Aquadag, the wave front becomes narrower and the vacuum forerunner

1 44

Chapter 8

ahead of the main wave disappears. In the limiting case of "instantaneous" explosive electron emission, the width of the wave front is of the order of the electrode gap of the transmission line. In the actual case of a finite time of explosive electron emission, the structure of the wave front appears to be more intricate (see Fig. 8 .4) and its width is larger than the electrode gap. As the potential at the wave front increases, there occurs the moment when the electron emission from the cathode becomes substantial. This is followed by a valley in current and voltage waveforms, and the leakages at the wave front are associated with the valley. As the voltage increases, the current downstream of the deep is observed to increase, which is accompanied by the cessation of the leakage currents. The nonlinear magnetic self-insulation wave can be reflected from the end of the line. This reflection is substantially different from that occurring in a conventional vacuum line. The reflection of the magnetic self-insulation wave was investigated by Van Devender ( 1 979) for 2-m long cylindrical lines with the electrode diameter ratio equal to 110.2, 1 .8/0.2, and 1 /0 . 1 (em) and the respective wave impedances 96, 1 32, and 1 3 8 Q for a positive and negative incident pulse of amplitude up to 500 kV. The line carried a resistive load based on a water solution of CuS04 whose resistance could be varied from a few ohms to several hundreds of ohms. The presence of a resistive load with a known resistance facilitated the interpretation of experimental data. As a voltage pulse was applied to the line with a wave impedance Z0 = 1 3 8 Q during a time of 35-40 ns, which was equal to the time of double run of the wave through the line, the input current did not depend on the load resistance. For t > 40 ns the pattern was different. In the case R1oad � Zo (with the "hot" impedance of the line Znne = 40 0), since there was no reflected wave, the input current did not depend on the load and the input impedance was close to the line "hot" impedance Znne· This is related to the fact that the resistance of a load at the end of a line cannot be over Vllmin · For resistances R1oad > Vllmin• the mode of magnetic self-insulation is provided by the passage of some portion of the current to the positive electrode at the end of the line near the load, resulting in a decrease of R1oad to Vllmin· Therefore, the input current-voltage characteristics remain unchanged. For R1oad < Znne. the input current-voltage characteristics of the line, because of the occurrence of a reflected wave, depend on R1oad, and as the load resistance is decreased, the input current increases, while the voltage decreases. Similar characteristics have been obtained for other values of the line impedance and voltage. The efficiency of the energy transfer through a line is determined by the load. The highest efficiency is achieved in the matched mode with the load resistance equal to the line "hot" impedance Znne· As the impedance of a line becomes lower or higher than its- "hot" impedance, the efficiency decreases.

VACUUM LINES WITH MAGNETIC SELF-INSULATION

145

As Zline is decreased relative to its matched value, a line with magnetic self­ insulation behaves as a conventional long vacuum line: the current /1oad increases, while Vout decreases. As R1oad is increased relative to its matched value, the output voltage of the line does not vary and is close to the voltage in the matched mode, while /1oad decreases. This behavior of the load current and output voltage implies that for R1oad > Zline the match is achieved due to the passage of a current near the load that shunts the load resistance. Additional losses that occur at the front of the nonlinear magnetic self­ insulation wave propagating through the line are due to the leakage electron current. The energy transfer efficiency 11 is estimated by the formula 11

=

(E. �), Ve

I 1-_ Cfp V

-

(8. 1 1 )

where I is the length of the line, fp is the pulse duration, and Ve is the velocity of propagation of an electromagnetic wave in the steady-stated mode. The experimentally found efficiency 11 of the beam transport on the MS machine at a voltage of 0.5 MV across the line made up 50%, while the theoretically predicted efficiency was 70%. A high efficiency of energy transfer (90%) through magnetically self-insulated plane lines of length 7 m was obtained on the MITE system at Sandia National Laboratories (Van Devender, 1 979). 1 .0

� :S

I

0.8 0.6 0.4

•

oo

0

•

•

0

....... �.::;- -: 0

-�

. C'l.A

0

•

•

0

2

4

6

8

10

I [kA]

Figure 8.6. Relative wave front velocity v,lc versus magnetization current I for the line voltage V = 220 (open circles) and 612 kV (solid circles). The solid and dashed lines represent the respective calculated dependences for the above voltages

A method for increasing the efficiency of energy transfer in magnetically self-insulated lines by applying an additional magnetic field to suppress the leakage electron currents at the wave front has been proposed by Van Devender ( 1 979). If the magnetic field is intense enough, the electron layer adjoins the cathode and the line is close by its parameters to a vacuum line.

Chapter S

1 46

In this case, the energy transfer may occur practically without loss. In this experiment, a line with a diameter ratio of 1 8/2 (mm) (wave impedance Zo = 1 3 8 Q) was additionally magnetized by a current passed through the inner electrode. As the magnetization current was increased, the velocity of the wave approached the velocity of light (Fig. 8.6) and the current pulse waveform was close to that typical of a vacuum line because the forerunner disappeared. The "hot" impedance of the line increased with magnetization current, testifying to a decrease in width of the electron layer. At a fixed value of the load impedance there is a magnetization current at which the greatest efficiency of energy transfer is achieved. In this case, the efficiency is low at a small magnetization current and it increases with current, reaching a maximum at the "hot" impedance of the line equal to the resistance of the load.

4.

PLASMAS AND IONS IN A LINE

Among the processes capable of restricting the energy fluxes and energy delivery to the load is the generation of plasma at the electrode surface. The plasma arises at the line electrodes during the action of a high-voltage pulse. The cathode plasma is generated due to the explosive electron emission from the cathode and the bombardment of the cathode by positively ionized atoms emitted from the anode plasma, while the anode plasma results from the interaction of electrons accelerated in the electrode gap with the anode surface. At both electrodes, plasma can be produced by intense illumination of the electrode surface with low-energy x rays, which is most likely to occur in the transition region between the line and the (diode or z-pinch) load. The moving plasma may cause the line gap to close and thus destroy magnetic insulation. Moreover, because of the decrease in effective gap spacing, electron and ion leakage currents may appear. The cathode plasma properties and dynamics in lines were investigated experimentally at electric fields of up to 2 MV/cm (Airapetov et al., 1 98 1 ; Woodall and Stinnett, 1 985; Stinnett and Woodall, 1 985). In these experiments, it has been established that the plasma is produced at the cathode within several nanoseconds. Its density is nonuniform, and at a distance less than 1 mm from the cathode it is 1 015-101 6 cm-3 and its temperature is several electron-volts. The plasma expands, with a velocity of ( 1 -2)· 1 06 crnls, in a diffusion manner since the pressure of the magnetic field on the plasma surface is greater than the gas-kinetic pressure. From spectroscopic measurements of the plasma composition, it follows that the basic contribution to the plasma luminosity is from the lines of hydrogen.

VACUUM LINES WITH MAGNETIC SELF-INSULATION

1 47

The reduced velocity of the plasma corresponds to the thermal velocity of hydrogen ions with a temperature of 2 eV. A model, which takes into account the influence of the expanding cathode plasma on the power transfer through a magnetically insulated vacuum line, is proposed by Stinnett et a/. ( 1 985). The plasma was considered to appear at an electric field of 0.3 MV/cm. Calculations were carried out for a line of length 2 m with an aluminum cathode of radius 6.2 em and an electrode gap of spacing 0.5 em. The line carried an inductive load of 1 8 nH at an applied voltage pulse of amplitude 0.5 MV and duration 1 50 ns. With the initial plasma parameters used in these calculations (temperature 5 eV, density per unit area 8.7· 1 0-7 g/cm2, and layer width 1 �m), the plasma is practically not decelerated by the magnetic field up to t = 60 ns (or up to the 50th nanosecond from the onset of explosive electron emission) and later the plasma front velocity decreases (at t = 1 20 ns it was 4· 1 05 cm/s). Up to the 1 20th nanosecond, the average velocity of the plasma front was 2 .4· 1 06 cm/s. From the results of these calculations it follows that a considerable portion of the current (up to 50% of the total line current) is transferred in the plasma sheath and the expansion of the cathode plasma results in a change in the effective gap spacing of the line and in an increase in the line current by 1 0-20% compared to the no plasma case. The evolution of the spatial distribution of losses at the anode was studied with the help of a three-frame electron-optical system. A thin plastic scintillator attached to the anode served as a converter of braking radiation. Typically, the luminosity consisted of luminous spots, each about 1 mm in size. The spots appeared and disappeared within the interframe interval ( 5 ns). Putting in correspondence the dynamics of spots observed on electron-optical pictures and the level of the leakage current density at the anode, one could estimate the current in individual local spots (about 1 kA). The plasma sheath at the anode serves as an emitter of ions, which, in actual accelerators, are not magnetized and are freely accelerated by the electric field in the vacuum gap. The leakage ion current is due to the distribution in the gap of the ion and electron space charge and depends on the position and dimensions of the electron layer. The equilibrium position of the layer should in turn vary, as ion leakages appear, because of the redistribution of the electric field. For practical use of an MIVL, it is important to determine the minimum current starting from which there is an equilibrium layer of electrons in the presence of an ion flow and the dependence of the leakage ion currents on the voltage and the gap width. The presence of ions in an electrode gap increases the minimum electron current of magnetic self-insulation. Qualitatively, this can be explained using the analogy to a conventional diode. In a planar vacuum diode with no electron emission, the electric field in the gap is a constant. As an electrode

148

Chapter 8

emits charged particles, the electric field at the electrode decreases to zero. The field in the electrode gap becomes nonuniform, increasing at the other electrode by 1/3 compared to that in a vacuum diode. A similar effect arises in a line with magnetic self-insulation of electrons in which emission of ions takes place. For y » 1 , when the electron layer is narrow, the minimum current is greater by 1/3 than Imin in a line without ions. For practical applications, the problem of the excess of the ion leakage current above its values obtained from the Child-Langmuir law is important. In experiments, the maximum (sixfold) excess has been obtained mainly due to the near­ electrode plasma layers expanding with a velocity of about 1 07 cm/s. In contrast to positive ions, negative ions present in a line increase the electric field in the electrode gap. Therefore, to realize magnetic insulation calls for a stronger magnetic field. Moreover, an increase in ion density can have the result that the balance of pressures in the electron layer fails to be maintained and magnetic insulation is disrupted (Sincemy et a/. , 1983). In experiments (Waisman and Chapman, 1 982; Korolev et a/., 1 983) carried out on 2-MV, 400-kA, 35-ns accelerators, in a line of length 6 m with magnetic self-insulation, leakage currents of negatively charged ions ( H-, H2 , c-, o-, 02 ) were detected with the help of a time-of-flight spectrometer and Faraday cups set on the diode. Although the current density in these experiments reached high values (50 A/cm2), the regions of ion leakages were localized in the line and did not give considerable losses. The losses depended on the distance along the line and were determined by the conditions of production of cathode plasma (the rate of variation of the electric field, the amplitude of the voltage forerunner, and the electric field strength). Magnetically insulated vacuum lines are widely used as transmission and energy storage units (Al'bikov et a/. , 1 990; Van Devender et a/. , 198 1 ; Turman et a/. , 1 985; Stinnett and Stanley, 1 982; Gordeev et a/., 1 983 ; Yonas, 1 98 1 ; Ware et al. , 1 985; McClenanan et a/. , 1 983; Babykin et a/. , 1 99 1 ; Koval' chuk and Mesyats, 1 985). This will be discussed in detail in Chapter 1 6.

REFERENCES Airapetov, A. Sh., Krastelev, E. G., and Yablokov, B. N., 1 98 1 , Operation of a Magnetized Vacuum Transmission Line, Zh. Tekh. Fiz. 51:1 548-1 550. Al'bikov, Z. A., Velikhov, E. P., Veretennikov, A. 1., Glukhikh, V. A., Grabovsky, E. V., Gryaznov, G. M., Gusev, 0. A., Zhemchuzhnikov, G. N., Zaitsev, V. 1., Zolotovsky, 0. A., Istomin, 0. V., Kozlov, I. S., Krasheninnikov, S. S., Kurochkin, G. M., Latmanizova, V. V., Matveev, Yu. A., Mineev, G. V., Mikhailov, V. N., Nedoseev, S. L., Oleinik, G. M., Pevchev, V. P., Perlin, A. S., Pechersky, 0. P., Pismenny, V. D.,

VACUUM LINES WITH MA GNETIC SELF-INSULA TION

1 49

Rudakov, L. I., Smirnov, V. P., Tsarfin, V. Ya., and Yampolsky, I. R., 1990, The Angara-5-1 Experimental Facility, At. Energ. 68:26-35 . Aranchuk, L . E., Baranchikov, E . I . , Gordeev, A . V., Zazhivikhin, V . V., Koro1ev, V . D., and Smirnov, V. P., 1 989, Investigation of a Magnetically Self-Iinsulated Line with Ion Leakages, Zh. Tekh. Fiz. 59: 142- 1 5 1 . Babykin, V. M., Gordeev, G . T., and Korolev, V. D., 1 99 1 , Dynamics of an REB in a High­ Current Diode with a Blade Cathode, Fiz. Plazmy. 17: 1 1 02- 1 1 1 0. Baksht, R. B. and Mesyats, G. A., 1 970, Effect of a Transverse Magnetic Field on the Current of the Electron Beam at the Initial Stage of a Vacuum Discharge, Izv. Vyssh. Uchebn. Zaved, Fiz. 7: 144-1 46. Baranchikov, E. I., Gordeev, A. V., Korolev, V. D., and Smirnov, V. P., 1 978, Magnetic Self­ Insulation of Electron Beams in Vacuum Lines, Zh. Eksp. Teor. Fiz. 75:2 1 02-2 1 2 1 . Baranchikov, E . I., Gordeev, A . V., Korolev, V . D., and Smirnov, V . P., 1 977a, Transportation and Focusing of Relativistic High-Current Electron Beams in Magnetically Insulated Coaxial Lines. In Proc. 2nd Symp. on Collective Acceleration Techniques (Dubna, 29 Sept. - 2 Oct. , I976) (in Russian), Dubna, pp. 27 1 -274. Baranchikov, E. I., Gordeev, A. V., Korolev, V. D., and Smirnov, V. P., 1 977b, The Wave Mode of Magnetic Self-Insulation in a Vacuum Line, Pis 'ma Zh. Tekh. Fiz. 3: 1 06-1 10. Bernstein, B. and Smith, I., 1 973, "Aurora", an Electron Accelerator, IEEE Trans. Nucl. Sci. 20:294-300. Brillouin, L., 1 95 1 , Electronic Theory of the Plane Magnetron. In Advances in Electronics (L. Marton, ed.), Vol. 3. Academic Press, New York, pp. 85-144. Danilov, V. N., 1 963, The Generalized Brillouin Mode of Electron Flows, Radiotekh. Elektron. 1 1 : 1 892-1900. Danilov, V. N., 1 966, On the Theory ofBrillouin Electron Flows, Ibid. 1 1 : 1 994-2007. DiCapua, M. S. and Pellinen, D. G., 1 979, Propagation of Power Pulses in Magnetically Insulated Vacuum Transmission Lines, J. Appl. Phys. 50:371 3-3720. DiCapua, M. S., Pellinen, D. G., Champney, P. D., and McDaniel, D., 1 977, Magnetic Insulation in Triplate Vacuum Transmission Lines. In 2nd Intern. Conf High Power Electron and Ion Beams, Ithaca, USA, Vol. 2, pp. 78 1 -792. Gordeev, A. V., 1 990, Theory of Magnetic Insulation. In Generation and Focusing of Relativistic High-Current Electron Beams (in Russian, L. I. Rudakov, ed.), Energoatomizdat, Moscow, pp. 8 1 - 1 22. Gordeev, A. V., Korolev, V. D., Sidorov, Y. L., and Smirnov, V. P., 1 975, Production and Focusing of High-Current Beams of Relativistic Electrons up to High Densities, Ann. N Y. Acad Sci. 251:668-678. Gordeev, E. M., Zazhivikhin, V. V., Korolev, V. D., Liksonov, V. I., Tulupov, M. V., and Chernenko, A. S., 1983, Effects of Local Plasma Generation during Energy Concentration in Magnetically Self-Insulated Vacuum Lines, Fiz. Plazmy. 19: 1 1 0 1 - 1 1 09. Kataev, I. G., 1 963, Electromagnetic Shock Waves (in Russian). Sov. Radio, Moscow. Korolev, V. D., 1 990, Magnetically Insulated Vacuum Transmission Lines. In Generation and Focusing of Relativistic High-Current Electron Beams (in Russian, L. I. Rudakov, ed.), Energoatomizdat, Moscow, pp. 43-8 1 . Korolev, V. D., Smirnov, V. P., Tulupov, M . V., Tsarfin, V . Ya., and Chernenko, A. S., 1983, Formation of Plasma Flows in High-Current Diodes, Dokl. AN SSSR. 270: 1 1 09-1 1 12. Koval'chuk, B. M. and Mesyats, G. A., 1 985, Nanosecond Pulse Generator with a Vacuum Line and a Plasma Opening Switch, Dokl. AN SSSR. 284:857-859. Lovelace, R. N. and Ott, E., 1 974, Theory of Magnetic Insulation, Phys. Fluids. 17: 1263-1 268.

1 50

Chapter S

McClenahan, C. R., Backstrom, R. C., Quintenz, J. P., et a!., 1 983, Efficient Low-Impedance High Power Electron Beam Diode. In Proc. 5th Int. Topical Conf. High Power Electron and Ion Beam Research and Technology, San Francisco, CA, pp. 147- 1 50. Ron, A., Mondelli, A. A., and Rostoker, N., 1 973, Equilibria for Magnetic Insulation, IEEE Trans. Plasma Sci. 1 :85-93. Sincemy, P., DiCapua, M., Stingfield, M., et a/., 1983, The Limit of Power Flow along a High-Power MITL. In Proc. 5th Intern. Conf. High Power Particle Beams, San Francisco, pp. 267-27 1 . Smith, I. D., Champney, P . D., and Creedon, J . M., 1976, Magnetic Insulation. In Proc. 1st IEEE Intern. Pulsed Power Conf., Lubbock, TX, pp. 1 1 -8. Stinnett, R. W., Allen, G. R., Davis, H. P., Hussey, T. W., Lockwood, G. J., Palmer, M. A., Ruggles, L. E., Widman, A., and Woodall, H. N., 1985, Cathode Plasma Formation in Magnetically Insulated Transmission Lines, IEEE Trans. Electr. Insul. 20:807-809. Stinnett, R. W. and Stanley, T., 1 982, Negative Ion Formation in Magnetically Insulated Transmission Lines, J. Appl. Phys. 53:38 1 9-3823. Stinnett, R. W. and Woodall, H. N., Kinetic Loss Experiments on MITE. In Proc. 5th IEEE Pulsed Power Conf., Arlington, VA, Pt III, pp. 503-506. Turman, B. N., Martin, T. H., Neau, E. L., et a/., 1 985, PBFA-Il, a 100 TW Pulsed Power Driver for the Inertial Confinement Fusion Program. In Proc. 5th IEEE Pulsed Power Conf., Arlington, VA, pp. 1 55- 1 6 1 . Van Devender, J. P., 1 979, Long Self-Magnetically Insulated Power Transport Experiments, J. Appl. Phys. 50:3928-3934. Van Devender, J. P., Stinnett, R. W., and Anderson, R. V., 1 9 8 1 , Negative Ion Losses in Magnetically Insulated Vacuum Gaps, Appl. Phys. Lett. 36:229-233. Voronin, V. S. and Lebedev, A. N., 1 973, Theory ofthe Magnetically Insulated High-Voltage Coaxial Diode, Zh. Tekh. Fiz. 43:2591-2598. Voronin, V. S., Kolomensky, A. A., Krastelyev, E. G., et a/., 1 979, Energy Transport in Magnetically Insulated Vacuum lines. In Proc. IIIrd Intern. Topical Conf. on High Power Electron and Ion Beams, Novosibirsk, Vol. 2, pp. 593-602. Waisman, E. and Chapman, M., 1 982, Vacuum Transition Lines in the Presence of Resistive Cathode Plasma, J. App/. Phys. 53:724-730. Ware, K., Loter, N., Montgomery, M., et a/., 1 985, Source Development on Black Jack 5. In Proc. 5th IEEE Pulsed Power Conf., Arlington, VA, pp. 1 1 8- 1 2 1 . Woodall, H. N. and Stinnett, R . W., 1 985, Injector Losses on MITE. Ibid. pp. 499-50 1 . Yonas, G . , 1 9 8 1 , Inertial Fusion Research Using Pulsed Power Drivers. I n Proc. lOth European Conf. Control. Fusion and Plasma Physics, Moscow, Vol. 2, pp. 134-138.

PART 4. SPARK GAP SWITCHES

Chapter 9 HIGH-PRESSURE GAS GAPS

1.

CHARACTERISTICS OF SWITCHES

Depending on the means of energy storage in a pulse generator, closing or opening switches are used for capacitive and inductive energy storage, respectively. In this chapter, we consider closing spark gap switches with a high-pressure gas discharge. This implies that the conditions in the discharge gap correspond to the right branch of the Paschen curve. Besides, low­ pressure discharges, vacuum discharges, discharges in liquid and solid electrolytes, and discharges over the surface of a dielectric are used. The characteristics of spark gap switches depend on the functions they perform in generators. First, these are time characteristics. It is necessary to have a short switching time ts (10-10-10-8 s), a short triggering delay time td (10-9-1 0-7 s), and a low jitter ll.td (10-10-10-8 s). Second, these are characteristics associated with the switch current and voltage. The peak current passed by one switch is generally I � 102-106 A at a voltage v� I 03-107 V. In some cases, a wide range of operating voltages is necessary which is characterized by the ratio of the greatest operating voltage Vmax to the least one Vmin, i.e., 8 = Vmax 1Vmin . Third, important parameters that are responsible for the efficiency of a generator are its residual resistance and inductance, and, while the first parameter is determined by the physical properties of the discharge plasma in the gap, the second one depends, besides, on the geometry and design of the switch components. Fourth, in some cases, generators should be capable of operating repetitively, and the pulse repetition rates range from some fractions of a hertz to 1 04 Hz and more.

1 54

Chapter 9

It should be noted that there are no generators whose switches meet all above requirements. However, there is one parameter of critical importance in nanosecond pulse power technology. This is the switching time fs that must be short. We already mentioned that one way of attaining short fs is to increase the gas pressure in the spark gap and the other is to increase the overvoltage across the gap. For qualitative estimation of the dependence of fs on gas pressure p for a gap operating under the conditions of de breakdown, we shall use the model of Rompe and Weizel. According to this model, we have pts - (Eipt2 • For a constant voltage of de breakdown of gas, Vdc = const, according to Paschen' s law (see Chapter 4), the product of gas pressure by gap spacing, pd, should also remain constant, and, hence, the quantity EdciP = Vdclpd will be constant as well. This implies that the time ts decreases with increasing gas pressure as t5 - lip (Vorob'ev and Mesyats, 1 963). Figure 9. 1 gives t5 as a function ofp for different gases (Mesyats, 1 974). The time ts was measured using the switching characteristic V(t) between the 80% and 10% levels of the de breakdown voltage, which was equal to 1 5 kV. A charged coaxial cable was discharged through a switch. The peak current was 1 00 A. Figure 9. 1 demonstrates that the time t5 actually decreases with increasing gas pressure p. For instance, ts � 20 ns for air at atmospheric pressure and about a nanosecond at 1 0 atm. Different gases have different switching characteristics. For example, argon has the best switching characteristic of those under consideration. Even at atmospheric pressure it shows the time ts - 5 ns, while for helium, even at p � 1 0 atm, ts � 30 ns. For hydrogen, we have fs � 1 00 ns at atmospheric pressure and Is � 3 ns at 6 atm. For some ts(p) curves, the decrease in Is with pressure becomes more abrupt when going from low to high pressures. This is due to the prolonged stepped decrease in gap voltage (Kunhardt, 1 990) that takes place for some gases at low pressures (p < 1 atm). For a de breakdown, a decrease in gap spacing leads to a decrease in t5• Actually, for the right branch of Paschen's curve, in the region close to the minimum, we have

E

Bt

= At + - . p pd For air, A t

(9. 1)

= 62· 1 03 V/cm·atm and B 1 = 340 V. Hence, (9.2)

that is, at a constant gas pressure, the time t5 will decrease with decreasing gap spacing d. This conclusion is illustrated by the plots of l5(p) for different

HIGH-PRESSURE GAS GAPS

1 55

d in Fig. 9.2. For d = 0.2 mm, we have a short time fs � 1 0-9 s even for air at atmospheric pressure. This effect is used in closing multielectrode switches (see Section 6 in Chapter 9), which have the time fs � 1 0-9 s even for air and nitrogen at atmospheric pressure (Mesyats, 1 974).

m Ri

��

\[6

1\ 1\

[I)�[\� 5 1\

1 3�

\.

�

4

"Jl \ �

�

!"-..

'r-...

-..\"\.. 1'\. ......

8 L-J

4

�\

"'�

1 03 p [mm Hg] Figure 9. 1. Pulse rise time as a function of fill gas pressure: 1 - air, 2 - carbon dioxide, nitrogen, 4 - hydrogen, 5 - freon, helium, and 7 - argon

6-

3-

12 10 "'

8

�

E.. 6 �

4 2 0

2

3

4 p [atm)

5

6

7

Figure 9.2. Time fs as a function of air pressure for d = 2.2 (1), 0.98 (2), 0.7 (3), 0.4 (4), and 0.2 mm (5)

1 56

Chapter 9

A switch is generally triggered by some action on its gap (or gaps), such that the condition

(9.3) is fulfilled. Here, Edc is the de breakdown electric field and E is the electric field in the gap. Condition (9.3) can be fulfilled by increasing E or decreasing Edc · Therefore, there are switches of two types. Three-electrode switches and numerous modifications of multielectrode switches, switches with low-energy electrons injected into the gas, and capacitive two-electrode spark gaps with gas depressurization pertain to the first type. The second­ type switches are gas spark relays, trigatrons, laser-triggered switches, etc.

2.

TWO-ELECTRODE SPARK GAPS

The elementary type of switch used in nanosecond pulse generators is the two-electrode spark gap with compressed gas, which is triggered by an applied voltage. Switches of this type are also referred to as self-breakdown spark gaps. The discharge in them occurs when, in accordance with (9.3), the electric field E becomes greater than the de breakdown electric field Edc · Generally, an energy storage line or capacitor, which is pulsewise charged from a Marx generator or pulse transformer, is discharged through such a switch into a load. When using this type of switch, fast charging of the line is desirable to reduce the switch dimensions, and, hence, inductance. However, during fast charging, a jitter may appear in the breakdown of the gap; therefore, the gap should be adjusted so that the breakdown would occur not when the charge voltage peaks, but some time earlier. This would decrease the amplitude of a nanosecond voltage pulse across the load. It seams that the optimal time it takes for the charging pulsed voltage to reach a maximum ranges between a microsecond and several microseconds. With these times, a two-electrode spark gap operates in fact in the mode described by Paschen's law. Therefore, it can be triggered up not only by increasing the voltage between the electrodes, but also by reducing gas pressure p or decreasing gap spacing d between cathode and anode. Two­ electrode switches are used in Marx generators and as the main switches in nanosecond pulse generators. Vorob' ev and Mesyats ( 1 963) describe a nanosecond relaxation generator in which a spark gap filled with nitrogen at 1 0 atm was broken down during the charging of a capacitor C through a resistor R. In this generator, the pulse repetition rate was determined by the time constant RC. Two-electrode spark gaps with SF6 that operated at megavolt voltages and Z1oad = 1 0 n (Fig. 9.3)

HIGH-PRESSURE GAS GAPS

1 57

are described by Harrison et a/. , ( 1 974). The characteristics of generators with two-electrode spark gaps are given in Table 9. 1 . (b)

(c)

4

3

Figure 9.3. Schematic diagrams of nontriggered gas switches: (a) 1, 4 - electrodes, 2 - pins, 3 - SF6 at 4-5 atm, 5 - housing; (b) 1 electrodes, 2, 6 - inner conductors, 3, 5 outer conductors, 4 - SF6 at 4-5 atm, 7 - insulators; (c) 1 - electrodes, 2, 5 - inner conductors, 4 SF6 at 1 2- 1 5 atm, 3 - outer conductor, 6 - slab insulator -

Table 9. 1 . Output voltage, MV 0.5 1 .0 2.0

Spark gap types in Fig. 9. 1 , a, b Inductance Zloadl., O·ns L, nH 90 1 16 1 69 1 35 305 248

-

Spark gap type in Fig. 9. 1 , c Inductance Zload!., O·ns L, nH 80 55 1 30 1 00 240 1 90

From the data listed in this table it follows that the pulse rise time is determined in the main by the inductance of the spark gap, that is, tr � L/Z1oad· High-pressure two-electrode spark gaps are widely used in generators operated repetitively with pulse repetition rates of 1 02-103 Hz (SINUS, Radan, SF, etc.) at voltages of 1 03 -106 V and average powers of 1 00 kW and more, which have been created at the Institute of High Current Electronics (IHCE) in Tomsk and at the Institute of Electrophysics (IEP) in Ekaterinburg. In the spark gaps of the SINUS generators, the gas is forced to flow at an optimum velocity. The gas flow velocity should be high enough to remove plasma from the gap within the pulse interval, but not too high to keep the discharge region at the cathode heated in order that initiating electrons could appear during the discharge initiated by the next pulse. This will be discussed in detail below. One of the factors that limit the repetitive operation capability of two­ electrode switches is the discharge channel through which the current flows. This channel, on the one hand, has a high inductance, which gives no way of obtaining the required short pulse rise times. On the other hand, because of the high current density in the channel, the latter leaves at the electrodes a strongly heated metal, slowly deionizing plasma, and a strongly heated gas.

1 58

Chapter 9

To resolve these problems, it was proposed to use spark gaps with a multiavalanche volume discharge (Mesyats, 1 974). In such a spark gap, the inductance is very low (< 1 nH), and the gas and electrodes are not heated because of the low current density in the spark gap, since j - 1/S, where I is the current and S is the electrode area. Generators of this type are capable of operating with pulse repetition rates of up to 1 04 Hz and more in the picosecond pulse mode. The construction of a switching device used in a generator is shown schematically in Fig. 9.4. Between plates 1 and 3 there is gas interlayer 5, which is formed because the plates adjoin one another at the places of microprotrusions present on the ceramic and metal surfaces. The average width of the gap between elements 1 and 2 is determined by the condition of the surfaces and generally lies in the range 1 0-30 J.lm. When a pulsed voltage is applied between the electrodes, a surface discharge develops along the ceramics through the points where the latter touches the metal. The luminescence of this discharge causes the appearance of electrons near the cathode that initiate an avalanche discharge in the air gap between ceramics 1 and metal electrode 3.

Figure 9.4. Schematic diagram of an avalanche gas switch: I electrodes; 4 silver coating; 5 air gap -

-

BaTi03 tablet; 2, 3

-

metal

-

Detailed information on the operation of two-electrode gas gap switches can be found in the monographs by Koval'chuk et a/. (1979) and Vitkovitsky ( 1 987) and in the review by Buttram and Sampayan ( 1 990).

3.

THREE-ELECTRODE SPARK GAPS

A three-electrode spark gap is arranged as follows (Fig. 9.5, a): Electrode 2 is generally connected to a source of high de voltage V and electrode 1 is grounded through a load. The width of the gap 2-3 is chosen such that the

HIGH-PRESSURE GAS GAPS

1 59

gap is not broken down at the voltage V, and the gap 1 -3 has such a width that it is not broken down at the voltage of the trigger pulse. As the trigger pulse, whose polarity is inverse with respect to V, arrives at the electrode 3, the gap 2 -3 is broken down and the middle electrode acquires the potential V. For the gap spacing ratio d2-id1_3 � 2, the spark gap has the greatest double range of operating voltages. Investigations of the operation of three-electrode spark gaps (Mesyats, 1 974; Stekol'nikov, 1 949) have shown that to decrease the triggering delay time and jitter, it is necessary to increase the amplitude and rate of rise of the trigger pulse. For the trigger pulse dV/dt = 40-50 kV/J.ls and amplitude making up 50-70% of V, the jitter was of the order of 1 o-s s.

(b) 0 2

(a) 0 2

01·

GD3 J

Figure 9.5. Schematic arrangement of electrodes for various types of triggered switch: a ­ three-electrode spark gap switch, b trigatron, c spark relay -

-

A generator was developed (Vorob'ev and Mesyats, 1 963) in which the gas in the three-electrode spark gap was illuminated with ultraviolet radiation generated by an auxiliary spark gap connected in series in the cable by which a trigger pulse was supplied. At voltages of 10-15 kV the three­ electrode gap was triggered with 1 ns jitter. Schrank et al. ( 1964) described a three-electrode switch whose gaps were illuminated with the ultraviolet radiation of a surface discharge along a high-& ceramics (barium titanate) to decrease and stabilize the triggering time. The spark gap was utilized in a pulse generator for powering a spark chamber. The voltage across the spark gap was 30 kV and the current was 5 kA. The working gas was a mixture of 90% N2 and 1 0% C02 at a pressure of 3.5 atm. The triggering delay time of the spark gap was 25 ns with a jitter of several nanoseconds. Short and stable triggering times are typical of three-electrode spark gaps triggered by the principle of field distortion (Mercer et al., 1 976). Figure 9.6 illustrates the distortion of the field in a typical spark gap operating in the megavolt region. The trigger electrode is generally placed in the middle of the electrode gap. This electrode has the shape of a thin plate with a sharp edge, but in the initial state, there is no enhanced electric field at this electrode because it is under the voltage corresponding to the equipotential line along which it is located. Then the trigger pulse changes the trigger

1 60

Chapter 9

electrode voltage to a value usually lower than the potential of the nearest main electrode. This distortion of the natural fields in the gap results in a very strong field at the edge, giving rise to a corona and a streamer. Initially, the gap between the trigger and the high-voltage electrode is generally broken down which is followed by the breakdown of the gap between the trigger and the grounded electrode. (a)

' .....

V

Main electrodes E 3 Trigger electrode

-

-

Figure 9. 6. Circuit diagram of a three-electrode spark gap triggered due to field distortion: a without a trigger pulse, b with a trigger pulse. The trigger electrode is located in the V/3 potential line

To ensure small jitters of breakdown (about 1 ns) and triggering, it is necessary to have a short breakdown delay time, about 10 ns. The breakdown delay time is determined by the development time of the streamer and depends in the main on the time of occurrence of the streamer at the edge of the trigger electrode; the elongation of the streamer occurs rather quickly. Hence, the efficiency of triggering of a spark gap is determined by the electric field created by the trigger pulse at the edge of the trigger electrode, and this field, in turn, appreciably depends on the amplitude of the trigger pulse and the radius of curvature of the edge. For multimegavolt spark gaps, the trigger electrode can be placed near the middle of the gap, applying a trigger pulse that changes its potential only by several hundreds of kilovolts. However, higher fields can be obtained at the edge of the trigger electrode if it is placed near one of the electrodes lengthways an equipotential line corresponding to several hundreds of kilovolts. The arrangement of the trigger electrode near a fixed equipotential line helps one to localize field distortion in a small region. Since spark gaps with field distortion are used at higher and higher voltages, this geometry appears very convenient. A spark gap of this type with an operating voltage of 3 MV and a breakdown delay time td 20 ns with about 1 ns jitter is described by Mercer et a/. ( 1976). Short values of td are realized due to high average electric fields in a discharge gap; therefore, the SF6 fill gas was used at a pressure of -10 atm. This has also made it possible to reduce the dimensions of the

=

HIGH-PRESSURE GAS GAPS

161

spark gap and its inductance. In SF6, the streamers from the positive electrode propagate with a higher velocity than those from the negative one. Therefore, the trigger electrode was mounted near the grounded electrode, since the main voltage was of negative polarity. A previously developed spark gap of similar design was used a trigger spark gap in the Aurora accelerator (Bernstein and Smith, 1 973). For a 1 .8-mm gap spacing between the trigger and the grounded electrode, the breakdown jitter was 2-3 ns. To reduce the jitter, it was decided to increase the field at the edge of the trigger electrode by increasing the gap spacing to 5 mm with a corresponding increase of the trigger pulse amplitude. Three-electrode spark gaps of other types can also be operated in parallel that to reduce the inductance of the discharge circuit at voltages of up to 100 kV. For instance, two parallel-connected three-electrode spark gaps were operated with 2 ns jitter (Mesyats, 1 974) describes the operation of is described; the jitter of the operation of these spark gap was 2 ns. 4.

TRIGATRONS

A trigatron (Fig. 9.5, b) consists of two main electrodes - cathode 1 and anode 2 - and trigger electrode 3 made as a metal rod, which is sometimes enclosed in a dielectric tube, and placed along the main axis. There are two mechanisms of the operation of a trigatron, depending on the construction of the trigger unit and the applied voltage. Let us first consider the operation of a trigatron at voltages of some tens of kilovolts. As a voltage pulse arrived at the trigger electrode, a discharge occurs between the rod 3 and the electrode 1 . The ultraviolet radiation of this discharge initiates breakdown between the main electrodes 1 and 2. The triggering delay time of this type of trigatron is generally I Q-6 s with a jitter of 1 0-7 s. Theophanis ( 1960) examined the possibility of triggering a trigatron with nanosecond jitter. The trigatron was in the atmosphere of freon at a pressure of 1 00 mm Hg. The operating voltage was 50 kV. The examination has shown that the operation time of the trigatron is shorter if the polarity of the trigger pulse is opposite to that of the potential of the ungrounded electrode. As a capacitor was discharged through the trigatron, a trigger pulse of amplitude 1 6 kV and rise time 20 ns appeared. When the trigatron voltage was 1 0% lower than Vdc, the delay time was 20 ns with a jitter of 1 ns. The delay time and jitter decrease with a decrease in rise time of the trigger pulse because of the increase in overvoltage between the electrodes 1 and 3. In the experiment performed by Lavoie et al. ( 1964), to reduce the amplitude of the pulse triggering a trigatron, the trigger electrode was coated

1 62

Chapter 9

with barium titanate (BaTi03 ), a dielectric with a high permittivity (s > 1 000). Between the dielectric coating of electrode 3 and electrode 1 there was a small gap across which almost all the voltage appeared to be applied on application of the trigger pulse. In spark gaps of this type, filled with air at atmospheric pressure, the highest operating voltage was 25 kV, the delay time ranged from 1 7 to 65 ns, depending on the required operation mode, and the jitter was not over 3 ns. The trigger pulse amplitude and rise time were, respectively, 0.5-1 kV and 5 ns. Markins ( 1 97 1 ) has demonstrated the possibility to achieve nanosecond jitters for a trigatron switch at voltages of the order of 106 V. The trigger voltage generally used ensured breakdown of the trigger gap in the absence of the main charge voltage. In the experiment, the amplitude of the trigger pulse was diminished to a value at which there was no breakdown of the trigger gap in the absence of the main voltage. However, when the main voltage was applied, no difference in the operation of the spark gap in these two modes was noticed. At a pressure of -5 atm, the breakdown of the trigger gap occurred with a delay of -10 ns and the delay to the breakdown of the main gap was 20-70 ns; the average velocity of the streamer in this case was -108 cm/s. Thus, for a trigatron operating at high voltages, it is necessary that breakdown first occurred between the electrodes 1 and 2 rather than between the electrodes 1 and 3. This is the second mechanism of operation of a trigatron. At a self-breakdown voltage Vdc = 0.95 MV, the triggering jitter varied from 1 .5 ns at V = 0.95 Vdc to 7 ns at V 0.6 Vdc · Thus, the stable triggering range was (0.55-l .O) Vdc · Four trigatrons of this type connected in parallel switched a line with a wave resistance of 1 .5 n, which was charged to 2 MV and produced a pulse of duration fp = 70 ns and rise time tr 20 ns (Markins, =

=

1 97 1 ).

Similar spark gaps were used in the experiments described by Martin

(1973) and on the improved Gamble I generator (Cooperstein et al., 1 973).

In the latter case, an eight-channel trigatron was used which operated at voltages of 1-3 MV with 2 ns triggering jitter of each channel. The inductance of such a spark gap was 70 nH, which made it possible to obtain the rise time of the output pulse equal to 20 ns in switching a 4-Q line into a matched transformer line. Trigatrons having a considerably shorter and more stable delay time were tested in experiments performed by Koval' chuk et a/. (1 979) and El'chaninov et a/. (1975). Figure 9.7 presents the delay time of operation of a trigatron, td, as a function of the voltage at trigger electrode 3 for different self-breakdown voltages between electrodes 1 and 2. The gap spacing was d = 5.5 em and the pressure of the working gas mixture 8% SF 6 + 92% N2 was 6 atm. This function has a minimum. The current-voltage characteristic

HIGH-PRESSURE GAS GAPS

1 63

of a trigatron depends on the polarities of the main and trigger voltages. The least delay time is generally obtained with negative main voltage and positive trigger voltage. 28 24 20 ti)

.s .:'2

16 12 8 4 0

50

1 00

200 1 50 Vtr [kV]

250

300

Figure 9. 7. Delay time as a function of trigger electrode voltage for VdciVtr 0.75 (2), and 0.7 (3)

=

0.93 (1),

The delay time td and jitter !J..td are affected by the composition of the working gas mixture. Generally, a mixture of nitrogen and SF6 is used. An admixture of argon to this mixture noticeably improves td and !J..td (Table 9.2) (Koval'chuk et al. , 1 979; El'chaninov et al. , 1 975). Table 9.2. Gas mixture

4.8±0.7

90% N2+ 1 0% SF6

80% N2+ 10% SF6 + 1 0% Ar

50% N2 + 50% Ar

40% N2 + 50% Ar + 1 0% SF6

5±0.7

3.2±0.5

3.1±0.4

2.3±0.3

Thus, trigatron initiation of a spark discharge at megavolt voltages makes it possible to obtain the discharge delay time td equal to a few nanoseconds and its straggling !J..td equal to some fractions of a nanosecond. This makes feasible parallel operation of a great number of spark channels in trigatrons. Now we shall consider in more detail the mechanism of the nanosecond discharge in a trigatron. There are two points of view on the mechanism of the operation of a trigatron. According to one of them, the excitation of the discharge in the main gap occurs because of the photoionization caused by the short-wave radiation from the spark of the trigger discharge. The second point of view (Shkuropat, 1 969) is based on the assumption that a discharge can be initiated in a trigatron before the breakdown of the trigger gap.

1 64

Chapter 9

In the experiment performed by El' chaninov et al. ( 1 97 5), the second mechanism of the breakdown of a trigatron was realized. The width of the trigger gap in these experiments made up not above 1 0- 1 5% of the width of the main gap. Delay times of about 3-5 ns were obtained at an amplitude of the trigger pulse making up no more than 1 0- 1 5% of that of the main voltage. To provide shorter td, it is necessary that, on application of a trigger pulse, the main gap become closed earlier than the breakdown of the trigger gap takes place. To meet this requirement, one should adjust correctly the proportion between the trigger gap formed by the electrodes 1 and 3, d1 _3 , and the main gap d and choose an optimum trigger voltage Vtr· For too high Vtr. the trigger gap is broken down first, the triggering potential is shunted by the low impedance of the spark in this gap, and td increases. When Vtr is low, the electric field gradient at the edge of the trigger electrode decreases, and this leads to an increase in td as well. It is necessary to have the ratio d1 _2/d1 _3 = 5- 1 0, since at smaller ratios the overvoltage across the trigger gap of width dtr decreases after the closure of the main gap, while at large dldtr the voltage Vtr should be substantially reduced. The short and stable delay time obtained for the trigatron ignition of spark gaps was good reason to hope that parallel operation of several spark gaps could be arranged with small transit time isolation, ftrans· Initially, experiments on the initiation of two parallel spark channels were carried out (Koval'chuk et al. , 1 979). Taking into account the small jitter (some fractions of a nanosecond) of the delay time in this type of triggering, two trigatron units were mounted in one spark gap at a distance of 8 em (ftrans = 0.27 ns) from each other (Fig. 9.8). Electrode 1 was made as a plate with rounded (R = 1 5 mm) edges. The electrode gap spacing was 5.5 em and the gas (8% SF 6 + 92% N2) pressure was 6 atm. The trigger pulse of amplitude 140 kV was applied simultaneously to both trigger electrodes 3 through resistors of resistance R = 1 03 n. The main discharge current in each channel was measured with the help of shunts of resistance 0.2 n, which were placed between the grounded electrode and the metal rings onto which the main discharge occurred. It has been shown that with two channels the switching time almost halves if the current is the same in both channels (32 ns with one channel and 1 8 ns with two ones). In these experiments, the switching time of the trigatron was determined by the ohmic resistance of the spark. The effect of the inductance was insignificant, and the total current in the two channels was 26 kA. Further investigations of the characteristics of a trigatron and of the multichannel operation of a high-current switch (Koval' chuk et al. , 1 979) were performed on a system with an eight-channel spark gap rated at 500 kV and a 3-Q coaxial line with a double electric length of 1 8 ns.

HIGH-PRESSURE GAS GAPS

1 65

4Jr

VD

4

l

PFL

3

1. 5 I

1 2

1. 6 I

Figure 9.8. Schematic diagram of a double-channel trigatron: 1 ground electrode, 3 trigger electrode, 4 dielectric sleeve, 5 Marx generator 2, VD voltage divider -

-

-

-

high-voltage electrode, 2 Marx generator I , and 6

-

-

-

(a)

50% N2 50% Ar

40% N2 80% N2 9 % 0 0 N2 50% Ar 10% Ar 10% SF6 10% SF6 10% SF6

3

2 0 3

(b)

2 0 3

(c)

2

� 0

"'

:::...

-

0 3

(d)

2

0 0 5 10 0 5 10 0 5 10 0 5 10 0 5 10 15 [ns]

t

Figure 9.9. Oscillograms showing the drop in discharge gap voltage for different gas mixtures and one (a), two (b), four (c), and eight channels (d)

1 66

Chapter 9

The switching characteristic of a switch depends on the fill gas. For instance, it is well known that an admixture of 50% argon to a mixture of N2 and SF 6 improves the performance of the switch (Moriarty et al. , 1 97 1). For an eight-channel trigatron, the highest rate of current rise was obtained with a mixture of 80% N2 + 1 0% SF6 + 1 0% Ar. The switching characteristics were obtained for one-channel and multichannel operation of a high-current spark gap filled with mixtures of SF 6 , N2, and Ar in different proportions (Koval' chuk et al. , 1 977). Typical oscillograms of the voltage across the spark gap are given in Fig. 9.9. From these oscillograms, it can be seen that addition of argon in great amounts to the gas mixture substantially delays the decrease in voltage. As the number of spark channels is increased, the rate of voltage ·drop increases early in the switching process. However, even for an eight-channel discharge, at the terminating stage of switching in a mixture containing 30-50% Ar, no less than 1 0- 1 5% of the initial voltage remains across the gap. The inductive resistance of a switch weakly depends on the gas type. Therefore, perhaps, the residual voltage is due to the high active resistance of the switch. This is also testified by the nonexponential voltage drop during the terminating stage of switching.

5.

SPARK GAPS TRIGGERED BY EXTERNAL RADIATION

5. 1

Ultraviolet triggering

A spark gap triggered by the ultraviolet radiation of an auxiliary spark gap is referred to as a spark relay. This device has two spark gaps (see Fig. 9 .5, c): the main spark gap between electrodes 1 and 2 and trigger spark gap 3 (Stekol'nikov, 1 949). The ultraviolet radiation of the spark in the gap 3, when hitting the cathode 2, gives rise to a photoelectric current from the cathode that initiates breakdown of the main gap. It has been demonstrated (Stekol'nikov, 1 949) that at a 1-2% undervoltage across the main gap and an operating voltage of about 1 0 kV the delay time td between the breakdowns of the trigger and the main gap is 1 o-s s. Spark relays played an outstanding role in developing triggered pulsed devices for first fast oscilloscopes. Stekol'nikov ( 1949) has shown that such relays, when properly adjusted, have td � 1 0 8, and Md « 1 0 8 s. Godlove ( 1 961) investigated the spark discharge triggered by an ultraviolet flash of duration 6 ns and has shown that the ultraviolet radiation with a wavelength of about 1 1 00 A is most efficient. This radiation is only slightly absorbed in -

-

HIGH-PRESSURE GAS GAPS

1 67

air and provides intense photoemission from a cathode. The delay time of triggering of a spark gap, td, decreases with an increase in voltage and approaches a limit equal to d/Ve. Mesyats ( 1 974), based on his concept of a multiavalanche discharge, has explained this result by the fact that the increase in current results from the avalanche multiplication of electrons produced at the cathode upon ultraviolet illumination of the latter. The main condition for this to occur is that the current of initial initiating electrons, /0, should be such that in the case of gas amplification with a factor of about 1 08, characteristic of the critical avalanche in a nearly de breakdown, the discharge current would reach a value at which a discharge starts developing. For instance, for a current of initiating electrons /0 ::::: 1 0-7 A and a gas amplification factor of 1 08 the main discharge current will reach 1 0 A. If we take into account that during the development of avalanches up to 1 08 electrons there will be an additional inflow of electrons from the cathode due to photoeffect, it is obvious that the total discharge current will be over 1 0 A. Under these conditions, the delay time to the breakdown of the main gap can be estimated by formula (4.25) that was used for a pulsed multielectron­ initiated discharge. If in this formula, we substitute for a its value from the Raether criterion for a de breakdown, a ::::: 20/d (Meek and Craggs, 1 953), thus assuming that the gas amplification of an avalanche is about 1 08, we get �

(9.4) which was established experimentally (Godlove, 1 96 1 ). If the voltage across the main gap is much lower than the de breakdown voltage, then, even if initiating electrons are present in great numbers, to complete the discharge needs several avalanche generations. This results in a substantial increase in time td compared to dive. Usov ( 1 964) showed that the relation td ::::: dive, which was obtained for voltages approaching the de breakdown voltage, is also valid for other gases such as helium, argon, and carbon dioxide. The time td was calculated for gaps irradiated with short ( 1 o-9 s) flashes of ultraviolet radiation at a voltage making up 90-95% of the de breakdown voltage (Stolen, 1 969). It has been found that dive < td « dlvi, where vi is the drift velocity of positive ions. In these calculations, the influence of the positive charge of the ions that are formed in the cathode region and distort the electric field in the gap was taken into account. However, the method of triggering of a spark gap by the ultraviolet radiation of an auxiliary spark has two disadvantages. The first one is the narrow range of operating voltages, which makes up only 95-98% of the de �

1 68

Chapter 9

breakdown voltage; otherwise the delay time and jitter abruptly increase. Second, the spark ultraviolet triggering cannot be used at high voltages (above 50 kV), since in this case breakdowns occur between the trigger and the main electrodes. The situation can be improved to some extent by using a grid anode through which the cathode surface is illuminated to induce emission of photoelectrons. The same principle of initiation of photoelectrons at the cathode underlies the triggering of gas gap switches from other ultraviolet radiation sources such as halogen and quartz lamps and excimer lasers. 5.2

Laser triggering

With no electrical coupling between the main and the triggering circuit, the triggering of spark gaps by a focused laser beam acting on the gas in the cathode-anode gap or directly on the surface of either electrode. Laser triggering of spark gaps was proposed and first used by Pendelton and Guenther ( 1 965). When a high-power laser beam acts on a gas, an electron avalanche appears (Raizer, 1965). Primary electrons are generated due to multiphoton ionization of the gas and are multiplied either as a result of direct ionization of atoms by electron impact or due to the breakoff of electrons from excited atoms under the action of the laser radiation. The ionization of gas is strongly influenced by the electric field of the light wave. There exists a threshold field, depending on the gas type and pressure, to which there corresponds a flux density at which a light breakdown is possible. The mechanism by which a laser-induced spark is formed alters if the beam is focused on the cathode. In this case, there occur heating of the cathode surface, thermoemission of electrons, and even an explosion of the cathode metal at the surface. In the presence of an electric field, the process develops in the same manner as in the presence of initiating plasma. It is interesting that the delay time of the discharge in the switch practically does not depend on which - anode or cathode - surface plasma is generated. This is similar to the development of an anode-directed or cathode-directed streamer. The time td depends on electric field, gap spacing, and streamer velocity. In an experiment performed by Moriarty et a/. (197 1 ) , the influence of the radiation of a ruby laser on the breakdown of a gas gap was investigated. The time delay between the arrival of the laser pulse and the appearance of a discharge current in air, nitrogen, and SF6 was measured. The power of the laser beam was 80 MW, the gas pressure was 1 00-1 400 mm Hg, the distance between the cathode and the anode was varied from 0.4 to 1 .5 em, and the field E was varied from 10 to 1 00 kV/cm. The time td varied in

HIGH-PRESSURE GAS GAPS

1 69

inverse proportion to the electric field, gas pressure, and distance of the focus from the anode surface. A series of experiments was carried out with laser triggering of single­ channel and double-channel megavolt switches (Moriarty et a/. , 1 97 1 ). The voltage across the high-voltage electrode was 4 MV. The laser beam entered the tube of the inner electrode of a coaxial line, passed through a sealed-off window, and was focused on the surface of the high-voltage electrode. The power of the focused laser beam was 1 64 GW/cm2 • Placing an optical divider on the beam path, on can pass the beam in two directions, thus producing two parallel discharge channels in the gap. The best results on laser triggering were obtained for an 1 1 -cm gap with a mixture of 50% argon, 40% nitrogen, and 1 0% SF6 at a pressure of 21 atm. In this case, the average triggering delay time at a voltage of 3.05 MV (94% of the self­ breakdown voltage) was 1 0 ns with a jitter of 1 ns. If the delay time was less than the duration of the laser pulse, the power density of the laser beam at the target had no effect on the delay time. Otherwise, as the power density at the target was reduced from 1 64 to 65 GW/cm2 , the delay time increased from 1 0 ± 2 to 1 8 ± 7 ns for a 7-cm gap at Elp = 26 V/cm·mm Hg and the breakdown voltage making up 83% of the self-breakdown voltage. Comprehensive information on laser-induced sparks can be found in the review by Williams and Guenther ( 1 990) and in the monograph by Raizer (1 974). 5.3

Electron-beam triggering

It was shown (Koval'chuk et a/., 1 970a, 1 970b) that a spark gap could be triggered with a nanosecond jitter by a beam of fast electrons. In subsequent experiments performed with a spark gap filled with a mixture of 20% SF6 and 80% N2 at a total pressure of 8.5 atm and a line charged to a pulsed voltage of 2 · 1 06 V, a delay time of 30 ns was obtained. The main problem with this type of switch is to attain a short and stable delay time to the switch operation at a low current of the beam. An efficient way of solving this problem is to inject a beam containing a large fraction of low-energy electrons, thus substantially increasing the field of the space charge of electrons thermalized in the gas filling the gap. During the injection of electrons into the gas, the field enhancement is due to the space charge of thermalized electrons and the nonuniform conductance of the plasma resulting from the nonmonochromaticity of the beam. The low­ energy electrons of the beam have a smaller penetration depth and a larger ionization cross section. Therefore, the plasma conductance during the injection of electrons through the cathode will decrease from cathode to anode, strengthening the electric field in the anode region.

1 70

Chapter 9

The effect of the thermalization of fast electrons is more substantial if their total range in the gas is less than the electrode gap spacing. Then the electric field between the front of the thermalized electrons and the opposite electrode increases by

=

=

=

(9.5)

where jb is the beam current density, t is the time, and eo is the dielectric constant. For jb 1 AIcm2, even in a time t 1 o-s s, we have Eth 105 VIem. For a spark to be initiated in air at atmospheric pressure in this field, a time of � 1 0-9 s is sufficient (see Chapter 4). El'chaninov et a/. ( 1 975) observed a decrease in time td as the energy of the injected electrons was reduced by reducing the accelerating voltage of the accelerator. As this was done, the electron current in the diode of the accelerator and the transparency of the metal foil through which electrons entered the gas decreased. The experimental setup is shown schematically in Fig. 9. 1 0. The results of these experiments are presented in Fig. 9. 1 1 . From the plot of the delay time of occurrence of a spark, td, as a function of the voltage applied to the electrode gap, V0, it follows that even a substantial decrease in injected electron current decreases td. For /b 1-50 A and V0 = 1 50- 1 80 kV, the time td was �1 0-9 s.

=

Figure 9. 10. Schematic of the 2.5-MV setup: MG - Marx generator; BI - bushing insulator; OC and IC - outer and inner conductors ofPFL; E 1 and E2 - electrodes of the test gas gap; I ­ insulator; P - pins made of organic glass; EA - electron accelerator; TSG - triggered spark gap; F - anode foil of the vacuum diode (in e-beam experiments); C - cathode; SU synchronization unit; VD I. VD2, and VD3 - voltage dividers

HIGH-PRESSURE GAS GAPS

171

The delay time td depends on the polarity of the voltage across the discharge gap (see Fig. 9. 1 1 ). The minimum td for the injection of fast electrons through the cathode ( 1 o-9 s) is attained at a considerably (by 30%) higher voltage, and the voltage control range of the spark gap becomes smaller. For fixed parameters of the injected beam, the efficiency of a fast breakdown of the spark gap increases with an increase in product pd (p being the gas pressure and d the gap spacing). This is accounted for by the increase in current density of electrons thermalized in the gas and by the increase in the field of their space charge. �

1 60

.... ..., "'

1 20

.E. 80 �

40

0

1 30

1 50

1 70

1 90

220

Vo [kV] Figure 9. 1 1. The triggering delay time as a function of voltage for an electron-triggered spark gap with the e-beam injected through cathode (1-3) and anode (4). E-beam current Ib = 50 (1), 1 0 (2), 1 (3), and 10 A (4)

Let us discuss this problem in more detail. Assume that the thickness of the aluminum foil through which electrons are injected is 50 !J.m and the product of the foil thickness, h, by the density of aluminum, p, is hp = 12.5- 1 0-3 g/cm2 • The losses of electrons of range 8 in a metal foil are small if 8 » h. For the energy of electrons 0. 1 5 MeV < To < 0.8 MeV, we have 8p � 0.4T04 1 3 (Siegbahn, 1 965). Hence, it is necessary to have To > 0. 1 MeV. Assume that To = 0.2 MeV. In nitrogen, electrons with this energy will run for 8p = 4 · 1 06 cm·Pa (Siegbahn, 1 965). Hence, for the thermalization of electrons be substantial, it is necessary to have pd > 4· 1 06 em· Pa. According to Paschen's curve, for these values of pd, the de breakdown voltage in nitrogen is Vdc = 2·1 Opd (Nunnally and Donaldson, 1 990), where Vdc is measured in kilovolts. Hence, for these conditions, one should expect a short triggering delay time at Vdc > 800 kV. From the above considerations, it can be concluded that in going to megavolt gaps one should expect shorter triggering delays. Experiments with

1 72

Chapter 9

megavolt spark gaps have confirmed this conclusion (El' chaninov et a!. , 1 97 5). Spark gaps with a voltage of up to 2.5 MV were used. The width of the discharge gap was 5.5 em. For the fill gas, nitrogen or its mixtures with SF 6 at a pressure of (4-1 1 )· 1 05 Pa were used. The electron energy was 200-300 keY and the current downstream of the metal foil ranged between 1 5 and 1 30 A. Figure 9. 12 gives the delay time td and the reduced electric strength EdciP measured for a 5.5-cm gap that are plotted as functions of the percentage of SF6 in a mixture of SF6 with nitrogen (El'chaninov et al., 1 975). The measurements were performed for the same charge voltage, 1 .4 MV, and the gas pressure varied from 1 . 1 · 1 06 (pure N2) to 4· 1 05 Pa (50% N2 : 50% SF6). 1t can be seen that a small admixture of SF6 (-1 0%) doubled the breakdown electric field for the gap filled with pure nitrogen; further increasing the percentage of SF 6 in the mixture changed the electric field insignificantly. According to the data of Bortnik ( 1 988), the relative electric strength of SF6 in comparison with nitrogen at a de voltage is 2.3-2.5. Thus, is inexpedient to use mixtures with the SF 6 content over 50%. It is also necessary to take into account that at a great content of SF 6 in the mixture the electric strength of the gas depends on the number of discharges. Thus, for Vc = 1 .45 MV and p = 4· 1 05 Pa (50% N2 : 50% SF6), even after 30 discharges of current I 40 kA and duration 60 ns (total charge transfer of 5 · 1 o-2 C), the electric strength of the gas decreased by 1 0%. In these experiments, the minimum td was 1 5 ns with a jitter of 0.8 ns (Vo!Vdc = 85%). Detailed information on electron triggering of switches can be found in a review by Mesyats ( 1 982).

=

� Q..

1 00

50 40

E ':::::

2:

30 0 ..:s

� � .....;

�

20

.;::?

,-.._

rJ

20

10

'-'

0

10

20 30 SF6 [%]

40

50

°

Figure 9. 12. The electric strength {1) and breakdown delay time (2) of a spark gap function of the SF6 percentage in nitrogen

as

a

HIGH-PRESSURE GAS GAPS 6.

1 73

SEQUENCE MULTIELECTRODE SPARK GAP SWITCHES

6.1

Principle of operation

A device that consists of a great number of spark gaps is referred to a sequence multielectrode spark gap switch. This type of switch was proposed by Gardner (1953). Vorob'ev (1 959) suggested using such a switch for shortening the pulse rise time, since a high overvoltage allows a short switching time. Mesyats (1 960, 1 974) performed a comprehensive study of the properties of this type of spark gap switch and showed the possibility to design nanosecond high-power switches with short td (1 o-s s) and !ltd (±1 0-9 s) capable of producing a series of pulses locked to each other in delay circuits, peakers, etc. A general diagram of the circuit of a sequence spark gap is given in Fig. 9. 13. The voltage is distributed over N gaps by a resistive divider R and each gap is shunted to the ground with a capacitor C0• The ground potentials of the upper electrodes are v�. V2 , , VN. A spark gap of this type can be triggered by applying a trigger pulse to any gap. If gap 1 is broken down first, the capacitor C is discharged onto this gap, creating a conducting channel in the gap. The capacitor C0 keeps a fixed potential at the point of its connection; therefore, the gap is broken down with an overvoltage ( V1 + V2)/ Vdc. where Vdc is the de breakdown voltage of gap 2. The discharge of Co creates a conducting channel in gap 2 and sustains the channel in gap 1 . Thus, all N gaps are sequentially broken down. The triggering of such a spark gap is also possible by applying a trigger pulse to another electrode, as shown in Fig. 9. 13. • • •

R

R

R

.-----I

R

I Ccoupl

R

R

Figure 9. 13. Circuit diagram of a multielectrode switch: Cs energy storage capacitance; R1oad - load resistance; C interelectrode capacitances; C0 ground capacitances of the electrodes; R - resistance of the voltage divider; Ccoupi - coupling capacitance V1, - trigger pulse; 1, 2, . , N - gap numbers -

-

. .

Chapter 9

1 74

The stability of operation of such a spark gap is affected by the ratio of the ground capacitance of the electrodes to the natural electrode capacitance, i.e., C0/C. Generally, for stable operation it is necessary to have Co/C ;::: 5. The triggering time decreases and stability of operation of such spark gaps increases if the sparks in the gaps illuminate the neighboring gaps with ultraviolet radiation. If the trigger pulse is applied to any intermediate spark gap, it suffices that only the neighboring gaps are illuminated (Mesyats, 1 960). For these spark gaps, at voltages of up to 1 00 kV, the total delay time can reach tens of nanoseconds with a jitter of several nanoseconds. The advantages of these switches are the very wide (tenfold and more) range of operating voltages and the low trigger voltage, since it generally suffices to initiate a discharge only in one gap, and then all remaining gaps operate sequentially. Such spark gaps have a short switching time even at atmospheric pressure of the working gas, since they operate at a high overvoltage. HV

Figure 9. 14. Circuit diagram of a spark gap switch with not increased ground capacitances of the electrodes: HV high voltage, L1oad - load inductance -

In some cases, it is impossible to provide a high Co/C ratio. It has been shown (Koval 'chuk. and Potalitsyn, 1 974) that a multielectrode spark gap can operate efficiently with no increase in its ground capacitance. Figure 9. 14 shows a circuit diagram of this type of spark gap. Additional capacitors of capacitance C = 4.7· 1 0- 1 ° F are connected in parallel with the spark gaps through resistors of resistance R1 = (3-5)- 1 03 n. The values of R1 and C are chosen so that the discharge time constant R 1 C be greater than the breakdown delay time td of individual spark gaps: 't = RIC � 1 0-6 s and td � 5 · 1 o-s s. With this proportion between 't and td, as the trigger cable is grounded with the help of the spark gap SGN, the potential of the trigger

HIGH-PRESSURE GAS GAPS

1 75

electrode substantially changes, while the potentials of the neighboring electrodes remain practically unchanged because ofthe large value of -r. As a result, the gaps neighboring the trigger electrode are broken down at a high overvoltage. After the breakdown of these gaps, the other gaps are broken down in a similar way until the operation of the spark gap is complete. 6.2

Sequence microgap switches

As we have shown in Section 1 in Chapter 9, if the gap spacings of a spark gap switch are some fractions of a millimeter, the switching time is 1 o-9 s even at atmospheric pressure. This property of short gaps is preserved if a great number of spark gaps are connected in series. For instance, for the number of gaps N = 1 0, the gap spacing d = 1 00 J..lm, and the pressure of air p = 1 atm, the switching time ts is about 1 o-9 s. This time is almost an order of magnitude shorter than fs for a single gap at p = 1 atm with the de breakdown voltage equal to the total voltage of all gaps, i.e., -10 kV, and is approximately equal to the switching time at V = 1 0 kV and p = 1 0 atm. Hence, with series-connected short gaps it is possible to reduce the time fs by an order of magnitude at fixed pressure and breakdown voltage, or to lower the gas pressure by an order of magnitude at fixed fs and breakdown voltage. A small gap has a short deionization time, and this time will decrease if the gap is subdivided into many gaps. This has stipulated wide application of spark gap switches with small gaps in energy spark gaps, in the control circuits of pulsed light sources, etc. In the latter case, when a multisection spark gap was filled with hydrogen, the pulse repetition rate was 1 0 kHz at a current of 6 kA (Zhiltsov and Slutskin, 1 963). A switch with a switching time of 1 o-9 s was designed (Vorob' ev et al. , 1 966) that showed simultaneously a highly stable triggering delay time without auxiliary power supplies, a low amplitude of the trigger pulse, a wide range of operating voltages at fixed gap widths, and, finally, a rather low pressure. This switch was triggered with no galvanic contact between the pulse-forming and triggering devices. The design of this switch is shown schematically in Fig. 9. 1 5 (Vorob'ev et al. , 1 966). Washers 1 , which serve as electrodes, are separated with gaps and are put on a hollow insulating base 2. The voltage is distributed over the gaps with the help of resistors 3. An energy storage cable 4 is connected to the last washer from above, and the pulse produced is tapped via cable 5, which is connected to the last washer from below. The trigger electrode is a metal cylinder 6 to which the pulse is supplied by cable 7. The device is placed in a metal housing 8, which is put, for insulation from high voltage, on an insulating cylinder 9.

1 76

Chapter 9

Figure 9. 15. Schematic diagram of a short-gap switch: 1 - washers; 2 insulating base; 3 resistor; 4 - energy storage cable; 5 transmission cable; 6 - trigger electrode; 7 - trigger cable: 8 - housing, and 9 - insulating cylinder -

-

This type of spark gap has a number of advantages over conventional switches: 1 . The decrease in pressure is achieved due to the use of small gaps. For the gap width d = 100-200 J.lm, the switching time in nitrogen, argon, air, etc., even at atmospheric pressure, is 1 o-9 s. With a great number of short gaps connected in series, it is possible, at high voltages and pressures as low as a few atmospheres, to produce a pulse of rise time 1 o-9 s.

HIGH-PRESSURE GAS GAPS

1 77

2. The low-jitter triggering of the switch is ensured because the major portion of the trigger voltage is applied to the first gaps, and they are broken down within 1 o-9 s, creating a high overvoltage across the subsequent gaps. This overvoltage results from the redistribution of the operating voltage after the breakdown of the first gaps, which is summed up with the trigger voltage. Therefore, the triggering delay time of the switch is short and the jitter is small. 3. The low amplitude of the trigger pulse is ensured because to trigger the switch it is necessary in fact to have a trigger voltage capable of breaking down only one gap. The minimum value of this voltage is determined by the de breakdown voltage of an individual gap. For example, in air at d = 1 00 J..Lm and p = 1 atm, the trigger voltage Vtr = 1 kV is required. To attain low-jitter triggering, it is necessary that Vtr be four or five times greater than the de breakdown voltage Vdc · It is important that the amplitude of the trigger pulse does not increase with increasing the maximum operating voltage. 4. Because ofthe high overvoltage across the gaps, multichannel operation of the switch takes place. It is very important at high voltages, when it is necessary to reduce the inductance of the spark. Four switch samples filled with nitrogen were fabricated and tested by Vorob'ev et al. ( 1 966) who reported data on the operation of switches with 200-J..Lm gaps and N = 30 and 1 5 . The dimensions of the switches were chosen proceeding from the requirement that they should be matched to the energy storage cable 4 and transmission cable 5 (see Fig. 9 . 1 5). The insulating bases 2 and cylinder 9 were made of organic glass and electrodes were made of stainless steel. Wirth an operating voltage V > 1 4 kV and a 5-kV trigger pulse the distortion of the pulse leading edge caused by the nonsimultaneous breakdowns of the last gaps was inappreciable. With a low operating voltage and the same voltage of the trigger pulse the distortion was substantial. It could be eliminated by connecting a capacitor between the last but one electrode and the ground or by increasing gas pressure. No distortion was observed throughout the tenfold range of operating voltages from 4 to 40 kV. When the switches operated at the highest operating voltage, the jitter was about several nanoseconds. 6.3

Spark gaps for parallel connection of capacitors

To make capacitors in high-power capacitor banks connected in parallel, trigatrons and three-electrode spark gaps are generally used. The triggering delay time and jitter of these switches strongly depend on the charge voltage of the bank, making impossible to switch the bank into a load whose

178

Chapter 9

impedance is greater than the wave impedance of the circuit without use of decoupling units. For elimination of these difficulties, it was proposed (Koval'chuk et al. , 1 969; Mesyats, 1 974) to use a multielectrode spark gap with a high ratio of the ground capacitance of the electrodes to the interelectrode capacitance. The electrodes were made as tubes enclosing a coaxial cable. A multielectrode switch has an advantage over a trigatron and a three­ electrode spark gap. Until the breakdown of the last gap in one of the switches takes place, all spark gaps operate separately from each other. After a complete breakdown of one or several spark gaps, the operation of the other spark gaps is in essence possible so long as the voltage across them is not lower than the hold-off voltage of an individual gap. If only one spark gap has operated, the voltage across the load increases, while the voltage across the other spark gaps decreases. Hence, for stable parallel operation of spark gaps, the jitter of their triggering should be much shorter than the time it takes for the load voltage to reach a maximum. In the experiment described by Koval'chuk and Potalitsyn (1974), two spark gaps showed low­ jitter parallel operation into a common inductive load in the voltage range 8-50 kV. The spark gap inductance was �3 · 10-8 H. The triggering delay time at V = 8 and 50 kV was 80 and 1 5 ns with a jitter of 5 and 1 ns, respectively. Baikov et al. (1970) give a description of a high-power current pulse generator with an energy of 40 kJ, an internal inductance of 1 o-8 H, and an operating voltage of 1 0-50 kV in which the above spark gaps were used. The peak short-circuit current was 2.5 MA. The use of the spark gap switches described above made it possible to deliver electrical energy to the load with no decoupling device. This was accomplished with the help of broad busbars constructed in a double line. The generator consisted of 12 capacitors with two spark gaps connected to each of them. Several multielectrode switches were designed for use in the primary energy stores of pulsed power devices based on Marx generators and line pulse transformers (Koval' chuk, 1 997; Corley et al. , 200 I). In the multielectrode switches intended for use in primary energy stores, to provide a uniform distribution of a quasi-static charge voltage over the gaps, a resistive voltage divider is required. This divider should hold off the total voltage (100-200 kV), have a resistance of the order of 109-10 1 0, ensure a lifetime no less than the lifetime of the other components of the switch, and fall within the switch clearance limits. It often appears that such a divider cannot be fabricated of commercially produced resistors. In these cases, a corona discharge is used as a resistive voltage divider (Koval'chuk, 1970). On the intermediate electrodes of the spark gap, needles are placed so that the tips displaying coronas were cathodes. The current of a corona discharge

HIGH-PRESSURE GAS GAPS

1 79

can be controlled by varying the length of the needles, and this current decreases with a decrease in needle length (and electric field at the tips). A corona should be initiated at a rather low voltage across the spark gap to eliminate the probability of self-breakdown. The corona current should be as low as possible, since, as it increases, the self-breakdown voltage of a spark gap decreases. Besides, the electrodes of the spark gaps are tied together with semiconductor rubber cord for providing a uniform potential distribution over all gaps. Figure 9. 1 6 presents a drawing of a 25-kA spark gap switch. High voltage is applied to flanges 1 that hermetically seal the cylindrical caprolon housing of the spark gap 2. Inside the switch, five electrodes 3, each on three spherical seats, are located. Thus, the discharge gap is subdivided into six gaps of length 6 mm. The charge voltage is uniformly distributed over the gaps with the help of a corona discharge. The needles displaying corona discharges are located along the axis of the switch on rods 5 welded to intermediate electrodes and on one (negative) lateral flange. In two-sided charging, the middle intermediate electrode of the switch has a zero potential. Two sleeves are brought to this electrode for bleeding and dumping dry air, and the trigger cable is connected to one of them. For leakproofuess, both sleeves are screwed in the housing with the use of a silicone sealant. The spark gap switch is intended to be operated in transformer oil or SF6 at a pressure of -1.5 atm. 1 59

6

A -A

Figure 9. 16. Spark gap switch with an operating voltage of ± l OO kV and a current of 25 kA : 1 - lateral flange; 2 cylindrical caprolon housing; 3 spark gap electrodes; 4 sleeve for air bleeding and damping, and 5 - rod holder of corona displaying needles -

-

-

1 80

Chapter 9

The switch is triggered by applying a voltage pulse of positive or negative polarity to the middle (trigger) electrode. With a positive trigger pulse, the potential difference across the negative half of the switch increases and it is broken down. In this case, depending on the type of trigger circuit, the potential difference across the second half can be more than doubled because of the presence of the transfer capacitances between the switch electrodes and the ground capacitance of the trigger electrode. The spark gap switch rated at a current of 100 kA is 1 59 mm long and the diameter of its housing is 134 mm; it has, as the 25-kA switch, six gaps of width 6 mm. These spark gap switches were designed for the LTD- 1 00 line pulse transformer. The spark gap switch rated at a current of 350 kA has a length of 230 mm with the housing diameter equal to 1 70 mm; it has eight 6-mm gaps. This switch was designed for Marx generators with two-sided charging. The number of channels that are initiated on the operation of these spark gaps was not specially investigated. After 1000 shots, all electrodes appeared to be uniformly eroded all over the circle, which practically had no effect on the self-breakdown voltage. In all spark gap switches, the electrodes were made of an ordinary stainless steel. �

6.4

Megavolt sequence spark gaps

The idea of sequence spark gaps operating in the mode of multichannel switching has appeared fruitful for megavolt switches connected to the output of intermediate capacitive stores charged pulsewise from a primary store in a time of I J.l.S. Thus, in these spark gap switches, the voltage is distributed over the gaps due to capacitive couplings, and there is no need to use an additional resistive voltage divider. For the first time a megavolt sequence spark gap switch (named Rimfire) with a voltage of up to 6 MV was used at Sandia National Laboratories (Turman et a/. , 1 983; Humphreys et al. , 1985). The triggering of this type switch occurs due to the breakdown of the first gap under the action of laser radiation. This device contains 26 gaps and serves as an intermediate switch to connect a water capacitor charged from a Marx generator and a pulse-forming line. The switch is triggered by the laser breakdown of the first gap, and then the other gaps operate relaywise. Switches of this type are used in the PBF A II and Hermes III systems. To do away with laser triggering, Volkov et al. (1999) proposed to use, instead of the first gap, an additional multielectrode switch (Fig. 9. 17). This concept was embodied in a device that has received the name HYBRID; it is incorporated in the APPRM facility (Sandia). The spark gap switch is subdivided into two halves, which can be conventionally termed as the trigger section and the self-breakdown section. The self-breakdown section �

HIGH-PRESSURE GAS GAPS

181

consists of 25 electrodes of the Rimfire spark gap switch that are separated by 8.4-mm gaps. The triggering section contains six composite electrodes (IHCE) separated by 8-mm gaps. A 4-J..!H inductor connected to the hemispherical electrode of a trigatron unit is also connected to the trigger electrode. The needle of the trigatron is connected to a spherical electrode outside the gas chamber of the switch for connecting the trigger cable. The switch is filled with SF 6 at a pressure of up to 5 atm and is immersed in transformer oil. The leakproofness of the housing is provided by tightening it with nylon rods. Trigger section

Self-breakdown section

Inductor Hemispherical electrode Trigatron ground electrode Figure 9. 1 7. HYBRlD, a 6-MV multielectrode switch

As a trigger pulse is applied to the needle of the trigatron, initiating the operation of the triggering section. Thereafter, an overvoltage wave develops in the self-breakdown section, which, as the next gaps are sequentially broken down, travels, with its amplitude increasing, from the trigger electrode toward the high-voltage electrode of the switch. After the breakdown of all gaps in the self-breakdown section, the charge voltage appears to be applied to the 4-J..!H inductor and, in parallel, to the gaps of the trigger section. The inductor is needed to restrict the rise rate of the current in the trigger gap and to hold the voltage across the gaps of the trigger section until they are broken down. After this breakdown, almost all discharge current flows in the mode of multichannel switching through the gaps of the trigger section. Because of the high overvoltage, multichannel switching occurs through all gaps of the switch. This is the reason for an abrupt decrease in self-inductance of the switch.

1 82

Chapter 9

REFERENCES Baikov, A. P., Iskoldsky, A. M., Koval'chuk, B. M., Mesyats, G. A., and Nesterikhin, Yu. E., 1 970, High-Power Current Pulse Generator, Prib. Tekh. Eksp. 6:8 1 . Bernstein, B. and Smith, 1., 1 973, "Aurora", an Electron Accelerator, IEEE Trans. Nucl. Sci. 20:294-300. Bortnik, I. M., 1988, The Physical Properties and Dilectric Strength of SF6 (in Russian). Energoatomizdat, Moscow. Buttram, M. T. and Sampayan, S., 1 990, Repetitive Spark Gap Switches. In Gas Discharge Closing Switches (G. Schaefer, M. Kristiansen, and A. Guenther, eds.), Plenum Press, New York, pp. 289-324. Cooperstein, G., Condon, J. J., and Boller, J. R., 1 973, The Gamble I Pulsed Electron Beam Generator, J. Vac. Sci. Techno/. 10:96 1 -964. Corley, J., Dixon, M., Johnson, D., Kim, A., Koval'chuk, B., Sinebryukhov, V., Volkov, S., Hodge, K., Degnan, S., Navarro, M., Avrillaund, G., and Lassalle, F., 200 1 , Tests of 6 MV Triggered Switches on APPRM at SNL. In Abstr. XIllth IEEE Intern. Pulsed Power Conf., Las Vegas, CA, pp. (H)4- 1 3 . El'chaninov, A . S., Emelianov, V . G., Koval'chuk, B . M., Mesyats, G . A., and Potalitsyn, Yu. F., 1 975, Methods of Nanosecond Triggeting of Megavolt Switches, Zh. Tekh. Fiz. 45:86-92. Gardner, A. L., 1 953, U.S. Patent No. 2 659 839. Godlove, T. F., 196 1 , Nanosecond Triggering of Air Gaps with Intense Ultraviolet Light, J. Appl. Phys. 2 : 1 589. Harrison, 1., Kolb, A., Miller, R., Shannon, J., and Smith, J. l., 1 974, Compact Electron Beam Generators for Laser and Fusion Research. In Proc. V Symp. on Engineering Probl. of Fusion Research, Washington, DC, pp. 1 1 7- 1 2 1 . Humphreys, D . R., Penn, K . J., Cap, J . S . , Adams, R . G., Seamen, J . F., and Turman, B . N., 1 985, Rimfire: A Six Megavolt Laser-Triggered Gas-Filled Switch for PBFA II. In Proc. Vth IEEE Intern. Pulsed Power Conf, Arlington. Koval'chuk, B. M., 1 997, Multigap Spark Switches, Proc. XIth IEEE Intern. Pulse Power Conf, Baltimore, MD, Vol. 1, pp. 59-67. Koval'chuk, B. M. and Potalitsyn, Yu. F., 1974, Fast Multielectrode Spark Gaps. In Nanosecond High-Power Pulsed Sources of Accelerated Electrons (in Russian, G. A. Mesyats, ed.), Nauka, Novosibirsk, pp. 77-83. Koval'chuk, B. M., Kremnev, V. V., and Potalitsyn, Yu. F., 1 979, Nanosecond High-Current Switches (in Russian). Nauka, Novosibirsk. Koval'chuk, B. M., Mesyats, G. A., and Potalitsyn, Yu. F., 1 969, Multielectrode Spark Gap, Inventor's Certificate of the USSR, No. 243 063 (in Russian), Bull. Izobr. 16:69. Koval'chuk, B. M., Kremnev, V. V., and Mesyats, G. A., l 970a, The Avalanche Discharge in Gas and Generation of Nano- and Subnanosecond High Current Pulses, Dokl. AN SSSR. 191:76-78. Koval'chuk, B. M., Kremnev, V. V., Mesyats, G. A., and Potalytsin, Yu. F., l 970b, Discharge in High Pressure Gas Initiated by Fast Electron Beam In Proc. X ICPIG, Oxford, England, 1971, p. 1 75 . Koval'chuk, B. M., Lavrinovitch, V . A., Mesyats, G . A., Potalytsin, Yu. F., and Toptigin, V. B., 1 977, Investigation of the Switching Characteristic ofthe High-Current Multi-Spark Discharge at the High Pressure in the Gas Mixtures SF6, N2 and Ar, Proc. XIII ICPIG, Berlin, pp. 397-399.

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Kunhardt, E. E., 1 990, Electrical Breakdown in Gases in Electric Fields. In Gas Discharge Closing Switches (G. Schaefer, M. Kristiansen, and A. Guenther, eds.), Plenum Press, New York, pp. 15-44. Lavoie, L., Parker, Sh., Rey, Ch., and Schwartz, D. M., 1 964, Spark Chamber Pulsing System, Rev. Sci. Instrum. 35: 1 567- 1 5 7 1 . Markins, D . , Command Triggering o f Synchronized Megavolt Pulse Generators, 1 97 1 , IEEE Trans. Nucl. Sci. 18 (Pt 2):296-302. Martin, T. H., 1 973, The "Hydra" Electron Beam Generator, IEEE Trans. Nucl. Sci. 20:283-293. Meek, J. M. and Craggs, J. D., 1 953, Electrical Breakdown of Gases. Clarendon Press, Oxford. Mercer, S., Smith, 1., and Martin, T., 1 976, A Compact, Multiple Channel 3 MV Gas Switch, Energy Storage, Compression, and Switching: Proc. 1st Intern. Conf on Energy Storage, Compression and Switching (Nov. 5-7, 1974) (W. H. Bostick, ed.), Plenum Press, New York-London, pp. 459-462. Mesyats, G. A., 1 960, Delay of the Breakdown of a Spark Gap at High Overvoltages, Izv. Vyssh. Uchebn. Zaved. , Fiz. 4:229-23 1 . Mesyats, G . A., 1 974, Generation of High-Power Nanosecond Pulses (in Russian). Sov. Radio, Moscow. Mesyats, G. A., 1 982, High-Power Injection Switches. In Injection Gas Electronics (in Russian, 0. B. Evdokimov, ed.), Nauka, Novosibirsk. Moriarty, J. J., Milde, H. 1., Bettis, I. R., and Guenther, A. H., 1 97 1 , Precise Laser Initiated Closure of Multimegavolt Spark Gaps, Rev. Sci. Instrum. 42: 1 767-1776. Nunnally, W. C., and Donaldson, A. L., 1 990, Self Breakdown Gaps. In Gas Discharge Closing Switches (G. Schaefer, M. Kristiansen, and A. Guenther, eds.), Plenum Press, New York, pp. 47-62. Pendleton, W. K. and Guenther, A. H., 1 965, Investigation of a Laser-Triggered Spark Gap, Rev. Sci. Instrum. 36: 1 546-1 550. Raizer, Yu. P., 1 965, Laser-Initiated Breakdown and Heating of Gas, Usp. Fiz. Nauk. 87:29. Raizer, Yu. P., 1 974, The Laser Spark and Propagation of Discharges (in Russian). Nauka, Moscow. Schrank, G., Henry, G., Kerns, Q. A., and Swanson, R. A., 1 964, Spark-Gap Trigger System, Rev. Sci. Instrum. 35: 1 326-1 33 1 . Shkuropat, P . I, 1 969, Investigation of Predischarge Processes in Trigatrons Operating in Air, Zh. Tekh. Fiz. 39: 1256-1263. Siegbahn K., ed., 1 965, Alpha-, Beta- and Gamma-Ray Spectroscopy. Amsterdam. Stekol'nikov, I . S., 1 949, The Pulsed Oscilloscope and Its Application (in Russian). USSR AS Publishers, Moscow-Leningrad. Stolen, S., 1 969, Breakdown Induced by Transient U.V. Irradiation, Proc. IX ICPIG, Bucharest, Romania, p. 259. Theophanis, G. A., 1 960, Nanosecond Triggering of High Voltage Spark Gaps, Rev. Sci. Instrum. 31:427-432. Turman, B. N., Moore, W. B. S., Seamen, J. F., Morgan, F., Penn, J., and Humphreys, D. R., 1 983, Development Tests of a 6 MV, Multistage Gas Switch for PBFA II, Proc. IVth IEEE Intern. Pulsed Power Conf, Albuquerque, NM. Usov, Yu. P., 1 964, Spark Triggering of Spark Gaps in Gases at Different Pressures. In Breakdown ofDielectrics and Semiconductors (in Russian, A. A. Vorob'ev, ed.), Energia, Moscow-Leningrad, pp. 79-82. Vitkovitsky, 1., 1 987, High Power Switching. Van Nostrand Reinhold Company, New York.

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Volkov, S. I., Kim, A. A., Koval'chuk, B. M., Kremnev, V. V., and Sinebryukhov, V. A., 1 999, Multichannel Closing Spark Gap Switch for Water Energy Stores, Jzv. Vyssh. Uchebn. Zaved., Fiz. 12:91 -99. Vorob'ev, G. A., 1 959, Device for Production of Short Rise Time Pulses. USSR Inventor's Certificate, No. 120 876 (in Russian), Byull. Jzobr. 1 3 . Vorob'ev, G . A . and Mesyats, G . A., 1 963, Techniques for the Formation of Nanosecond High- Voltage Pulses (in Russian). Gosatomizdat, Moscow. Vorob'ev, P. A., Mesyats, G. A., and Potalitsyn, Yu. F., 1 966, New Triggered Nanosecond High-Power Switch, Zh. Tekh. Fiz. 36: 1492-1 498. Williams, P. F. and Guenther, A. H., 1 990, Laser Triggering of Gas Filled Spark Gaps. In Gas Discharge Closing Switches (G. Schaefer, M. Kristiansen, and A. Guenther, eds.), Plenum Press, New York, pp. 145-1 87. Zhiltsov, V. P. and Slutskin, E. Kh., 1 963, The Multichamber Component of a Circuit Connecting Strobotrons in High-Speed Photography, Prib. Tekh. Eksper. 4: 1 32.

Chapter 1 0 LOW-PRESSURE SPARK GAPS

1.

VACUUM SPARK GAPS

Based on the data on the mechanism of discharges in vacuum (see Chapter 3), it can be concluded that for two-electrode vacuum spark gaps the switching time is determined by the cathode-anode gap spacing, d, and the velocity of motion of the cathode plasma, ve: ts ;::: dive. Hence, the average current rise rate is dlldt = Ia Veld , where Ia is the peak current in the spark gap. Since we have Ve ;::: 2· 1 06 cm/s, to obtain the time fs ;::: 1 o-9 s, it is necessary to have d = 20 J.lm. In fact, the gap spacing should be a little greater since the anode plasma will move toward the cathode plasma with a velocity of -106 cm/s. In small gaps, this plasma appears practically simultaneously with the cathode one due to the intense heating of the anode by the current of explosive electron emission. The delay time of triggering of this type of switch, td, is determined by the density of the current of field emission (FE), j, from cathode microprotrusions: td = hIf , where h is the specific current action during the FE-current-induced explosion of a microprotrusion. The current density strongly depends on the average electric field at the cathode, E. According to the Fowler-Nordheim formula (3. 1 ), we have j = AoE2 e - BoiE , where A0 and B0 are constants depending on the work function of the metal,
1 86

Chapter 1 0

the switching time 15 decreases and does not depend any more on gap spacing. Let there be a cylindrical dielectric disk of height h and diameter Dd resting on a plane anode of same diameter and a cathode of diameter De « Dd be put on this disk. Then the plasma that appears at the cathode will start moving toward the anode only as it arrives at the edge of the dielectric. Therefore, the switching time 15 will be determined by the properties of the discharge over the end face of the dielectric and will be � 1 o-9 s (Bugaev and Mesyats, 1 966; Mesyats, 1 974). Second, the delay time of triggering of the spark gap will be stabilized, since at the cathode-dielectric contact there are metal-dielectric-vacuum triple junctions, which, as shown above, provide a much more stable time of the discharge occurrence. Finally, the voltage pulse amplitude at which the discharge is initiated becomes considerably lower. Thus, a way of triggering a vacuum spark gap is to increase the electric field, as in a gas-filled spark gap. Therefore, triggered vacuum spark gaps can have two electrodes, three electrodes or a sequence of many electrodes. Besides, there are vacuum spark gaps triggered by plasma, a laser beam, an electron beam, etc. However, as shown above (see Chapter 3), the key point of all these methods is the creation of plasma at the cathode and its interaction with the cathode surface. The simplest mechanism of a plasma­ initiated vacuum breakdown is the charging of dielectric films and inclusions by plasma ions, followed by breakdown of them. Many types of cathode-plasma-triggered vacuum spark gap are known. For example, Brish et al. ( 1 958) developed miniature vacuum spark gaps of the vacuum spark relay (VSR) type. In these spark gaps, the breakdown of the main gap is initiated by an auxiliary discharge over the surface of mica that separates the electrodes of the trigger gap. The use of this insulating layer allows one to lower the breakdown voltage of the trigger gap and thus reduce the amplitude of the trigger pulse. Spark gaps of the vacuum relay type have a broad range of operating voltages. For example, the VSR-7 device reliably operates with the operating voltage varied from 1 0 kV to 1 00 V. The delay time and jitter of triggering of a spark gap depend on the design and on the rise rate of the triggering pulsed voltage. The coaxial design appeared to be the best one (Fig. I 0. 1 ). With a triggering pulse amplitude of 2.2 kV and voltage rise rate of 225 kV/J..ts, the triggering delay time for this type of spark gap is about 3 · 1 o-8 s with a jitter of less than 1 · 1 o-8 s. Several types of triggered vacuum spark gaps were described by Hagerman and Williams ( 1 959) and Mather and Williams ( 1 960). Hagerman and Williams ( 1 959) used nine series-connected gaps formed by bronze washers with a hole in the middle, which were insulated from each other by Teflon rings. Plasma was created by a discharge over the surface of glass that was initiated by a triggering voltage. This plasma penetrated through the holes and initiated a discharge in all nine gaps. A spark gap of this type is

LOW-PRESSURE SPARK GAPS

1 87

capable of switching a current of 1 MA with a delay of 1 .5 J.lS. Wilson et al. (1983) used a plasma source with a discharge over the surface of BaTi03 in a trigatron-type system. To trigger this type of spark gap, it suffices to have a voltage pulse of amplitude not above 1 kV. A

Figure 10. 1. Design of a triggered vacuum spark gap: A - anode, C - cathode, T - trigger electrode, and D - dielectric lining (mica)

An important place among vacuum spark gaps is occupied by devices with liquid mercury cathodes, which are called ignitrons. With a charge of about 1 C passed in a pulse, they have a lifetime 2-3 orders of magnitude longer than vacuum spark gaps with a cold solid cathode. The mercury cathode, being self-recovering and not prone to erosion, is responsible for both the unique qualities of the spark gaps (record-braking service life at a switched charge of up to several hundreds of coulombs and currents of up to 500 kA) and their serious disadvantages such as the small range of operating temperatures, the restriction in spatial orientation of the spark gap, the impossibility of operation in mobile systems and in conditions of weightlessness, the rather low reliability of the device, and, finally, the toxicity ofmercury. A number of laser-triggered vacuum spark gaps were investigated (Slivkov, 1 986). A laser beam focused on the cathode created plasma that, as in the previous cases, initiated EEE and a vacuum discharge. For the range of operating voltages 5-50 kV, the breakdown delay time varied within the limits 1 2- 1 5 ns (Kovalenko et al. , 1 974). Makarevich and Rodichkin (1973) investigated a spark gap with d = 5 mm. As the vacuum was changed from 2 · 10-3 to 3 · 1 0-6 mm Hg, they noticed no difference in time characteristics of the spark gap. The discharge delay time was 7-9 ns. When a laser pulse acted on the cathode (A. = 0.69 J.lm, fp = 30 ns, d = 1 .2 em, V = 8 kV), the switching time did not vary as the energy density at the cathode was varied from 0. 1 to 1 .5 J/cm2 and was -45 ns (Slivkov, 1 986). As this took place, the delay time td decreased from 1 20 to 50 ns. The ratio d/t5 was about 2. 7 · 1 06 crn!s. This is somewhat greater than the velocity of expansion of the cathode plasma, which is related to the counterdirected motion of the anode plasma. With a laser beam acting on the anode, the threshold energy density

1 88

Chapter 1 0

at which a vacuum discharge was initiated increased by more than an order of magnitude, and the time t5 decreased substantially (by almost two orders of magnitude), being 0.8 ns for a gap of 0.5 mm and a voltage of 1 5 kV. A more detailed discussion of the mechanism of the laser triggering of vacuum spark gaps is given in the monographs by Slivkov (1986) and Mesyats (2000) and in the review by Thompson (1 990).

2.

PULSED HYDROGEN THYRATRONS

The classical pulsed hydrogen thyratron (PHT) is a triggered gas-filled hot-cathode device operating in the pressure range approximately 10-50 Pa, which corresponds to the left branch of Paschen's curve (Fortov, 2000). A schematic diagram of a device with a glass envelope is given in Fig. 1 0.2. Its main structural elements are anode 2, a grid disk with holes 3, and a hot cathode, which is usually made hollow (in this case, the internal surface of cylinder 6 serves as a cathode emitting surface). In the initial state, a positive high voltage is applied to the anode, and the grid is connected to the cathode through a resistor of resistance about 1 kQ. As a result, the grid and the cathode appear at the same potential and the fall voltage is localized between the anode and the grid, the distance between which is typically d = 3-4 mm The grid meshes have a size comparable to d and the grid thickness is chosen such that the anode is screened from the cathode-grid chamber. In addition, a screening disk 4, usually connected to the grid, is used. As a whole, the measures described prevent the electron flow from coming through the holes in the main gap of the device and exclude occasional initiation of a discharge in the main gap. The grid and the screen completely cover both the cathode and the anode disk, so that the electric strength of the device is determined by the anode­ grid gap. The thyratron is triggered by applying a voltage pulse of positive polarity to the grid-cathode gap. Since the gap spacing is chosen rather large to facilitate the discharge ignition and there are a great number of initiating electrons from the hot cathode in the gap, a discharge with the current determined by the trigger circuit develops in a time less than 1 00 ns. It is important that the electrode system consists of a hot hollow cathode and a hollow anode, and a discharge with a negative anode fall potential operates in this system. The discharge plasma fills the anode cavity and penetrates into the slit between screen 4 and grid disk 3 as well as in the grid holes. In fact, at this stage the trigger disk 3 behaves as a plasma cathode in relation to the main gap. The electron flow is extracted from the grid meshes into the main gap, initiating a discharge in the main gap. .

LOW-PRESSURE SPARK GAPS

1 89 1

anode lead, 2 Figure 10.2. Schematic drawing of a glass-envelope pulse thyratron. 1 anode, 3 - grid disk, 4 - screening disk, 5 - top screen of the cathode, 6 - emitting surface of the cathode, 7 - heater, 8 - thermal screen of the cathode, and 9 - screen -

The range of working pressures in a thyratron corresponds to the conditions under which the mean free path of an electron capable of participating in the reaction of ionization is greater than d. Nevertheless, the gas medium plays an important part in the discharge initiation and sustaining. This is an intermediate case between a "pure" vacuum discharge and a classical gas discharge, in which the mechanism of breakdown is related to the development of electron avalanches initiated by single electrons. For the development of a cathode-initiated breakdown, a substantial initial electron current close to the limiting electron current of the vacuum diode is necessary. The idea of the mechanism of breakdown under these conditions was proposed by Langmuir. For these conditions, an important notion is the so-called critical concentration of neutrals, ncr (or the critical gas pressure Per), in the gap, given by

n

cr

=

1 (3m) 2 M

1 __ '

( 1 0. 1 )

cr-d l

ml

where cri is the average cross section for ionization of neutrals under the action of the electron beam starting from the cathode and M is the electron-to-ion mass ratio.

1 90

Chapter 1 0

The average number of ionization events induced by an individual electron in a gap is ncrcrid « 1 . If the concentration of neutrals na < ncr. a gas discharge cannot be initiated, and the main gap will behave as a vacuum electron diode with ion neutralization. For the conditions that take place in a thyratron, na < ncr. and the main contribution to the discharge development is from the excessive space charge of positive ions that builds up in the gap in due course. This occurs because some electrons from the total flow participate in the reaction of ionization, and the time it takes for ions to leave the gap, ti, it is much longer than that for electrons. Then the electric field in the gap is distorted so that the potential distribution becomes nonmonotonic. Near the anode, a potential hump region arises which is a trap for electrons. Due to the oscillating motion of electrons in this region (similar to the electron oscillations in a glow-discharge hollow cathode), efficient generation of plasma in the near-anode region is provided and the plasma front propagates toward the cathode (grid). The characteristic time of occurrence of a potential hump region is of the same order as ti (Korolev and Frank, 1 999). As the plasma front approaches the grid, a pulsed potential appears at the grid, since the potential of the anode is transferred to the main gap during the propagation of the ionization front. Then plasma is generated in the grid holes, a high-current discharge develops in the grid-cathode gap, and the switching process is complete. A high-current discharge with a low fall voltage between the cathode and the anode can be classified as an arc with a hot hollow cathode. Here, the grid appears under a near-floating potential. This implies that there is a non-neutralized space charge of positive ions near the internal surface of the grid holes, providing the existence of a negative fall potential region of length I « D, where D is the hole size. The negative fall potential V and the length I are self-consistently established so that the chaotic electron current from the plasma, overcoming the potential barrier e V, is equal to the current of the ions generated in the region of meshes (the total current onto the grid is close to zero). For a thyratron to be capable of operating with high pulse repetition rates, fast deionization of the gas in the anode-grid and grid-cathode gaps during the pulse interval is necessary. In modem high-current devices, the degree of ionization of the fill gas makes up 1 0% (the plasma density -10 1 5 cm-3 ). At the initial stages, the deionization is caused by recombination. As the plasma density decreases, the ambipolar diffusion of charged particles to the walls and their outgoing under the action of the electric field become significant. In this connection, to reduce the deionization time, it is recommended to use electric circuits providing a low (a few hundreds of volts) fall voltage between the grid and the cathode and between the grid and the anode. For this purpose, additional electrodes are sometimes used which promote charge dispersal at the late stages of plasma decay.

LOW-PRESSURE SPARK GAPS

191

Triggered thyratrons have been known since the 1 920s. These devices were filled with gases of low ionization potential (Ar, Kr, Xe) or mercury. The cathode was poorly screened from the anode-grid chamber, and triggering occurred as the negative potential of the grid decreased, i.e., this type of thyratron was a potential-triggered device. Hot-cathode thyratrons were used in low-frequency rectifying and inverter circuits, while cold­ cathode thyratrons served as low-power amplifiers, indicators, and switches in logic circuits. However, their production was stopped once more reliable and long-living solid-state devices, such as light-emitting diodes, transistors, and thyristors had appeared. The development of pulsed hydrogen thyratrons, using hydrogen or deuterium as a fill gas, and the beginning of their industrial production were related to the development of radar location where they served as modulators of microwaves in magnetrons. The strong screening of the cathode from the high voltage of the anode has the result that a thyratron opens only if plasma of sufficiently high density appears in the cathode-grid chamber, and therefore PHT's can be characterized as current-triggered devices. A hydrogen thyratron is placed in an envelope made of borosilicate glass or alumoxide ceramic which is tightly soldered to the metal electrodes and leads. Cermet materials provide better cooling conditions for the electrodes, significantly higher operating voltages, and greater mechanical durability at much smaller dimensions in comparison with other materials. The soldered joint (vacuum-dielectric-metal triple junction) is the key element of the envelope. In this junction, the electric field is enhanced and the probability of emission and discharge initiation at this place is high. Therefore, either the junction is protected with a screen or the electrodes are designed so that the electric field at the soldered joint is reduced. The dielectric strength of the internal surface of the envelope, which is in vacuum, is higher than that of the external one, which frequently is in atmospheric conditions. In this connection, the length of the envelope is determined by the surrounding medium and by the range of operating voltages. PHT's with anode voltages of up to 25 kV are designed for the operation in open air. Devices with anode voltages over 50 kV operate for the most part in transformer oil having high dielectric strength, which makes it possible to reduce the device dimensions and mass. A well-conditioned high-voltage gap in a thyratron can hold off a voltage of up to 40 kV. However, its electric strength decreases in prolonged operation. Therefore, the warranty is usually given only for a voltage of 30-35 kV at most. To increase the operating voltage of a PHT, sectioning is employed. The number of sections (graded electrodes) in modern cermet PHT's reaches eight, allowing one to operate them at voltages over 200 kV.

1 92

Chapter 1 0

One of the basic elements of a PHT is the cathode assembly. It consists of a hot cathode and a high-temperature heater. Most commonly used in PHT's are oxide cathodes, which are very economical and provide a current density of up to 20 A/cm2• In high-power PHT's, dispenser cathodes are often used which consist of a metal matrix (W or W-Mo), in which pores and on which surface there is an active substance based on various oxides having high thermoemissive properties. The temperatures of the cathodes of PHT's range between 700 and 1 000°C. The lifetime of the cathode is limited by the evaporation of the active substance, destruction of the surface by ion bombardment, and poisoning with gases released from the electrodes. The service life is strongly affected by the fluctuations in cathode temperature (e.g., on varying the heating power) and by the reduction of the hydrogen pressure, resulting in substantial power losses in the discharge. The high mobility of hydrogen ions ensures a short deionization time, and due to the low mass of the ions, the damage to the cathode by a discharge is not as pronounced as in other gases. The choice of hydrogen makes these devices capable of operating at high frequencies, and the up-to­ date design features make it possible to have its stock in special heated reservoirs (hydrogen generators) and fill up its natural loss due to absorption by the electrode materials. The grid in a PHT plays the role of a trigger and high-voltage electrode and must provide both the passage of high-density current through the holes and its reliable cutoff in pulse intervals. The grid temperature strongly affects the electric strength of a PHT. This effect is strengthened by the active substance deposited during the operation of the hot cathode and by the dielectric evaporated in the interaction of the arc discharge with the envelope and deposited on the grid surface. In this connection, the temperature of the grid should be limited to a level of 300-400°C by moderating the mode of operation or by forced cooling. In PHT's of improved design, an additional grid is used, which is located near the cathode. This allows one to reduce energy losses and to shorten td and 11td. A de or pulsed voltage is applied to this grid (in advance of the pulse that triggers the other grid). The direct current of the preparatory discharge, which lies in the range 1 0-1 00 rnA, reduces the delay time to 1 00 ns and jitter to 1 ns. When the first grid is powered by a pulsed current of up to 1 00 A, a CX1 599 thyratron (EEV, England) provides ultrafast switching within several nanoseconds. Conventional thyratrons have the properties of rectifying elements. In some cases, for example, where oscillating currents are used, reversible conductivity is required. Such conductivity can be realized by connecting in series the anodes of two thyratrons. In a reversible PHT, there are cathodes on both sides of the

LOW-PRESSURE SPARK GAPS

1 93

device, which is more convenient than the use of two thyratrons. The same purposes are served by hollow-anode PHT's in which the anode, on fast application of a reverse voltage, operates as cathode, and a discharge arises from the residual plasma. These devices are cheaper than reversible PHT's. They are used in the power supplies of high-power lasers. A thyratron designed for operation at frequencies of tens of kilohertz, for example, in power supply circuits of metal-vapor lasers, must recover its electric strength within several microseconds. In the anode-grid chamber, due to its small volume, large electrode surfaces, and some potential difference between the electrodes, deionization is finished earlier than in the cathode-grid chamber. Therefore, the recovery characteristics of this type of PHT are determined by the plasma decay in the volume between the cathode and the grid, which is much greater than that of the anode-grid chamber. On the other hand, the highest attainable operating frequency also depends on the electrode temperature, which increases with frequency and power losses. To speed up deionization, a negative bias voltage of 50-100 V is applied to the grid, and to reduce the electrodes temperature, intense cooling is used. In conventional thyratrons, the maximum operating frequency is limited to 1 0 kHz. To increase the operating frequency, the modem PHT's are designed as tetrodes or penthodes. The design of a thyratron with three closely spaced grids isolated from each other and good heat removal to the environment enables switching of pulsed powers of up to 12.5 MW at a frequency of up to 80 kHz. In the space between the grids, being under different potentials, the plasma quickly decays, providing recovery of the insulating properties of the gap within 3 J..I.S. Table 1 0. 1 gives the characteristics of pulse thyratrons commercially produced in Russia. The first three types are glass-envelope devices and the other three cermet-envelope ones. As can be seen from the table, the self­ inductance of the high-power pulse hydrogen thyratrons rated at voltages of some tens of kilovolts and currents of up to a few kiloamperes is about 0.3 J.!H. For a pulse-forming device with a low internal resistance, Z0 � 1 0 Q, the time constant of current rise, LIZ0, is large and this is why high-power thyratrons are inapplicable for the production of nanosecond high-voltage pulses. At the same time, in contrast to other gas-discharge devices, thyratrons have a number of extremely valuable qualities such as high reliability, simplicity of triggering, high pulse repetition rate, etc. In addition, several thyratron can be operated both in parallel and in series. To shorten the pulse rise time of hydrogen thyratrons, nonlinear inductors, such as ferrites, are used. This will be discussed in detail below.

Chapter 1 0

1 94 Table 10. 1. Thyratron type Parameters

TGI-1 400/1 6

TGI-1 700/25

TGI-1 2500/35

TGI-1 1000/25

TGI- 1 3000/50

TGI-1 500/16

Pulsed anode current in the nominal mode, A

400

700

2500

1 000

3000

500

Pulsed anode current in the nominal mode at tp = 1 00 ns

1 03

2 · 1 03

7·103

3·103

1 0· 103

1 03

4

0.5

Average anode current, A

0.5

1 .0

2.5

Pulse repetition rate, Hz

450

500

250

700

Peak anode voltage, kV

16

25

35

25

50

Heat current, A

11

20

55

20

87

Peak reverse voltage, kV

5

5

5

5

Average output power, kW

4

25

43

25

Discharge ignition j itter in the nominal mode, ns

±1

±1

±4

±1

Pulse rise time in the nominal mode at a 6.3-V heat voltage, ns

20

25

35

Minimum pulse rise time at Vheat = 6.3 V, ns

12

15

Thyratron inductance, �-tH

0. 1 5

0.35

1 03 16 15 3.2 250

8

20

25

15

24

15

15

10

0.7

0.2

0.3

0. 12

Table I 0.2. Characteristics of cermet-enveloEe th�ratrons Thyratron type

Peak voltage, kV

Peak current, A

Average power, kW

7621

8

1 00

4

86 13

16

500

8

7322

25

1 500

25

7390

33

2000

66

7890

40

2400

52

8479

50

5000

1 00

HY-7

40

40 000

1 000

The characteristics of some cermet-envelope thyratrons developed in the United States (Creedon, 1 990) are given in Table 1 0.2. The characteristics of last one refer to a burst mode: 30 s on and 1 0 min off. Recent theoretical results and experimental data on hydrogen thyratrons can be found in a review by Penetrante and Kunhardt ( 1 990).

LOW-PRESSURE SPARK GAPS 3.

1 95

PSEUDOSPARK GAPS

Pseudospark gaps (PSG's) are low-pressure spark gaps which, like thyratrons, operate on the left branch of Paschen' s curve for which the mean free path of an electron is greater than the electrode separation: A. > d. They are also similar to thyratrons by design and breakdown mechanism. The distinguishing feature of a PGS is the use of a cold hollow cathode inside which the trigger unit is placed. When comparing the thyratron design in Fig. 10.2 and the design of a typical pseudospark gap, one can conclude that the role of hollow cathode in a PGS is played by a grid onto which the total current closes, while the cathode unit is used only to initiate the discharge. In this connection, the PGS is sometimes referred to as a grounded-grid thyratron. Various designs of such a spark gap have the following characteristics: the current rise rate dlldt � 1 0 12 A/s, peak voltage up to 200 kA, pulse repetition rate up to 1 02-104 Hz, and triggering delay time about 100 ns with a jitter of several nanoseconds. The number of pulses that such spark gaps withstand without failure is sometimes over 1 08• The discharge initiation in such a device is generally reduced to the production of plasma in the cathode region. This gives rise to the ignition of a cold-cathode dense pulsed glow discharge. The characteristics of this type of discharge were investigated by Klyarfeld and co-workers (Abramovich et a/., 1 966). As the current rises, a dense glow discharge transforms into a so-called superdense glow discharge and then into an arc with constricted current attachment in the cathode spot. The mechanism of breakdown in the electrode system of a pseudospark gap is described in detail in a review by Korolev and Frank (1999). Lobov et a/. ( 1960) were among the first developers of spark gaps of this type. The arrangement of the electrodes in a pseudospark gap is shown schematically in Fig. 1 0.3. The gas pressure and electrode separations are established so that the breakdown voltage of the main discharge gap A-C correspond to the left branch of Paschen's curve and the voltage across the trigger gap A-T be nearly its minimum. Before the arrival of the trigger pulse, an "on-duty" discharge with a current of 1 0 J..LA operates between the trigger electrode T and cathode C. As a negative trigger pulse arrives at electrode T, the gap T-C is broken down. As this takes place, electrons pass through the hole H in the cathode and move directly toward to the anode, initiating the main discharge between anode A and cathode C. Such spark gaps operate in the voltage range 2-10 kV with a trigger pulse of amplitude 2 kV and current rise rate 10 1 0 A/s. The triggering delay time is 20-40 ns and the operating current is up to 5 kA. In modern pseudospark gaps, the initiating plasma is produced by various methods such as ultraviolet irradiation of the cathode cavity, a surface

1 96

Chapter 1 0

dielectric discharge, and an auxiliary glow discharge similar to that described by Lobov et a/. (1960). Important contribution to the development of modern pseudospark gaps has been made by Christiansen and Schultheiss ( 1979), Mechtersheimer et a/. (1986), Kirkman and Gundersen (1986), Gundersen and Schaefer ( 1989), and Bochkov et a/. (2001 ).

Figure 10.3. Design of a low-pressure spark gap. trigger electrode

A -

anode, C - cathode, H - hole, T ­

Figure 10. 4. Schematic diagram of a pseudospark chamber

The electrode geometry of such a discharge is shown in Fig. I 0.4. This type of hollow-cathode and hollow-anode discharge is used in high-current repetitive switches, which surpass thyratrons in performance, and in electron sources. This type of discharge is of special interest due to the mechanism of emission that provides an average current density of �104 A/cm2 • The principal characteristics of pseudosparks are as follows: The mean free path of electrons in the electrode gap is greater than the gap spacing: f... > d. After the ignition of a discharge in the hollow cathode, the discharge plasma penetrates into the region of the hole, and an electron beam with a current of 1 0-1 00 A is formed. At this stage there occur desorption of the gas from the surface and its ionization, and the gas density in the hole region reaches 1 0 1 6 cm-3 • In Fig. 1 0.5, a pseudospark gap is shown in which an auxiliary glow discharge is used. The discharge operates in the system of electrodes 8 and 9. The distance between the electrodes is chosen large enough to provide the ignition of a discharge at voltages of 1-2 kW corresponding to the left branch of Paschen's curve. As a voltage pulse is applied to the electrode 9,

LOW-PRESSURE SPARK GAPS

1 97

there occurs an amplification of the current between the electrodes 8 and 9 and, besides, a discharge is ignited over a long path between the electrode 9 and the cathode cavity of electrode 4. Thus, plasma appears in the cavity beneath the electrode 4, and electrons are extracted into the main discharge gap, initiating the breakdown of this gap. Trigger systems of this type make it possible to achieve pulse repetition rates of up to 1 00 kHz. However, their disadvantage is that an auxiliary glow discharge permanently operates in the device.

Figure 10.5. Schematic of a two-electrode pseudospark switch triggered by a pulsed glow discharge. The complex design of the electrodes is necessary to prevent metallization of the insulator by the sputtered material of the electrodes (1, 2, 3 anode; 4, 5 - cathode; 6 hollow cathode; 7 - blocking electrode; 8, 9 - trigger electrodes) -

The geometry of a modem pseudospark gap with ultraviolet illumination is given in Fig. 1 0.6. The spark gap has a hollow cathode and a hollow anode. The ultraviolet radiation ignites a discharge in the hollow cathode. The plasma of this discharge penetrates into the region of the cathode hole. The diameter of the glow channel is approximately equal to the hole diameter. A high-current discharge with a current density of 1 04 A/cm2 is formed when the plasma glow, expanding with a velocity of 1 08 cm/s, fills the electrode gap. The discharge voltage decreases to several hundreds of volts. It is localized within a layer of thickness 1 0-4 em and creates a field of strength E = ( 1 -5) · 1 06 V/cm at the cathode (Christiansen, 1 989; Kirkman­ Amemija et al. , 1 989; Hartman and Gundersen, 1 989).

1 98

Chapter 1 0 5

1

2

Figure 10. 6. Triggered pseudospark gap. 1 - cathode, 2 - anode, 3 - triggering ultraviolet lamp, 4 - glass case, 5 - gas supply, 6 - quartz window

The cathode microrelief resulting from the operation of pseudosparks is similar to that formed under the action of an arc discharge. The erosion rate, measured by Christiansen (1989), is � 1 0-5 g/C, which is typical of an arc discharge [(5-8)- 1 0-5 g/C for a molybdenum cathode]. Taking into account the character of cathode erosion, one can suggest that the high average current density of a pseudospark is provided by explosive emission of electrons. The studies of the physical processes of initiation and development of a vacuum breakdown and the mechanism of emission in the cathode spot of a vacuum arc and in a volume gas discharge, considered above, have made it possible to establish a number of relationships which prove that the phenomenon underlying the mechanism of operation of a pseudospark is explosive electron emission (Mesyats and Puchkarev, 1 992). The erosion traces, as in a vacuum discharge, are microcraters produced by individual microexplosions. Let us proceed from the estimates that the average current density �104 Ncm2 in a pseudospark is provided by �103 ectons, each carrying a current of �10 A. The current density in an ecton can reach 1 08 Ncm2 • Ectons may appear within a time td, provided thatftd = const. For an initial current of �109 Ncm2 , the value of td lies in the nanosecond range. It has been shown (Mesyats, 2000) that for a molybdenum cathode conditioned in high vacuum, at an average electric field at the cathode E > 2 · 1 06 V/cm, td < 1 0 ns. The field created by a volume discharge at the initial stage of formation of a pseudospark is of the same order of magnitude, and, hence, there are conditions for the formation of an ecton within t < 10 ns. It is important to note that one or several ectons are not able to shunt the layer and, hence, the voltage across the layer does not change. The number of ectons increases until the total current causes a redistribution of the voltage between the current source and the diode. The situation is similar to that with the formation of a high-current volume discharge in gas for which

LOW-PRESSURE SPARK GAPS

199

it was also noticed that the cathode spot appears as the field in the near­ cathode layer reaches E > (1-2) · 1 06 V/cm. The subsequent transition of the discharge into a constricted spark depends on Elp and, for the conditions of a pseudospark, it is hampered by the low pressure in the electrode gap and by the great number of simultaneously appearing ectons. Kirkman-Amemija et a/. (1 989) observed the occurrence of ectons at the cathode of a BL T switch and a constricted spark during some first operations of the switch. Subsequently, as the electrodes were conditioned by discharges, sparks disappeared and the discharge went into a diffuse stage. Based on this observation, the authors have concluded that there was a so­ called superemission. This effect can be explained as follows (Mesyats and Puchkarev, 1 992): In first operations of a spark gap with fresh electrodes, the electric field in the gap is E � 105 V/cm. The field at the cathode is enhanced many times and this results in field emission followed by explosive electron emission. The discharge develops, like a vacuum discharge, from individual cathode microregions. In the course of conditioning, the electric strength increases and, as soon as bulk ionization begins in the electrode gap and the field becomes localized in a thin near-cathode layer within 1 ns, conditions are created for spontaneous occurrence of explosive electron emission followed by the formation of ectons over a large area. Since the current of one ecton seems to be not over 10 A and the plasma in an ecton is completely ionized and radiates in the ultraviolet region with the spot size being less than 0. 1 mm, these cathode spots are imperceptible on the background of the bulk luminescence. The statement that the so-called superemission in pseudosparks is explosive electron emission is confirmed by the results of experiments on electrode erosion. The electrode erosion is more pronounced in that place where the electric field is a maximum, i.e., on the edge ofthe hollow cathode. REFERENCES Abramovich, L. J., Klyarfeld, B. N., and Nastich, Yu. N., 1 966, A Superdense Glow Discharge with a Hollow Cathode, Zh. Tekh. Fiz. 36:7 14-7 19. Bochkov, V. D., Dyagilev, V. M., Ushich, V. G., Frants, 0. B., Korolev, Yu. D., Shemyakin, I. A., and Frank, K., 200 1 , Sealed-off Pseudospark Switches for Pulsed Power Applications (Current Status and Prospects), IEEE Trans. Plasma Sci. 29:802-808. Brish, A. A., Dmitriev, A. B., Kosmarsky, L. N., Sachkov, Yu. N., Sbitnev, E. A., Heifets, A. B., Tsitsiashvili, S. S., Eig, L. S., 1958, Vacuum Spark Relays, Prib. Tekh. Eksp. 5:53-58. Bugaev, S. P. and Mesyats, G. A., 1 966, A Spark Peaker. USSR Inventor's Certificate No. 1 86 033 (October, 1964). Christiansen, J., 1989, The Properties ofthe Pseudospark Discharge. In Physics andApplications of Pseudosparks ( M. A. Gundersen and G. Schaefer, eds.), Plenum Press, New York, pp. 1-13.

200

Chapter 1 0

Christiansen, J . and Schultheiss, C., 1 979, Production o f High Current Particle Beam by Low Pressure Spark Discharges, Z. fUr Physik. A. 290:30. Creedon, J., 1 990, Design Principles and Operation Characteristics of Thyratrons. In Gas Discharge Closing Switches (G. Schaefer, M. Kristiansen, and A. Guenther, eds.), Plenum Press, New York, pp. 379-407. f<.''-t'�v. V. E., ed., 2000, Encyclopedia of Low-Temperature Plasmas (in Russian). Nauka, Moscow. Gundersen, M. A. and Schaefer, G., eds., 1989, Physics and Applications of Pseudosparks. Plenum Press, New York. Hagerman, D. C. and Williams, A. H., 1959, High-Power Vacuum Spark Gap, Rev. Sci. Instrum. 30: 1 82. Hartman, W. and Gundersen, M. A., 1989, Cathode-Related Processes in High-Current Density, Low Pressure Glow Discharge. In Physics and Applications of Pseudosparks (M. A. Gundersen and G. Schaefer, eds.), Plenum Press, New York, pp. 77-88. Kirkman, G. F. and Gundersen, M. A., 1986, Low Pressure, Light Initiated, Glow Discharge Switch for High Power Applications, Appl. Phys. Lett. 49:494. Kirkman-Amemija, G., Liou, R. L., Hsu, T. H., and Gundersen, M. A., 1989, An Analysis of the High-Current Glow Discharge Operation of the BLT Switch. In Physics and Applications of Pseudosparks (M. A. Gundersen and G. Schaefer, eds.), Plenum Press, New York, pp. 1 55-165 . Korolev, Yu. D. and Frank, K., 1999, Discharge Formation Processes and Glow-to-Arc Transition in Pseudospark Switch, IEEE Trans. Plasma Sci. 27: 1 525-1537. Kovalenko, V. P., Makarevich, A. A., Rodichkin, V. A., and Timonin, A. M., 1 974, Study of the Laser-Triggered Vacuum Discharge, Zh. Tekh. Fiz. 44:23 1 7-232 1 . Lobov, S . 1., Tsukerman, V . A., and Eig, L . S., 1960, A Triggered Low-Pressure Spark Gap, Prib. Tekh. Eksp. 1 :89. Makarevich, A. A. and Rodichkin, V. A., 1 973, A Laser-Triggered Vacuum Spark Gap, Ibid. 6:90-9 1 . Mather, J . W. and Williams, A. H., 1960, Some Properties of a Graded Vacuum Spark Gap, Rev. Sci. Instrum. 31:297. Mechtersheimer, G., Kohler, R., Lasser, T., and Meyer, R., 1986, High Repetition Rate Fast Current Rise Pseudospark Switch, J. Phys. E. 19:466. Mesyats, G. A., 1 974, Generation of High-Power Nanosecond Pulses (in Russian). Sov. Radio, Moscow. Mesyats, G. A., 2000, Cathode Phenomena in a Vacuum Discharge: The Breakdown, the Spark and the Arc. Nauka, Moscow. Mesyats, G. A. and Puchkarev, V. F., 1992, On Mechanism of Emission in Pseudosparks, Proc. XV ISDEIV, Darmstadt, Germany, pp. 488-489. Penetrante, B. M. and Kunhardt, E. E., 1 990, Fundamental Limitations of Hydrogen Thyratron Discharges. In Gas Discharge Closing Switches (G. Schaefer, M. Kristiansen, and A. Guenther, eds.), Plenum Press, New York, pp. 45 1 -472. Slivkov, I. N., 1 986, Processes at a High Voltage in Vacuum (in Russian). Energoatomizdat, Moscow. Thompson, J. E. 1 990, Triggered Vacuum Switch Construction and Performance. In Gas Discharge Closing Switches (G. Schaefer, M. Kristiansen, and A. Guenther, eds.), Plenum Press, New York, pp. 271-285. Wilson, J. M., Boxman, R. L., Thompson, J. E., and Sudarshan, T. S., 1983, Breakdown Time of a Triggered Vacuum and Low-Pressure Switch, IEEE Trans. Electr. Insul. 18:238-242.

Chapter 1 1 SOLID-STATE AND LIQUID SPARK GAPS

1.

SPARK GAPS WITH BREAKDOWN IN SOLID DIELECTRIC

In high-power pulse generators with high rates of rise of the discharge current (up to 10 1 4 A/s and more), switches with a discharge in a solid dielectric, having a number of advantages, are often used. Due to the high dielectric strength of solid dielectrics (Mylar, polyethylene, polypropylene, etc.), the discharge gap can be very small and the inductance and active resistance of the spark gap can be rather low. This makes it possible to switch currents as high as millions of amperes and produce current and voltage pulses with very short rise times. The breakdown delay time for solid dielectrics quickly decreases with increasing overvoltage, being a few nanoseconds at an overvoltage factor of 1 .5 and more (Mesyats, 1 96 1 ). The first solid-state spark gaps with mechanical triggering (puncturing a dielectric with a sharp metal punch) intended for the production of microsecond current pulses of amplitude up to 1 06 A were developed by Komelkov and Aretov (1 956). Mesyats (1961) paid attention to the opportunity of using solid-state spark gaps in generators of high-power nanosecond pulses when, in his experiment on the breakdown of NaCl crystals and fluoroplastic, he obtained a switching time of 1 o-9 s. More often solid-state spark gaps are used in generators with strip transmission lines in which a stack of thin dielectric sheets is used for insulation. In this case, there is no need in bushing insulators, the nonuniformity at the joint of the line with the switch is absent, and multichanneling is possible, which enables the inductance and active resistance of the switch to be made extremely low. The de breakdown

202

Chapter 1 1

electric field of a dielectric, Edc, usually equals several megavolts per centimeter, and it increases with decreasing dielectric thickness. For example, in thin (5 · 1 0-4 em) Mylar films, Edc � 8 MV/cm has been achieved. Therefore, solid-state spark gaps, similar to strip lines, are made of stacks of dielectric films impregnated with liquid dielectric. However, Edc depends not only on the film thickness, but also on the area of the film surface on which the electrode is put. Hence, we can speak of the dependence of Edc on the volume V of the dielectric to which the field is applied. J. C. Martin (Martin et al, 1 996) recommended the empirical formula

Edc yuio = K '

(1 1 . 1)

where the electric field Edc is measured in megavolts per centimeter and the volume V in cubic centimeters. The quantity K is equal to 2.5 for Teflon and polyethylene, 2.9 for polypropylene, for Lucite, and �.6 for thin Mylar. Solid-state spark gaps can operate based on the self-breakdown principle or be triggered by some external action. Self-breakdown can be realized by destroying the dielectric placed between the spark gap electrodes. In the simplest case, to destroy the insulation and close the gap, an electrodynamic hammer is used that is brought in motion by a pulsed magnetic field (Rogers and Whittle, 1 969). Such a spark gap has a rather low active resistance (-1 0-6 n), which is determined by the resistance of the metal bar that connects the electrodes. However, the triggering delay time of spark gaps of this type is at the best some tens of microseconds, which substantially restricts the field of their application. Another type of self-breakdown is the breakdown resulting from the action of a pulsed voltage much in excess of the de breakdown voltage. However, in this case, the triggering delay time of the spark gap is rather unstable since the breakdown occurs over irregularities and inclusions, which are always present in commercially produced dielectrics. To eliminate the statistical influence of these inclusions, it was proposed (Martin et al, 1 996) to stabilize the breakdown voltage by creating artificial irregularities in the dielectric. These irregularities can be created, for example, by caving small metal cones or thin wires into the dielectric. In such a spark gap, with the help of heated thin needles pressed into the dielectric, blind channels were made in which a discharge developed. Such a channel is capable of transmitting a limited current, and the breakdown voltage for one channel is stable within -6 %. Therefore, many channels - no less than 30 - were made in the dielectric. In this case, the breakdown voltage was stable within -2 %. An increase in number of channels substantially reduces the inductance of the discharge circuit and increases the rate of rise of the pulsed voltage produced. The simultaneity of formation of a great number of channels depends on the rise rate of gap

3. 3

SOLID-STA TE AND LIQUID SPARK GAPS

203

voltage. It has been revealed that as a pulsed voltage with dV/dt < 10 1 1 V/s was applied to the dielectric, only one channel was formed. For all channels to be broken down simultaneously, it is necessary to have dV/dt � 10 1 2 V/s. In this case, all channels are formed within -10-9 s (Vitkovitsky, 1 987). To trigger solid-state spark gaps, various methods are used. The simplest one is based on the principle of operation of a three-electrode spark gap, such that a metal plate is built in between two dielectric sheets clamped between the cathode and the anode. On application of a trigger pulse, the dielectric between the trigger electrode and one of the main electrodes is broken down and then, due to overvolting, the second dielectric is broken down. Spark gaps in which the dielectric is destroyed by exploding a small charge of explosive, a wire (Huber, 1 964), or a foil (Henins and Marshall, 1 968) are also used. With an exploding wire, breakdown occurs along the cracks formed in the dielectric under the action of the shock wave. Spark gaps with the use of an explosive have a somewhat lower resistance since the electrode gap is bridged by the metal jet formed on explosion. The triggering delay time of "explosive" switches is a few microseconds. Bayes et a/. (1966) describe a spark gap in which a dielectric is destroyed under the action of the gas-kinetic and magnetic pressure produced by a spark. The spark is initiated between two auxiliary foils that are separated with a dielectric having a hole, in which the triggering discharge occurs. To trigger such a spark gap, high-power capacitor banks are used, and the triggering current is several hundreds of kiloamperes. A detailed review of solid-state spark gaps is given in the monograph by Vitkovitsky (1987).

2.

SPARK GAPS WITH BREAKDOWN OVER THE SURFACE OF SOLID DIELECTRIC

The mechanism of the operation of surface-discharge spark gaps in gas is determined by the presence of triple (metal-dielectric-gas) junctions (TJ's) at the places of contact between the cathode and the dielectric. Even a single electron appearing at this junction and hitting the surface of the dielectric produces plasma necessary to initiate a discharge over the dielectric surface. Depending on the electric field at the surface of a metal protrusion in the TJ, there are three options for a discharge to develop. First, if the field is high enough (-1 08 V/cm) to cause field emission, the protrusion is heated by the Joule mechanism and explodes, a cathode spot appears, the plasma starts expanding over the dielectric, and a discharge is initiated. High electric field at the protrusion may be due to high dVIdt or high permeability of the dielectric. Second, if the field at a TJ is not very high (5 · 1 07 V/cm), the number of electrons appearing during the voltage pulse suffices to initiate a

204

Chapter 11

surface discharge. The moving plasma gives rise to a displacement current, which passes through a metal protrusion in the TJ, heating the protrusion by the Joule mechanism and then exploding it. As a result, a cathode spot and cathode plasma appear, and the latter speeds up the surface discharge process. Finally, the third option takes place, in particular, in a de breakdown when a few electrons get from a TJ on the cathode, initiate an avalanche of secondary emission electrons, positively charge the dielectric, and ionize the gas near the dielectric surface. In this case, a cathode spot can appear either on the interaction of the discharge plasma with the cathode surface or as the gap is bridged by the plasma. In the second and third cases, a corona discharge develops over the dielectric surface. The mechanism of surface discharges in gas was investigated on the nanosecond scale in the experiment described by Mesyats (1974). The rate of voltage rise in this experiment was � 10 1 2 V/s with a time delay to breakdown of the order of 10-9 s. Looms (1961) was the first to develop gas surface-discharge single-channel spark gaps intended for the operation at de voltages. Pulsed multichannel spark gaps were designed by Dashuk and his co-workers (Dashuk, 1 976; Dashuk and Chistov, 1 979). This work was further developed by Hasson and von Bergmann (1 976), Johnson et al. (1 982), and Von Bergmann (1990). The most important property of this type of spark gap is that it is capable of providing multichannel switching and thus enabling low L and R of the spark during switching. This is because with strip cathode and anode both there are many effective triple junctions at the cathode. From these junctions, at a voltage rise rate dV/dt � 10: 2 V/s, many surface discharges start. The time of discharge channel growth and gap closure is d/v, where d is the gap spacing and v is the velocity of motion of the discharge plasma over the dielectric, which increases with dV/dt. This time should be long enough in order that many discharges be initiated at the cathode TJ's. By varying d and dV/dt, it is possible to attain a situation where N channels appear practically simultaneously. Spark gaps of this type can operate both in the self-triggering mode and in the mode of triggering by an external pulse. The circuit of a self-triggered spark gap is shown in Fig. 1 1 . 1 . During the discharge, the dielectric behaves as a chain of capacitors with volumetric and surface specific capacitances C1 and C2. The ratio of these capacitances determines the rate of development of the discharge (Mesyats, 1974). Figure 1 1 .2 presents different triggering schemes for surface discharge spark gaps. The spark gap shown in Fig. 1 1 .2, a is self-triggered, while those in the other figures operate from a trigger pulse. In Fig. 1 1 .2, b, the trigger electrode is put on the surface of the dielectric; in Fig. 1 1 .2, c it is built in the dielectric, and in Fig. 1 1 .2, d it is located some distance from the dielectric surface. Figure 1 1 .3 shows the

SOLID-STATE AND LIQUID SPARK GAPS

205

pattern of a triggered multichannel discharge at different voltages between cathode and anode for the case of a built-in trigger electrode (Fig. 1 1 .2, c).

' _c' T T T T T f L 1l[ l[....l[... l[ l[ -

A D

Cz

__

.

c

________.... _ ___, ... s

_

__

Figure 11. 1. Arrangement of the electrodes and dielectric in a nontriggered surface spark gap: A and C - electrodes, S - substrate, D dielectric, C1 - specific volumetric capacitance, C2 specific surface capacitance of the dielectric

(a)

C�smfmms:=d (f ) ) \\ ' 1

2

1

2

3

(a)

(b) 3

1

{c)

2

r:::sssssssC:ssssss=J p 2

1

--

Figure 1 1.2. Typical geometries of triggered surface spark gaps: 1 and 2 main electrodes, 3 trigger electrode, 4 - dielectric, 5 strip conductors

(c)

\ I

1} \ {

d t Wll ! W1 I ( I

f· :gure 1 1 . 3.

Photographs of a surface discharge demonstrating multichanneling: Triggering voltage = 1 0 (a), 20 (b), and 30 kV (c). Charge voltage = 30 kV. Gap spacing = 8 mm

Spark gaps of the above types are capable of switching megaampere currents at a voltage of up to 1 00 kV with triggering delay time td :::. 1 0-8-1 0-7 s and jitter !ltd ::;; 1 0-9-1 0-8 s. They can operate repetitively at pulse repetition rates of 1 02- 1 03 Hz, currents of 1 0 kA, and voltages of up to 30 kV with gas flow velocities ;::: 1 03 cm/s. The dielectrics used are ceramics, Plexiglas, polyethylene, epoxy-fiberglass, etc. The pressure of the fill gas (air, nitrogen, nitrogen-SF6 mixtures, etc.) varies in the range 1 0-760 mm Hg. At currents of � 1 0 kA these spark gaps hold 1 06 shots, while at 1 06 A only about 1 03 - 1 04 shots because the dielectric surface becomes covered with a film of the electrode metal. The number of channels per meter in switches of this type is sometimes over 1 00. These spark gaps are used in the pumping

206

Chapter 1 1

systems o f gas lasers, in charged particle accelerators as high-current pulse peakers, etc. In pulsed gas lasers, they are also employed as sources of ultraviolet radiation for preionization of the gas. A review of the work on the development of dielectric-surface-discharge spark gaps is given by von Bergmann (1990).

3.

LIQUID SWITCHES

In pulse generators with liquid energy storage and transmission lines, liquid spark gaps are often used as switches. Owing to the high pulsed dielectric strength of liquid dielectrics, the cathode-anode gap can be made small, and, accordingly, the inductance of the discharge channel is low and the switching time is short. Moreover, the replacement of conventional discharge switches by liquid ones makes it possible to simplify the generator design, since in this case there is no need of using bushing insulators between the gas of the switch and the liquid dielectric of the line. On the other hand, these switches have a number of disadvantages. First, the working liquid is decomposed polluted in electrical discharges; therefore, it has to be purified after a number of shots. Second, high-power discharges in liquids generate shock waves, and to prevent a harmful action of these waves, mechanical constructions in a line should be strong enough. The discharge in transformer oil was used for the generation of short waves even by Hertz. The description of other early experiments in this field is given in the monograph by Binder (1928). It has been shown (Mesyats and Vorob'ev, 1 962) that a water spark gap can be used to attain switching times of several nanoseconds. The capability of liquid spark gaps to operate in the multichannel mode is their very important property. Multichannel water spark gaps can operate in two modes: self-breakdown and triggered. Levine and Vitkovitsky (197 1 ) have shown that in the self­ breakdown mode at a voltage of 250 kV it is possible to ignite in water up to three channels with 1 0-7 s jitter. For this purpose, to locally enhance the electric field, protrusions were made on the cathode. Burton et a/. (1 973) used the Gamble II generator to investigate how the efficiency of multispark operation depends on the time of charging of the energy store, the degree of enhancement of the field at the positive electrode, and the distance between neighboring spark channels. Voltage pulses of amplitude 4 MV and more and rise time 1 00 and 600 ns were applied to electrodes of diameter 7.6 em. The degree of electric field enhancement was varied by placing rods of clifferent diameter on the electrode. In single-channel breakdown experiments with a charge voltage rise time tr ::::: 1 00 ns it was found that at a field enhancement factor �E = 1 2 . 4 and a voltage of 6.8 MV the root-mean-

SOLID-STATE AND LIQUID SPARK GAPS

207

square jitter in triggering time was 10 ns. For �E = 1 0 it decreased to 6 ns and for �E = 28 to 3 ns. Successful multichannel operation was observed at tr = 100 ns and �E = 1 0-28. Increasing the pulse rise time to 600 ns substantially worsened the multichannel operation. For instance, only two channels were observed in five cases of twenty. Thus, multichannel operation in the self-triggering mode is possible with tr ::;; 100 ns. In the Triton generator (Liksonov et a!. , 1 974), multichannel switching was realized due to fast charging of a line Ctr 1 30 ns). Six spark gaps were located in regular intervals on the periphery of the outer electrode of a Blumlein energy storage line. More than three spark gaps were triggered within 5 ns with 90 % probability. At a voltage of 5 · 105 V and a current of 2.2 · 1 05 A, the switching time was 1 5 ns. An experiment on multichannel switching at a voltage of up to 3 MV was described by Van Devender and Martin (1975). A generator with strip lines and spark gaps was used. The spark gaps had an extended sharp edge of length 1 . 12 m, which was equal to the width of the strip lines. The generator consisted of three strip lines and two series-connected water spark gaps. The first strip line was charged from a Marx generator within (2-5) · 1 o-7 s. As this took place, five channels on the average were operative. As the first spark gap operated, the second line was charged within 6 · 1 o-8 s. Due to this, the electric field in the second spark gap reached 1 .6 MV/cm, and the discharge in this gap occurred through, on the average, twenty channels. The jitter of triggering of the first spark gap was -10 ns for tr = 2.6 · 1 0-7 s and increased to -20 ns for tr 5·1 o-7 s. The second spark gap was triggered with 3 ns jitter. The output pulse had a peak voltage of 1 .5 · 106 V, current of 7 .5 · 1 05 A, rise time 3 ns, and duration of 1 .3 · 1 o-9 s. Thus, to ensure low-jitter multichannel switching, it is necessary to charge the energy store within 1 00-200 ns, and the electrodes of the spark gap should have special surface irregularities such as protrusions or extended edges. For energy stores with long charging times (> 0.5 J.lS), triggered liquid switches are used. For triggering, three-electrode spark gaps with field distortion, liquid trigatrons, laser-triggered switches, microconductor­ explosion switches, and other type of switch are employed. In the most powerful pulse generators designed for the production of high-power electron, ion, and x-ray beams (Aurora, PULSERAD, OWL, Gamble, etc.), three-electrode spark gaps are used. One of the first switches of this type was proposed by J. C. Martin (Martin et al., 1 996). A schematic diagram of such a switch is given in Fig. 1 1 .4. If pulsed charging of an energy storage line is used, spark gap 4 operates because of the voltage redistribution that takes place due to the presence of self-capacitances in the spark gap. As a result, the gap between electrodes 2 and 3 and then the gap between the main electrodes 1 and 2 are broken down. When several spark gaps of this type

=

=

208

Chapter I I

operate simultaneously, it is necessary to apply a trigger pulse to the gas­ filled spark gap 4. For water-filled spark gaps, it is recommended that the spacing ratio between the gaps I-3 and 3-2 be 7 : 1 (Martin et al. , 1 996).

Figure 11.4. Triggered liquid spark gap: 1 and 2 - main electrodes (1 - cathode), 3 - trigger electrode, and 4 - gas gap

Smith ( 1 976) described the operation of the Aurora system. This machine, which contains four coaxial Blumlein energy storage lines with a triggered three-electrode spark gap, has the following characteristics: voltage 1 5 MV, current 1 .6 MA, and pulse duration 1 25 ns. A unique feature of the Blumlein lines of the Aurora is the use of specially developed multichannel oil spark gaps with external triggering. The recovery capability of nontriggered (self-breakdown) oil spark gaps is insufficient to synchronize four output pulses. Besides, they in any case form one spark channel and therefore have too high inductance. The wave impedance of each internal transmission line is 12 n, and the switch transfers a current of 1 MA. The switch of a Blumlein line operates by the principle of a three­ electrode spark gap triggered by the method of electric field distortion. The electrode separation can be varied with the help of a hydraulic drive by moving the intermediate cylinder in the axial direction. The maximum electrode separation in this spark gap is 6 1 em. A large disk with a very flat surface, located about 7.6 em distance from the flat end face of the inner cylinder serves as trigger electrode. This distance changes with the help of a hydraulic system mounted in a steel column, which, as a console, puts the disk forward from the inner electrode of the Blumlein line where the units of the trigger circuit are located. A part of the console design is a 2-MV gas spark gap. When the Blumlein line is charged to 12 MV, the voltage at the trigger disk increases since the latter behaves as a capacitive voltage divider. The gas spark gap is triggered from the outside and is broken down. About 200 ns later, there occurs a multichannel breakdown in the oil, which is initiated at the sharp edge of the trigger disk. The jitter is about 10 ns;

SOLID-STA TE AND LIQUID SPARK GAPS

209

shorter values can be achieved with a spark gap of similar design at a higher triggering voltage. A spark gap of the same type was used in the Gamble II accelerator (Shipman, 1 97 1 ) . The negative and positive electrodes were connected to the inner conductors of the storage and transmission line, respectively. The middle, trigger electrode had the shape of a disk with a sharp edge, which was supported and isolated from the transmission electrode by a gas switch filled with SF6 • At a required moment of charging, the gas switch was triggered. This abruptly distorted the electric field in the region of the middle electrode and initiated streamers propagating toward the negative electrode. When these streamers bridged the gap, the potential of the middle electrode became high enough to cause fast breakdown of all spark gap. Such a water spark gap (Dobbie et a/. , 1 974), at a voltage of 4.5 MV and current of 670 kA, formed a pulse of rise time 40 ns. No less than five channels were ignited, and this provided an output pulse of stable amplitude and rise time. The switch was triggered with jitter less than 6 ns. Prestwich et al. (1975, 1 976) described the Harp and Proto I electron accelerators in which triggered multispark three-electrode oil gaps were used. These accelerators had the following parameters of the output pulse: 3 MV, 0.8 A, and 24 ns. A Marx generator charged three intermediate water energy stores within 0.9 J.LS. From the intermediate stores, Blumlein lines were charged through a three-electrode spark gap within 0. 1 8 J.l.S. To trigger the three-electrode switch, SF6-filled trigatrons were used. With a trigger pulse of peak voltage 1 50 kV and rise time 70 ns, a jitter less than 1 ns was attained.

Figure 1 1.5. Three-electrode liquid rail spark gap

Energy was transferred from a Blumlein line to the load through a three­ electrode oil-filled rail spark gap (Fig. 1 1 .5). The trigger electrode of length 1 20 em and thickness 6.4 mm had a sharp edge of radius 0. 1 mm . The trigger pulse had amplitude of 2 MV and rise time of 30 ns. For normal operation of the spark gap, it was necessary that the distance between the

Chapter I I

210

trigger electrode and the grounded electrode be 1 /3 of the total interelectrode distance of the rail spark gap. The triggering delay time of this spark gap was 25 ns with 1 .3 ns jitter. With the use of the Proto I machine, tests of nontriggered two-electrode rail spark gaps were carried out as well. Table 1 1. 1. Charging time, ns

Multispark triggering jitter, ns

Average number of channels

90

3.9

4.2

8.8

1 20

4.8

4.1

9.4

1 30

5.5

3.2

9.7

1 70

7.3

2.5

1 1 .0

Switching time, ns

Table 1 1 . 1 presents the results of these tests. If the charging time was

< 200 ns, the breakdown delay time showed high stability and the switching

time was short. Ushakov ( 1 975) and Muratov and Ushakov ( 1 976) performed investigations of the trigatron triggering of water switches. A trigatron with a voltage of up to 1 MV operated most efficiently if the trigger (rod) electrode was protruded for some distance above the surface of the main electrode. The optimal conditions that provided the least td and l'!.td were as follows: 1 . The discharge should be initiated on the anode side by a pulse of positive polarity. 2. The length of the protrusion ofthe trigger electrode should be (0. 1-0.2)d, where d is the distance between cathode and anode. 3. The optimal amplitude of the trigger pulse was (0.2-0.3) Va, where Va is the peak voltage between the cathode and the anode. 4. The trigger pulse should be applied within 1 00- 1 50 ns before the moment the cathode-anode gap voltage peaks, and the pulse rise time should be no less than 50 ns. Under these conditions it was possible to trigger megavolt trigatrons within td � 1 00 ns with l'!.td = 6 ns (Muratov and Ushakov, 1 976). If a voltage of (0.75-0.95 ) Vdc, where Vdc is the de breakdown voltage, was applied to such a trigatron, it was possible to provide simultaneous operation of three trigatrons. Some researchers investigated laser-triggered spark gaps filled with water (Demidov et al. , 1 974) and transformer oil (Guenther et a/. , 1 976). The best results were obtained by Guenther et a/. ( 1 976) who used a laser to initiate a discharge in an overvolted spark gap filled with transformer oil with td � 1 5 ns and l'!.td = 1 ns at a voltage of 700 kV. Ushakov ( 1 975) reported on the study of the possibility to trigger a spark gap with the help of electrically exploded wires. A capacitor of capacitance

SOLID-STA TE AND LIQUID SPARK GAPS

21 1

I 0-7 F and voltage 2 1 kV was discharged into a copper wire of diameter 50 J..lm and length 1 4 mm that was placed 2 mm distance from the electrode surface. For an anode-initiated discharge, the jitter was 50 ns, while if the discharge was initiated at the cathode it was an order of magnitude greater. This triggering technique has not found application since a new wire is required after each operation of a spark gap and, moreover, the resistivity of water appreciably decreases after several shots and the water has to be purified. Detailed reviews on liquid spark gaps are given in the monographs by Vitkovitsky ( 1987) and Koval'chuk et a/. ( 1 979).

REFERENCES Bayes, D. V., Hucklesby, R. J., and Ward, B. J., 1 966, A Passive Crowbar for the I MJ Thetatron Bank Using 32 Solid Dielectric Switches in Parallel. In Proc. IV Symp. on Engineering Problems in Thermonucl. Res. , Frascatti, Italy. Binder, L., 1 928, Die Wanderwellenvorgiinge auf Experimenteller Grundlage. Springer, Berlin. Burton, J. K., Conte, D., Lupton, W. H., Shipman, J. D., and Vitkovitsky, I. M., 1 973, Multiple Channel Switching in Water Dielectric Pulse Generators, Proc. V Symp. on Engineering Problems ofFusion Res., Princeton University, pp. 679-683. Dashuk, P. N., 1 976, U.S. Patent No. 4 092 559. Dashuk, P. N. and Chistov, E. K., 1 979, Some Features of the Electric Field Distribution in Systems Forming a Sliding Discharge, Zh. Tekh. Fiz. 49: 124 1 - 1 244. Demidov, B. A., Ivkin, M. V., Petrov, V. A., and Fanchenko, S. D., 1 974, Laser-Triggered High-Voltage Water Spark Gap, Prib. Tekh. Eksp. 1: 120-122. Dobbie, C. B., Fargo, V., Kolb, A. C., Korn, P., Phelps, D. A., and Rumrus, A. A., 1 974, High Current Relativistic Electron Beam Accelerator for Fusion Applications. MLR-357, San Diego, CA. Guenther, A. H., Zigler, G. L., Bettis, J. R., and Copeland, R. P., 1 976, Laser Triggered Switching of a Pulsed Charged Oil Filled Spark Gap. In Energy Storage, Compression, and Switching: Proc. of the 1st Intern. Conference on Energy Storage, Compression and Switching (Nov. 5-7, 1974) (W. H. Bostick, ed.}, Plenum Press, New York-London, pp. 441 -450. Hasson, V. and von Bergmann, H. M., 1 976, High Pressure Glow Discharges for Nanosecond Excitation of Gas Lasers and Low Inductance Switching Applications, J. Phys. E. : Sci. Instrum. 9:73. Henins; I. and Marshall, J., 1 968, Fast Metallic Contact Solid Dielectric Switch for High Voltage and Current, Rev. Sci. lnstrum. 39 ( 1 0). Huber, H., 1 964, Wide Voltage Range High Energy Solid Dielectric Switch, Ibid. 35 (8). Johnson, D., Kristiansen, M., and Hatfield, L., 1 982, Multichannel Surface Discharge Switch. In Proc. Conf on Electrical Insul. and Die/ec. Phen., Amherst, MA, p. 573. Komelkov, V. S. and Aretov, G. N., 1 956, Production of High Pulsed Currents, Dokl. AN SSSR. 1 10:559-56 1 . Koval'chuk, B . M., Kremnev, V . V., and Potalitsyn, Yu. F., 1 979, High-Current Nanosecond Switches (in Russian). Nauka, Novosibirsk.

212

Chapter 1 1

Levine, L . S . and Vitkovitsky, I. M., 1971, Pulsed Power Technology for Controlled Thermonuclear Fusion, IEEE Trans. Nucl. Sci. 18 (Pt 2): 105- 1 12. Liksonov, V. 1., Sidorov, Yu. L., and Smirnov, V. P., 1 974, Generation and Focusing of a High-Current Electron Beam in a Low-Impedance Diode, Pis 'rna Zh. Eksp. Tear. Fiz. 19:5 1 6-520. Looms, J. S. T., 1 96 1 , Switching by Surface Discharges, J. Sci. Instrum. 38:380. Martin, T. H., Guenther, A. H., and Kristiansen, M., eds., 1 996, J. C. Martin on Pulsed Power. Plenum Press, New York. Mesyats, G. A., 1 96 1 , Candidate's Thesis Development and Study of Nanosecond High­ Voltage Pulse Devices with Spark Gaps. Tomsk Polytechnic Institute, USSR. Mesyats, G. A., 1 974, Generation of High-Power Nanosecond Pulses (in Russian). Sov. Radio, Moscow. Mesyats, G. A., and Vorob'ev, G. A., 1962, On the possibility of using liquid-filled spark gaps in nanosecond pulsed high-voltage systems, Izv. Vyssh. Uchebn. laved. , Fiz. 3:2 1 -23. Muratov, V. M. and Ushakov, V. Ya., 1976, Study of Triggered Discharges in Water. In Development and Use ofIntense Electron Beam Sources (in Russian, G. A. Mesyats, ed.), Nauka, Novosibirsk, pp. 36-42. Prestwich, K. R., 1 975, "Harp" a Short Pulse, High Current Electron Beam Accelerator, IEEE Trans. Nucl. Sci. 22:975-978. Prestwich, K. R., Miller, P. A., McDaniel, D. H., Poukey, J. W., Widner, M .M., and Goldstein, S. A., 1 976, "Proto-1" Switching and Diode Studies, Proc. Topical Corif. on Electron Beam Research and Technology. SAND. 76-5122 (Feb. 1976), Sandia Labs., Pt 1 , pp. 423-428 . Rogers, P . J . and Whittle, H . R., 1 969, Electromagnetically Actuated, Fast-Closing Switch Using Polyethylene as the Main Dielectric, Proc. lEE. 1 16: 1 73-1 79. Shipman, J. D., 1 97 1 , The Electrical Design of the NRL "Gamble II" 1 00 Kilojoule, 50 Nanosecond, Water Dielectric Pulse Generator used in Electron Beam Experiments, IEEE Trans. Nucl. Sci. 18 (Pt 2):243-246. Smith, 1., 1 976, Liquid Dielectric Pulse Line Technology. In Energy Storage, Compression, and Switching: Proc. of the Ist Intern. Conference on Energy Storage, Compression and Switching (Nov. 5-7, 1974) (W. H. Bostick, ed.). Plenum Press, New York-London, pp. 5-23. Ushakov, V. Ya., 1 975, Pulsed Electrical Breakdown of Liquids (in Russian). Tomsk State University Publishers, Tomsk. Van Devender, P. J. and Martin, T. H., 1 975, Untriggered Water-Switching, IEEE Trans. Nucl. Sci. 22:305-309. Vitkovitsky, 1., 1 987, High Power Switching. Van Nostrand Reinhold Company, New York. Von Bergmann, H. M., 1 990, Surface Discharge Switches. In Gas Discharge Closing Switches (G. Schaefer, M. Kristiansen, and A. Guenther, eds.), Plenum Press, New York, pp. 345-373.

PART 5 . GENERATORS WITH PLASMA CLOSING SWITCHES

Chapter 1 2 GENERATORS WITH GAS-DISCHARGE SWITCHES

1.

DESIGN PRINCIPLES OF THE GENERATORS

All the switches considered in Chapters 9-1 1 are, in essence, plasma switches. However, the plasma in them is generated by different types of discharge such as a discharge in a high-pressure or low-pressure gas, a discharge over the surface of a dielectric in vacuum or gas, and discharges in liquid or solid dielectrics. We shall conditionally refer to all switches belonging to this class as plasma closing switches. We name them "plasma switches" to distinguish them from semiconductor and magnetic closing switches, which will be considered below. We use the term "closing" since there also exist various types of plasma opening switch about which we shall speak later. The overwhelming majority of nanosecond high-power pulse generators use gas-filled spark gaps for which the product of gas pressure by gap spacing, pd, falls on the far right portion of Paschen's curve. For generators of this type to operate properly, two conditions must be satisfied. First, the switching time fs must be short (10-1 0-1 0-8 s, depending on the parameters of the pulses and their purpose). Second, proper values of the discharge delay time td and jitter Md (depending on the purpose, td � 1 0-9-10-7 s and !ltd = 10-1 0-10-8 s) should be provided. In gas-discharge switches, these conditions, as shown in Chapters 4 and 9, are satisfied by increasing the electric field E, or the gas pressure, or the number of free initiating electrons in the gap. To reduce 18, there is one more way: increasing the gas pressure in the gap.

216

Chapter 12

As we have shown in Chapters 1 and 2, two basic schemes for the production of nanosecond high-power pulses with the use of gas-filled spark gaps are known: one with the discharge of a previously charged energy store into a load, and its various versions, and the other with the discharge of a capacitor (Vorob'ev and Mesyats, 1 963). To these types of generator there correspond equivalent circuits of the discharge circuit, which are used to calculate the pulse rise time (Fig. 1 2. 1). In Fig. 12. 1 , Z0 is the wave impedance of the line, L is the inductance of the discharge circuit, Rs is the (nonlinear) resistance of the spark, V0 is the charge voltage, and C is the storage capacitance. In Chapters 1 and 2, we considered the operation of pulse generators with perfect switches with the switching time equal to zero. Here, we shall take into account the spark resistance in the simplest form.

� L

(b)

CIT

Figure 12. 1. Equivalent discharge circuits of pulse generators with a storage line for t = 2tp (a) and with a storage capacitor (b)

For the calculation of the waveform of the pulse produced by any of the above circuits, it is necessary to know the dependence of the spark resistance Rs on current and time. For rather low currents (up to 1 0 kA) one can use the spark resistance obtained from the Rompe and Weizel model (Rompe and Weizel, 1 944) (see Chapter 4). It should be noted that though we speak in this section only about generators with voltages of up to 100 kV and currents of up to 1 0 kA, all the main principles stated below are applicable to megavolt and megaampere systems. The only difference is that one should take into account the features of the physical processes occurring in switches and peakers at high currents and voltages.

GENERA TORS WITH GAS-DISCHARGE SWITCHES

217

GENERATORS WITH AN ENERGY STORAGE

2.

LINE

To analyze the effect of various factors on the current rise during the pulse produced by discharging an energy storage line, we shall consider the transient process in the circuit presented in Fig. 1 2. 1 , a. This circuit contains a generator with a charged line of wave impedance Z0 and a load of resistance R1oad; the line is discharged through a spark gap. A schematic circuit of the generator is given in Fig. 2. 1 . We shall consider only time intervals shorter than the time of the double run of a wave through the storage line. The current in the circuit, in view of formula (4.27) for the spark resistance R5, is described by the equation

(12. 1) where x = IRIVo ; 't = tiS ; 8 = 2pd2 1aV02 ; A = LIRS ; R = Z0 + R1oad ; d is the width of the spark gap; a is the factor in the Rompe-Weizel formula that characterizes the gas type, and V0 is the charge voltage of the line. We shall first consider the case where the inductance of the discharge circuit can be neglected. Then A = 0 and Eq. (12.1) becomes substantially simpler, and the time dependence of current will have the form e

[ (--) -2I)I

t = - In

2

1 10 - 1

+

J

(310 ° + Const , 4(10 - 1)2

(12.2)

where Const is a constant of integration which depends on the way by which the time zero is specified, and 10 = V01R. For t = 0 we have 1110 = 0.01 and Const = 1 .537. From (12.2) it follows that at a current I = 0.25 V01R the rate of current rise takes a maximum value given by

( dl )

x

= 0. 1 05aV0 E pR dt ma

2

(12.3)

To estimate the pulse rise time, it is convenient to determine the switching time fs from the relation

()

-2 lo = 9.5 E = fs (dlldt)max ap p

( 12.4)

218

Chapter 12

where E is the electric field at which the gap is broken down and p is the gas pressure. From ( 1 2.4) it follows that at a fixed gas pressure the time t5 decreases with increasing electric field E. At a fixed spark gap width, the field E can be increased due to the gap overvoltage resulting from pulsed breakdown. For a de breakdown, the quantity Elp can be expressed in terms of the product of gas pressure by gap width. According to Paschen's law, for V0 = const we have Elp = const; hence, from ( 1 2.4) we obtain that Is oc p- 1 , i.e., the time ts decreases with increasing gas pressure. Figure 9.2 presents the relation ts(p) for different gaps subject to de breakdown. From the figure it follows that for rather wide gaps the time fs decreases with increasing pressure more rapidly than this takes place for small gaps. To take into account the effect of the inductance of the discharge circuit on the pulse rise time, it is necessary to solve Eq. ( 1 2. 1 ) with A * 0. A numerical solution of this equation with A * 0 was performed by Grunberg ( 1 965). The function x = f('t) obtained in this work is plotted in Fig. 12.2, a. Using the curves of x = f('t) , one can calculate the relative voltage across the gap as a function of time for different A, the so-called switching characteristic y = V/V0, where V is the voltage across the gas gap (Fig. 12.2, b). From these figures, it follows that the current rise in the gap and the voltage drop across the gap proceed in two stages: fast and slow. This corresponds to experimental results (Vorob' ev and Mesyats, 1 963). This run of the switching characteristics and current waveforms delays the transition from the leading edge to the top of the pulse. Therefore, to determine the pulse rise time, it is more convenient to use formula (12.4). For 0 � A � 25, the pulse rise time is given by the approximate formula

L tr = fs + - . R

(1 2.5)

In formula ( 1 2.5), the first term is determined by conditions in the spark gap and the second one by the parameters R and L of the discharge circuit. From this formula it follows that if we neglect the effect of the time constant of the discharge circuit, the pulse rise time can be found as tr - pd 2 I V02 • As we already mentioned, for a fixed breakdown voltage of a gap, V0, according to Paschen's law, we have pd = const, and, hence, tr oc lip. Besides, from formula (1 2.5) it follows that for a rather high gas pressure the decrease in pulse rise time is limited by the time constant of the circuit, LlR. It is necessary to pay attention to one feature of the switching characteristics calculated by Eq. ( 1 2. 1 ) (see Fig. 1 2.2, b). With A = 0-25 the voltage drop curves lie close one to another; therefore, the switching characteristic can be described by one function, for instance, by the

219

GENERA TORS WITH GAS-DISCHARGE SWITCHES

exponential function Vs = V0 exp ( -a0t). Vorob'ev and Mesyats ( 1 963) obtained

ao :::::

0.075aV02 pd2

The function

( 1 2.6)

YsiV0 = exp (-0.075aVif/pd2 )

is plotted in Fig. 12.2.

(a)

0

40

20

60

(b)

20

0

40

60

80

1 00

Figure 12.2. The relative load current x (a) and relative gap voltage y during switching (b) functions of normalized time t

as

The proposal that for a gas-discharge switch the pulse rise time is merely the sum of the switching time and the time constant of the discharge circuit, LIR, made by Vorob ' ev and Mesyats ( 1 963), was later supported by J. C. Martin (Martin, 1 996) for solid-state and liquid switches. Let us analyze one more possible way of finding the rate of current rise for A ;r 0 that follows immediately from Eq. ( 1 2. 1). From Fig. 1 2.2, a it can be seen that in the region of the maximum rise rate, the function x('t) is almost linear. Therefore, to determine the maximum steepness of the curve x('t) , it suffices to determine approximately the current value at which the rise rate is a maximum. In particular, it can be assumed that in some range of A values the steepness of current and voltage curves is a maximum at x 114 (as well as at A 0). Based on these considerations, the following

=

=

220

Chapter

expression for the maximum 1 963):

(dV) dt

max

=

27 256

where

F(A) Ao -

_

=

1 - (2sh

dV/dt

was obtained (Vorob'ev and Mesyats,

aV� pd F(A) ,

�

3)/

J3A;

12

( 1 2.7)

;

27 . A 128 '

<1> = arcsh

3

J3A; . 2

(12.8)

Checking the validity of the assumptions made in deriving formula (1 2.7) gives for A � 1 0 an error not over 5%. We now consider the features of the operation of generators in which a line is discharged into a load through a gas-discharge switch. The simplest generator of this type was developed by Fletcher ( 1 949) (Fig. 12.3). The generator had a three-electrode spark gap filled with nitrogen at a pressure of 40 atm. The capacitor was connected to the electrodes of the spark gap, as shown in the equivalent circuit diagram (Fig. 1 2.3, b), where Z0 is the wave impedance of the cables L 1 and L2 and is the capacitance of the adjusting capacitor. This generator was capable of producing voltage pulses of amplitude up to 20 kV and rise time 0.4 · 10-9 s. The pulse duration depended on the length of the pulse-forming cable and was equal to (2-3 ) 1 0 9 s.

Ca

-

-

(a) 1 3

Figure 12.3. Generator with a capacitive peaker. (a) schematic diagram: 1 - pulsed current from the trigger generator; 2 - adjusting high-frequency capacitor; 3 - output; (b) equivalent circuit of the charging device

GENERATORS WITH GAS-DISCHARGE SWITCHES

22 1

A feature of this generator is the adjusting capacitor Ca, which is connected in parallel to the storage cable and is built in the spark gap (Fig. 12.3, b). With an optimal choice of the capacitance Ca, the pulse rise time for this generator can be doubled. A detailed analysis of this effect is given by Mesyats ( 1 974). If the switching characteristic is represented by an exponential function: Vs (t) = Vo e - aot '

( 1 2.9)

the voltage across a matched load, formula

Vo [

V(t) = 2

1-2

=

R1oad

2 1-B B e-001 - -- e- B 2-B 2-B

aot

--

Z0,

]

will be determined by the

,

( 1 2. 1 0)

where V0 is the charge voltage of the cable and B = aoZ0C3• The relation between 2 VIV0 and the parameter a0t is given in Fig. 1 2.4 for different values of B. As B is increased, the pulse rise time decreases and an overshoot appears at the pulse top that deforms the pulse shape. With Ca = 1 .4/a0p the overshoot makes up 5%. As the switching time is t5 2.2/a0, the optimal value of the capacitance is =

1 .4 0 . 63t5 Ca - -- -_ -- . Zo ao Zo

( 1 2. 1 1)

_

0

2 aot

4

Figure 12. 4. Dependence of the pulse waveform on parameter a0 for different Bo

222

Chapter 12

However, as follows from expression ( 1 2. 1 0), an ideal adjustment without an overshoot is possible. Actually, for B = 0 we have V(t) = ! V0 (1 - e - aot ) , i.e., the pulse waveform is described by a conventional exponential with the rise time tr = 2.2/a0 determined between the 1 0% and 90% voltage levels. For B = 1 , from ( 1 2. 1 0) we get V(t) = ! V0 (1 - e - 2 aot ) , i.e., the exponential steepness doubles, and the rise time becomes tr = l . l la0• In this case, we have Ca = 0.45tsfZ0 • The slow voltage rise in the transition region from the pulse leading edge to its top (Fig. 1 2.2, a) can be avoided by using a nonuniform energy storage line (Mesyats, 1 974). Let the time of current rise on the "fast" segment is equal to zero, while on the "slow" segment it varies linearly. Thus, the pulsed voltage across a matched load in a circuit with a uniform energy storage line will be written as (12.12) where A0 is some constant, which determines the pulse waveform. For a nonuniform line with wave impedance

[

Zo (x) = Rtoad 1 +

(1 - Ao )x Ao l

]

2 ,

(12. 13)

where x is the running length of the line counted from the switch and l is the total line length, we obtain a rectangular pulse of amplitude A V(tp) across the load of resistance R1oad · Nonuniform lines are convenient to design in strip version. When a nonuniform symmetric strip line with the wave impedance varied from 2.8 to 4. 1 n was used in a 1 -kA current generator, the 1 5% overshoot of the pulse was eliminated (Mesyats, 1 974). The influence of the nonlinear resistance of a spark on the discharge of a capacitor into a load was analyzed by Weizel ( 1 953).

3.

SPARK PEAKERS

A peaker is a device intended for shortening the pulse rise time. Generally, a peaker (P) is connected in series with lines (L 1 and L2) (Fig. 1 2.5). A pulse V1 (t) with a rather long rise time tr1 arrives at the peaker through the line L 1 and a pulse V2(t) with a short rise time tr2 arrives at the load through the line L2 • The principle of operation of the peaker relies on that within a time t � tr 1 , its resistance is much greater and then becomes

GENERATORS WITH GAS-DISCHARGE SWITCHES

223

much lower than the wave impedance of the line. It can readily be seen that a spark gap possesses this property if its breakdown delay time ( 1 2. 14) while fs « tr 1 . The most widespread peakers are two-electrode gas gaps. Let us analyze the operation of such a peaker.

Q

Vr(t)

Figure 12.5. Sketch of the connection of a peaker

Assume that the primary pulse voltage, within the rise time, increases linearly: ( 1 2. 1 5) and for t > tr1 it indefinitely long remains equal to the peak voltage Va (Fig. 1 2.6). It should be borne in mind that the voltage between the peaker electrodes is doubled because of the occurrence of a wave reflected from the spark gap. The pulse rise time at the output, tr2, depends on the breakdown delay time td and rise time tr1 • The time td, with other things being equal, depends on the gap spacing d and is statistical in character. For td « tri> the longer td, the greater the breakdown voltage Vbr of the gap and the shorter the pulse rise time tr2, si11ce tr2 decreases with increasing the electric field during breakdown. Let the statistical component of the time td be eliminated. It can be shown that if breakdown occurs at the point of transition from the pulse leading edge to its top, the time tr2 will be a minimum. Actually, if breakdown occurs at the point n (see Fig. 1 2.6), tr2 will be determined by the magnitude of the electric field, 2 Vafd. If the gap spacing is increased to a value d > d0, where d0 is the optimal gap spacing, the breakdown voltage does not change and the field decreases, and, hence, tr2 increases. For d < d0, tr2 increases as well due to the increase in component t;. In the limit d = 0, we have tr2 = trl· Hence, there is some gap spacing d = do at which the pulse rise time is a minimum (Vorob ' ev and Mesyats, 1 963). Calculations of the relation between tr 1 and tr2 for an atmospheric pressure air gap exposed to intense ultraviolet irradiation (multielectron initiation of breakdown) have shown that to obtain tr2 < IQ-9 s, it is necessary

224

Chapter

12

to have the pulse rise time equal to several nanoseconds. This is confirmed by the data of experiments described by Mesyats (1 974). It has 0.6 ns at 1 atm, it is necessary to been demonstrated that to obtain one should increase the pressure have � 2 ns. To increase the ratio in the peaker.

tr1

tr2 =trdtr2, p =

tr1

n

/

/

,/" td

J

�

/

t;

Va

t;' lr2

lri

Figure 12. 6. Transformation of the front of a wave by a peaker

The optimal gap spacing in a peaker, d0, can be estimated if the dependence of the discharge formative time on pressure and field is known. It was shown (Mesyats, 1 963) that the electric field is an optimum, i.e., the discharge in a peaker occurs at the point of transition from 1 . Here, 1 .9 · 10-2 and the pulse leading edge to its top, if o 0 . 2 1 if Va is measured in kilovolts and in nanoseconds. From this formula, in view of Vald0, it follows that

=

Eo=

11Eot�1tr=1

p Eo E 1=

(12. 16) This formula is valid for a discharge in air at atmospheric pressure for Va 5-100 kV. Let the rise time is so long that the breakdown of the gap in a peaker is similar to a de breakdown. Generally, this takes place for � 10-6 s. Then from Fig. 12.6 it follows that

=

tr1

tr1 ·

(12. 1 7) where

td - Vdc(pd)fa r1

.. ..::.....c :..:. - ----=-=-....

2V:

'

(12. 1 8)

GENERATORS WITH GAS-DISCHARGE SWITCHES

225

and is the de breakdown voltage. The time is approximately equal to the switching time for a de breakdown of a spark gap. For > 1 atm, we have = const and � where is the switching time at atmospheric pressure. In view of the above considerations, Eq. ( 1 2. 1 7) becomes

Vdc s f Vdc ts ts1 1p , ] frz -fpsl + frl [ Vdc(pd) 2Va tr2 fsllp. �

1

t;

p

fsi

( 1 2. 1 9)

·

-

From ( 1 2. 1 9) it follows that if we increase so that the bracketed term � tends to zero, we get Another possible way of increasing the ratio is to use several peakers connected by segments of cable. This is the so-called sequence peaking (Mesyats, 1 963). When three peakers were used, the rise time of a 30-kV pulse decreased from 0.8 · 1 o-6 to 1 o-9 s. With peakers operated in this mode, microsecond pulsed charging of a coaxial line was used in fact for the first time. In this charging scheme, the first peaker is the main switch. This scheme is currently the basic one in creating nanosecond high-power generators. For the first time, a peaker was used by Hertz in 1 9 1 7 in his experiments with short waves. He utilized a series connection of a transmission line and a two-electrode spark gap filled with transformer oil. In 1 926, Burawoy developed and built a generator with a peaking spark gap in oil to produce voltage pulses with a rise time of several nanoseconds and amplitude of about 1 50 kV. A description of these experiments was given by Binder ( 1 928). The first generator with a gas peaker was developed by Fletcher ( 1 949). Figure 1 2.7 shows a circuit where a high-pressure spark gap is used for peaking a pulse. The initial pulse is generated by the coaxial cable L�. which is charged through a resistor R 1 from a source with a voltage of +20 kV. To reduce the rise time of the primary pulse, the trigger spark gap is broken down under an overvoltage created on the operation of a three­ electrode switch.

pd

tr11tr2

+ 20 kV

Figure 12. 7. Schematic of a nanosecond pulse generator using a compressed-gas peaker in the primary charging device: 1 mercury lamp; 2 trigger spark gap; 3 peaker; 4 output pulse -

-

-

-

226

Chapter 12

A peaking spark gap separated from the trigger gap by the cable L2 is used to increase of the steepness of the pulse. The primary pulse arrives, through the separating line, at a spark gap with a rather small electrode separation, which, under the action of this pulse, is broken down at a high overvoltage. To attain a required delay time, the peaking gap is filled with nitrogen at a pressure of about 1 00 atm. This generator produced pulses of amplitude 1 0 kV with a rise time of 0.3 · 1 o-9 s. A peaker operating in atmospheric air with short-rise-time primary pulses was used in a generator described by Vorob'ev and Mesyats ( 1 963). The primary pulse rise time was 5 ns. For the primary switch, a switch with three spark gaps was used and an adjusting capacitor was connected in parallel with the energy storage line. Two-electrode gas-discharge peakers have a narrow range of operating voltages. To remedy this flaw, it was proposed (Mesyats, 1 974) to use for the peaker a great number of series-connected small gas gaps (microgaps of width �0. 1 mm). As the gaps are very small, an output pulse of short rise time can be obtained even at atmospheric pressure, and the value of td necessary for condition ( 12. 14) to be satisfied is chosen by varying the number of gaps and the ground capacitance of the electrodes. For this type of peaker, a wide range of operating voltages can be realized without rearrangement of the gaps. With the number of gaps N = 25 and the width of each gap equal to 200 J..lm for the range of pulse amplitudes from 1 5 to 40 kV, a pulse rise time of 0.7 ns was obtained (Mesyats, 1 974) (Fig. 12.8).

Figure 12. 8. Design elements of the peaker: 1 - washer; 2 - fixing dielectric washer; 3 dielectric cylinder, and 4 - metal screen

A wide range of operating voltages of a peaker can also be attained with a discharge over the surface of a dielectric in vacuum at a nonuniform field in the cathode region. As shown above, if the field at the cathode is

GENERA TORS WITH GAS-DISCHARGE SWITCHES

227

nonuniform and there is a significant normal field component, the dielectric surface discharge in vacuum features the time td weakly dependent on voltage and highly stable from discharge to discharge and a short switching time (� 1 o-9 s). Besides, if the difference in diameters between the cathode and the dielectric is great, the pulsed breakdown voltage is much lower than the de breakdown voltage because of the highly nonuniform field distribution over the dielectric surface under the action of pulses (see Chapter 3). It was proposed (Bugaev and Mesyats, 1 964) to harness these properties of a discharge over a dielectric in vacuum in developing nanosecond peakers with a wide range of operating voltages that have highly stable time characteristics and small dimensions due to the high dielectric strength of vacuum. Figure 1 2.9 presents the arrangement of a vacuum peaker (Mesyats, 1 974). Used for the dielectric was a steatite ceramic disk of thickness 1 mm and diameter 1 1 mm; the diameter of the cathode was 5 mm. The vacuum in the peaker was 1 o-s mm Hg. The peaker operated without rearrangement in the range of operating voltages from 5 to 40 kV with the rise times of the primary and the secondary pulse equal to 20 and 0.5 ns, respectively. The range of operating voltages of the peaker can easily be varied by varying the dimensions of the ceramics. When changing the pulse polarity, it is necessary to interchange the input and the output of the peaker.

2

Figure 12. 9. The main elements of a vacuum peaker: 1 cathode; 2 -anode; 3 - dielectric; 4 screen protecting the envelope from electrode metal vapors, and 5 envelope -

-

For the production of nanosecond high-current pulses, water-insulated lines are used as energy storage and transmission lines. In this case, to do away with the bushing isolator between the line and the peaker, the peaker is immersed in water.

228

Chapter 12

REFERENCES Binder, L., 1 928, Die Wanderwellenvorgiinge auf Experimente/ler Grundlage. Springer, Berlin. Bugaev, S. P. and Mesyats, G. A., 1 966, A Spark Peaker. USSR Inventor's Certificate No. 1 86 033 (October, 1 964). Fletcher, R. C., 1 949, Production and Measurement of Ultrahigh Speed Impulses, Rev. Sci. Instrum. 20:86 1 . Grunberg, R., 1 965, Gesetzmiij3igkeiten von Funkenentladungen im Nanosekundenbereich, Z. for Naturforsch. A. 20:202-2 12. Martin, T. H., Guenther, A. H., and Kristiansen, M., eds., 1 996, J. C. Martin on Pulsed Power. Plenum Press, New York. Mesyats, G. A., 1 963, Theory of the Peaking Spark Gap, lzv. Vyssh. Uchebn. Zaved. , Fiz. 1 : 1 37- 1 4 1 . Mesyats, G . A., 1 974, Generation of High-Power Nanosecond Pulses (in Russian). Sov. Radio, Moscow. Rompe, R. and Weizel, W., 1 944, Uber das Toeplersche Funkengesetz, Z. filr Physik. 122:636. Vorob'ev, G. A. and Mesyats, G. A., 1 963, Techniques of the Formation of Nanosecond High- Voltage Pulses (in Russian). Gosatomizdat, Moscow. Weizel, W., 1 953, Berechnung des Ablaufs von Funken mit Widerstand und Selbstinduktion im Stromkreis, Z. filr Physik. 135:639-657.

Chapter 1 3 MARX GENERATORS

1.

NANOSECOND MARX GENERATORS

We spoke of the Marx voltage multiplication circuit in Chapter 1 . Recall that in this circuit a number of capacitors are charged in parallel to a voltage V0• Then the capacitors are connected in series by means of closing switches and are discharged into a load at a voltage NV0, where N is the number of capacitors (see Fig. 1 .2). In circuits of this type, gas-filled spark gaps are used, as a rule, as switches. These circuits have found very wide application in pulsed power technology. In the technology of generation of high-power nanosecond pulses, Marx generators (MG's) are used in two cases. First, they are used as charging devices for the energy storage lines of generators. In this case, they operate on the microsecond time scale. An MG-charged energy storage line is discharged to generate a nanosecond pulse. The voltage of generators of this type reaches ten megavolts. Second, when properly configured, an MG is capable of generating pulses of duration 1 o-s or even 1 o-9 s directly across the load. The peak voltage, as a rule, is not over 1 MV. In this section, we shall deal with the first and second types of Marx generator. To initiate a discharge in a Marx generator, an additional electrode is mounted in the first spark gap or the gap and the cathode are illuminated with ionizing radiation. All other spark gaps are broken down sequentially due to an overvoltage across the discharge gap. It should be noted that the breakdown and the discharge sustainment in the spark gaps are possible in the presence of stray capacitances. Stray capacitances should sustain the discharge before the breakdown of the last spark gap into the load. The

Chapter 13

230

problems concerned with the design calculations of charging and discharge circuits and the determination of the pulse parameters for Marx circuits were discussed by Smimov and Terentiev (1964). The equivalent circuit diagram of the discharge circuit of a nanosecond pulse generator is similar to that given in Fig. 1 2. 1 . Here, C0 = C N, is the MG capacitance; instead of V0 it is necessary to take n V0, where C and V0 are, respectively, the capacitance and voltage of a stage of the MG; L is the inductance of the discharge circuit, Rs is the resistance of the spark gaps; K is a perfect switch, and N is the number of stages. Depending on the conditions (the pressure in the spark gaps, the parameters of the circuit, the operating voltage, and the type of the load), the value of one or another parameter of the circuit can be neglected. We assume that the spark gaps are broken down under near-de conditions. Then the process in the discharge circuit can be analyzed assuming that the spark resistance varies by the Rompe-Weizel formula. For the pulse FWHM with RioadCo/9 � 20, it can be obtained that

I

lp

::::: 2.28 12.3Rload2 Co , 2pd /aV0 R1oadCof9

(13.1)

+

where e ::::: If » 10, the spark will have almost no influence on tp. Thus, the pulse amplitude and duration depend not only on the parameters R1oad and C of the discharge circuit, but also on the value of 9, which is determined by the gas properties and pressure and by the electric field in the discharge gap. The smaller 9, the larger the amplitude of the pulse and the shorter its duration. For a fixed voltage V0 pd, we have 9 oc p- 1 • Hence, the higher the gas pressure, the smaller the value of 9. For air at atmospheric pressure and d = 1 , we have 9 ::::: 2 ns, i.e., according to (13.1 ) , the pulse duration, even if the circuit has no inductance and resistance, cannot be shorter than 4 ns. Hence, the necessary condition for the production of pulses of nanosecond duration is that the spark gap should be immersed in compressed gas. At a high gas pressure, the value of 9 becomes so small that the spark gap can be considered a perfect switch. For the circuit shown in Fig. 1 2. 1 , the pulse rise time between 10% and 90% of the amplitude will be given by tr = 2.2L/Rload · Hence, to produce a pulse of rise time about 1 o-9 s, it is necessary that the inductance of the discharge circuit, L, be not over 1 o-9R1oad· For R1oad = 1 00 0, it is necessary to have L < 1 o-7 H. The inductance of the discharge circuit, L, is determined in the main by the dimensions of the generator. For a given pulse amplitude, these dimensions are determined by the dielectric strength of the medium surrounding the generator. To increase the dielectric strength of the medium, it is necessary to place the generator as a whole in •

:::::

MARX GENERATORS

23 1

compressed gas since in this case the value of e and the inductance L of the discharge circuit ofthe generator simultaneously decrease. Some versions of generators of nanosecond high-voltage pulses, designed based on the Marx circuit are known. A first generator of this type with a voltage of up to 400 kV was built by Schering and Raske (1935). To reduce the switching time, the spark gaps were placed in a chamber with carbon dioxide under a pressure of 1 3 atm. The generator produced voltage pulses with a rise time of 1 o-8 s. In another version of the generator (Mesyats, 1 960), to reduce the inductance of the discharge circuit, six coaxial lines were used as energy storage devices. This generator was capable of producing rectangular pulses of voltage 100 kV and rise time 10-8 s. In the experiment described by Broadbent (1960), to shorten the triggering delay time of an MG, trigger electrodes were mounted in its discharge gaps. It is well known that the stability of operation of spark gaps depends on the intensity of ultraviolet irradiation of the cathode. To make the operation of the spark gaps of an MG more stable, Smith (1 958) proposed to shunt the first spark gap by a capacitor whose capacitance was comparable to that of one stage of the generator. In this case, intense illumination from a high-power spark formed in the first gap considerably shortened and stabilized the breakdown of all subsequent gaps. Charbonnier et al. ( 1 967) described a Marx generator in which 1 60 stages with the capacitors of an individual stage having a low self-inductance were used for the production of 2-MV pulses of duration 50 · 1 0-9 s. To reduce the dimensions and to shorten the time delay to breakdown of the gaps, the generator units were placed in compressed gas. A small-sized nanosecond high-voltage pulse generator was developed (Gygi and Schneider, 1 964) in which the discharge circuit had a low inductance because the system as a whole was immersed in compressed gas. The generator consisted of ten stages connected in a Marx circuit and was used to power a spark chamber. At the output of the generator, a pulse of duration �5 ns and amplitude 200 kV was obtained. The delay between the application of the trigger pulse and the onset of the output voltage rise was �10 ns with a jitter no more than 1 ns. In contrast to the conventional MG circuit, coupling capacitors were connected between the individual stages of the generator and this considerably speeded up the process of breakdown of the spark gaps. The use of coupling capacitors allowed, if the first gap was broken down, a 100% overvolting of the second gap irrespective of the number of stages. To eliminate statistical fluctuations of the breakdown delay time, an auxiliary corona discharge was used. This discharge was initiated at needles placed opposite the discharge gaps and provided permanent presence of free electrons at the cathode. The system as a whole,

232

Chapter 13

together with the spark gaps and charging resistors, was immersed in nitrogen at a pressure of 7 atm. Keller and Walschon (1 966) developed a 1 00-kV pulse generator. To stabilize the breakdown of the gaps, an optical path was used that was formed by the chamber walls coated with a reflecting material. The nitrogen pressure in the chamber was 3 atm. The rise time of the pulsed voltage across a resistive load was 3 ns.

Figure 13. 1. Schematic diagram of a Marx generator with controllable pulse duration and peak voltage: I - ring insulators (organic glass); Rt. R2 - charging resistors; SG1-SG1 5 module spark gaps; SGP - peaking spark gap; SJ, s2 - bellows of the cathode-moving hydraulic drive; Cd - capacitive voltage divider; C - cathode holder; A - anode unit; Rsh diode electron-current shunt; SGch - chopping spark gap; C1-C1 5 - module capaciwrs; T 1 -T3 - triggers; SG1r - trigger spark gap; V0 - charge voltage; Id - diode current; Vd - diode voltage

A 500-keV nanosecond electron accelerator was developed (El'chaninov 1 974) based on a ceramic capacitor MG that produced pulses of controllable duration and amplitude. Besides, it showed low-jitter operation (Fig. 1 3 . 1 ). Each of the 1 5 stages of the generator represented a unified section consisting of six capacitors connected in parallel, spark gaps so�. and charging resistors R 1 and R2 • The stages were stacked with the help of organic-glass ring insulators 1 to form a column. The section high-voltage insulator was assembled from alternating metal and polyethylene rings; the potential was distributed over them with the help of resistors. The second and third stages of the generator were equipped with devices intended for illumination of the spark gaps. This stabilized the triggering of the spark gaps and extended the range of their operating voltages. Illumination was

et al. ,

cl

MARX GENERATORS

233

carried out with the ultraviolet radiation of a ferroelectric surface discharge; each illuminating device was triggered from the previous stage. The Marx generator was driven by a pulse generator with a thyratron at a jitter no more than 5 ns. To control the pulse duration within the limits 3-50 ns, a chopping spark gap SGch with smooth adjustment of the gap spacing was connected to the generator output. The generator was placed in a steel tube filled with nitrogen at a pressure of 1 0 atm. The graphite cathode produced a beam with current density uniformly distributed over a large area. The MG voltage could be controlled within 20% by varying the charge voltage, and by varying the pressure in the MG column it was possible to vary the output voltage, not changing the width of the spark gaps, in the range 80-450 kV.

2.

CHARGING OF A CAPACITIVE ENERGY STORE FROM A MARX GENERATOR

The idea of pulsed charging of the capacitive energy store (capacitor or line) of a generator with the use of a Marx generator proposed by Mesyats ( 1 962) was of fundamental importance in the production of high-power nanosecond pulses. Vorob'ev and Mesyats ( 1 963) described a Marx generator that charged, through an additional spark gap, a coaxial line segment filled with transformer oil. The circuit diagram of the MG with a compensating capacitor (Cc) is given in Fig. 1 3 .2. Originally, this capacitor was intended to compensate the influence of the self-inductance of the Marx generator on the pulse rise time. A theory that interprets the operation of this type of generator in various modes is given by Vorob' ev and Mesyats ( 1 963).

Figure 13.2. Circuit diagram of a Marx generator with a compensating capacitance (a) and its discharge circuit (b)

234

Chapter 13

The MG's using an additional capacitive energy store have found wide application. Vorob'ev et a/. (1963) described a generator producing a 1 50-kV pulse of rise time 5 ns across a resistive load. The design of the coaxial capacitor was similar to that described by Vorob' ev and Mesyats ( 1 963 ). A description of a voltage generator capable of producing 500-kV pulses with a rise time of 1 .5 ns was given by Vorob'ev and Rudenko ( 1 965). The compensating capacitor was insulated with glycerin (s 40). Due to the increase in dielectric strength of the insulator at short times of voltage action, the capacitor and the discharge chamber, which was structurally united with the capacitor, could be considerably reduced in dimensions. The design of the generator is shown schematically in Fig. 1 3.3. The low-inductance capacitor 3 is a coaxial line segment consisting of two cylinders with the space between them filled with glycerin. The capacitance of capacitor 3 was 1 nF and the capacitance of the Marx generator used as a high voltage source was 12.5 nF at a voltage of 1 50 kV. The inner cylinder of the capacitor also served as the case of the discharge chamber 4 filled with nitrogen at a pressure of 1 6 atm in which a spark gap switch was placed. The distance between the electrodes of the spark gap could be adjusted without depressurization of the chamber.

=

2

:I �6 : I � II :I �6 II '-I-�

5

Figure 13.3. A 500-kV nanosecond pulse generator

The transmission line 5 of length 4 m with a wave impedance of 1 00 Q was made as a brass tube 8 em in diameter with an inner conductor 8 mm in diameter, filled with transformer oil. Capacitor 1 was connected to the MG output through an additional inductor 2. This provided a more efficient multiplication of voltage across the capacitor; however, the amplitude of the first wave was not twice, but only by a factor of 1 . 7 greater than the operating voltage of the generator. At the open end of the transmission line, the voltage doubled and, as a result, it was a factor 3 .4 greater than the voltage developed by the Marx generator. Voltage pulses of amplitude 1 MV and rise time about 5 ns were produced (Vorob'ev et al. , 1 968) by discharging a low-inductance capacitor charged to about 250 kV into a

MARX GENERA TORS

235

transformer consisting of uniform line segments with an increasing wave impedance. MG's of this type were used to power the first Soviet streamer chambers. The optimum conditions for energy transfer from the capacitors of an MG to an energy storage line was given by Graybill and Nablo ( 1 967), Link ( 1 967), Martin ( 1 969), and Bernstein and Smith ( 1 973).

3.

TYPES OF MICROSECOND MARX GENERATOR

The occurrence of new fields of application of pulsed accelerators of electrons and ions, such as inertial confinement fusion, high-power gas lasers, and sources of soft and hard x radiation, called for high-power generators rated at megaampere and higher currents and voltages of up to ten megavolts. Marx generators have found wide use in these fields. To reduce the overall dimensions of these devices, when they are insulated with compressed gas or dielectric liquid, close-type MG's became widespread in recent years. A generator of this type is placed in a metal tank, and this increases the capacitance of the stages relative to the grounded walls of the tank. To increase the power of an MG and decrease its inductance, several sections are connected in parallel. To make the operation of these sections this connection reliable, new circuits have been designed that use capacitive and other type coupling elements, three-electrode spark gaps in each stage, and special high-impedance trigger sections. It is well known (Kremnev and Mesyats, 1 987) that simultaneous operation of several MG's is possible if they are switched into the load within a time during which an increase in voltage across the load yet does not reduce the voltage across the spark gaps of the output stages; that is, the spread in operation times of the generators should be much less than the rise time of the voltage across the load, which is several microseconds for the generators used for charging capacitive energy stores and not over 0. 1 J.lS for the generators operating into a resistive load. Hence, for stable simultaneous operation of several generators, it is necessary that the generators operate with the same delay time and about 1 0 ns jitter. If in the switches have air gaps of width about 1 em under a pressure of 1-2 atm, it is possible to attain jitters less than 1 0 ns under the conditions of a uniform field of about 1 00 kV/cm with preliminary illumination of the gaps. Stable simultaneous operation of several MG sections is attained, first of all, by eliminating the possibility of the self-operation of a section in the case where the voltage between the electrodes of the trigger spark gap is much lower than the de breakdown voltage. This implies that the factor of safety

236

Chapter 13

ks = Vdc i Voper , where Vdc is the de breakdown voltage and Voper is the gap operating voltage, is greater than unity. At the same time, it is necessary to have electric fields of the mentioned strength in the spark gaps. All this resulted in the creation of special versions of Marx generator and Marx-like systems (Fitch, 1 97 1 ) . The need in MG' s of higher and higher power resulted in the zigzag configuration of energy storage capacitors. It has been revealed that adjacent capacitors of even and odd stages have stray capacitive couplings among themselves, which speed up the operation of the spark gaps of the first stages. Using this phenomenon, an MG with additional capacitive or resistive couplings through one or several stages has been developed. An essentially new point here is the theoretical opportunity of producing more than a double overvoltage across the two-electrode gaps of the MG and fast and reliable operation of the MG into a load. It has appeared inexpedient to increase the power of single MG's because of the high self-inductance of the discharge circuit, the high inductance and active resistance of the operating gaps, the rather unreliable operation of this type of MG under the conditions of emergency breakdowns, and the difficulties involved in the standardization of the design elements. The development of high-power generators has gone on a way of parallel connection of a great number of MG's of comparatively low power (Bernstein and Smith, 1 973; Kremnev and Mesyats, 1987; Prestwich and Johnson, 1 969). In this case, the failure of one of the capacitors causes lesser disturbances in the operation of the system. Besides, the techniques of manufacturing and assembling of an MG, the replacement of defective units, and the combining of the generator output parameters become simpler. For the continuous operation of many MG sections, the triggering of individual sections, their operation into a common load, the influence of stray couplings between elements on the operation of the spark gaps, and some accompanying phenomena are of principal importance. For triggering a great number of simultaneously operating MG's, rather low-power trigger MG's are used (Fitch, 197 1). In simultaneously triggered MG's, the spark gaps are made three-electrode; a pulse from the trigger MG is applied to the trigger electrode of each of them. Making a parallel connection of MG's more reliable, this, however, complicates the circuit as a whole and calls for modeling tests. With increasing number of stages, the losses increase and the influence of the stray parameters or the chopping spark gap on the overvolting during the operation of the MG and, consequently, on its triggering becomes substantial (Bastrikov et a/. , 1981 ) . This complicates the realization of one or another idea in a multisection MG placed in a metal tank. The main design features and schematic circuits of the most high-power, megajoule MG's are described below.

MARX GENERATORS

237

Prestwich and Johnson ( 1 969) described the circuit of the MG's used in the Hermes I and Hermes II accelerators. In these generators, the energy storage capacitors were charged on two sides from sources of de voltage, + V0 and V0, through charging resistors. As a high-voltage pulse was applied to the trigger electrode of each spark gap in the first (bottom) row, the capacitors of this row were connected in series. The voltage at the output of the row was equal to NV0, where N is the number of capacitors in the row (number of stages). The Hermes I machine was capable of storing 0. 1 MJ of energy for the MG output voltage equal to 4 MV. For the Hermes II accelerator, an MG was developed which was structurally similar to the previous one with the only difference that each stage contained two parallel-connected 0.5-J..tF , 1 00-kV capacitors. To increase of the breakdown voltage, the lengths of the spacers were changed. The MG consisted of 1 86 capacitors, arranged in 3 1 rows, and 93 spark gaps. It was placed in a steel tank of diameter �6 m and length � 1 2 m, filled with transformer oil. The minimum distance from the MG to the tank wall was about 1 .2 m. The generator was capable of storing 1 MJ of energy with the capacitors charged to 1 03 kV. The MG capacitance with the capacitors connected in series was 5.38 nF. The total inductance and the series resistance were equal to 80 J..tH and 20 n, respectively; the charging resistance of each section was 1 .5 kQ. The generator could charge a long line of capacitance 5.6 nF to a voltage of 16. 1 MV within 1 .5 J.!S; however, its operating parameters were the following: charge voltage 73 kV and stored energy 0.5 MJ. For this MG, the generator capacitance was estimated to be 45 pF, the capacitance of capacitors in a stage 1 90 pF, and the ground capacitance of a stage < 1 0 pF. Both MG's, judging by the diagram of the breakdown of the spark gaps given by Prestwich and Johnson (1 969), were triggered within -2 J..lS . With these triggering delay times, there was no need to illuminate the spark gaps or specially strengthen the field in them. Therefore, the pressure in the spark gaps was not over several atmospheres, and the electrode geometry had no peculiarities. Since in all cases the insulator was transformer oil, there was no need to speed up the process of charging of the line. Bernstein and Smith ( 1 973) described the Aurora system capable of storing 5 MJ of energy. Four MG's connected in parallel served as primary energy stores. Each MG consisted of 95 stages, each stage containing four parallel-series-connected 1 .85-J..tF , 60-kV capacitors. The capacitance of each MG was 78 nF for the output voltage equal to 1 1 .4 MV; its inductance was 1 2 J..tH . For triggering the spark gaps of these MG's, a special MG with an output voltage of 600 kV was used. In the high-power MG's, the first three stages became series-connected as trigger pulses were arrived simultaneously at the trigger electrodes of their spark gaps. With a small -

238

Chapter 1 3

stray capacitance between adjacent rows and a rather large interelectrode capacitance, the initial overvoltage across the unbroken gaps was rather low at small N. It is difficult to take into account the influence of "ground" capacitances of stages. All this results in the need to include additional resistive couplings in the circuit and to replace the corresponding two­ electrode spark gaps by three-electrode ones. Thus, we obtain a hybrid MG circuit with resistive couplings. The presence of couplings of this type allows one to extend the range of controllable operation to reduce the rms time spread in triggering of all MG's to approximately 1 0 ns with the triggering delay time of each MG equal to 1 f..I.S and to reduce the jitter even in no-load operation. The charging of all capacitors of the MG demanded 2 min. To exclude erroneous start of the Aurora system as a whole with incompletely charged capacitors, the output of the MG to the double lines was shunted with resistors, which were disconnected on complete charging of the capacitors. The diagram of connection of the gaps in the MG circuit was not given by Prestwich and Johnson ( 1 969). Relevant data were reported in detail for the MG's used in the PBFA II ion accelerator (Schneider and Lockwood, 1 985; Woolston and Ives, 1 985). In total, the PBFA II accelerator consisted of 36 Marx generators, each capable of storing 370 kJ of energy. Each of the 60 1 .37-f..I.F capacitors of the MG was charged on two sides to 95 kV. The output voltage of the MG was 1 7 MV (Turman et a/. , 1 985). The mass of one generator was 7.2 t, its overall dimensions were: length 2. 1 m, width 1 .8 m, and height 4.2 m. Five columns of capacitors on one side of the assembly were coupled to form five columns on the opposite side. Two adjacent columns on the different sides of the assembly formed a discrete row. Between these columns, three-electrode spark gaps operating by the principle of field distortion were connected. Their trigger electrodes had holes. Adjacent columns on one side were connected by flat aluminum busbars. The 30 spark gaps of the MG operated in SF6 under an optimum pressure of 0.2 MPa. The final version of the trigger circuit of the MG provided an average triggering delay time of -200 ns with 4-ns jitter for an individual generator. Much attention was given to the trigger circuit of a single MG for the PBFA II accelerator (Schneider and Lockwood, 1985). The zigzag configuration that had been used earlier (Bernstein and Smith, 1 973) was retained. In the previous versions (Bernstein and Smith, 1 973; Prestwich and Johnson, 1 969), insufficient attention had been given to the jitter of the operation of an MG. Since in PBFA II thirty six MG's operated independently, each into its own module, it was required to reduce the rms jitter of the triggering delay time of one MG to 4 ns. This was achieved by means of numerical modeling and comparison of the predictions with

MARX GENERATORS

239

experimental data obtained with the use of light and magnetic gages (Lockwood, et a/. , 1 985). The trigger pulse of amplitude 500 kV and rise time 80 ns was applied, through resistors, simultaneously to the trigger electrodes of all spark gaps of the first row. This pulse was generated by a six-stage trigger MG with twelve 0. 1 5-j..!F capacitors charged on two sides to 50 kV. The experiments showed, first, that the jitter of the operation of the main MG decreased with increasing charge voltage or decreasing the gas pressure in the discharge gaps, and the optimum pressure was determined. Second, it was found that the main contribution to the jitter was given by the triggering of the gaps of the first two rows, and that the jitter decreased when additional resistive couplings were introduced between the trigger electrodes of the first and second rows. A similar principle of powering one module from one Marx generator was developed for the Angara-5 system (Bolshakov et a/. , 1 982) earlier than the publication by Woolston and Ives ( 1 985) had appeared. This system consisted of individual modules arranged in radii around a reactor chamber in which a target was placed. Each module represented a pulsed electron accelerator producing electron beams of energy 2 MeV and current 0.8 MA with a pulse duration of 85 ns. In each module, the primary energy store was a Marx generator capable of storing 200 kJ of energy. The MG of a module consisted of three parallel branches (sections), each containing 14 stages. For the spark gaps of the MG, three-electrode spark gaps with field distortion, immersed in gas, were used. To reduce the inductance of the discharge circuit, the spark gaps were arranged on the outer perimeter of the generator. To attain low-jitter operation of the MG sections, longitudinal and transverse resistive couplings were used in them. The generator was erected in a compartment of the common tank of diameter 3 m, filled with transformer oil. With the energy storage capacitance of the generator equal to 78.6 nF, the output voltage of the MG was 2.3 MV. The average triggering delay time of the generator reached 600±30 ns with a 1 00- 1 50 ns spread in triggering of individual branches. This rather large spread seems to be due to the absence of illumination of the trigger electrodes of the spark gaps (Sterligov et a/. , 1 976). 4.

MULTISECTION MARX GENERATORS

Koval' chuk and his co-workers, when developing the Gamma, GIT-4, and GIT- 1 2 machines at IHCE, have created multimodule Marx generators capable of storing large amounts of energy. These generators contain a great number of parallel-connected sections being also Marx generators, each

240

Chapter 13

storing a much lower energy with the same voltage as the main MG (Kremnev and Mesyats, 1 987; Bastrikov et al. , 1 989; Koval'chuk et al. , 1 989). Let us consider the operation of this type of MG with the Gamma microsecond electron accelerator as an example (Koval' chuk et al. , 1 989). For generators of this type, a wide range of powers and energies can be achieved by parallel-series connection of identical sections and use of various types of capacitors. It has been shown (Vorob ' yushko et a/. , 1977; Babykin and Bartov, 1 972) that simultaneous operation of MG sections is possible if they are switched into a load when the voltage across the load yet does not reduce the voltage across the spark gaps of the output stages, i.e., the spread in triggering delay times of the sections must be much shorter than the rise time of the voltage across the load. In every specific case, the rise time is determined by the characteristics of the generator and load, making some microseconds for generators used to charge capacitive energy stores and less than 0. 1 f.!S for those operating into a resistive load. Hence, for stable simultaneous operation of generators, the spread in their triggering delay times must be no more than 1 0 ns. If the discharge gaps are about 1 em wide and operate in air at a pressure of 0. 1-0.2 MPa and if they are pre­ irradiated and the (uniform) electric field in them is about 1 00 kV/em, it is possible to attain a less than 1 0-ns jitter of their triggering delay time (Kremnev and Mesyats, 1 987). For stable continuous operation of the sections, it is necessary, first of all, to eliminate the possibility of their self­ operation; that is, the voltage Vsa between the electrodes of the spark gaps must be much lower than the de breakdown voltage and then we have for the factor of safety ks = Vsa > 1 . At the same time, it is necessary that the field in the spark gaps be as strong as mentioned. Figure 1 3 .4 shows the complete circuit of a section of an MG with three­ electrode spark gaps and capacitive coupling of the middle electrode with the previous stages (Bastrikov et al. , 1981 ). The designations in this figure are as follows: and are, respectively, the capacitances of coupling capacitors (259 pF), energy storage capacitors (0.4 f..I.F), equivalent = 40 pF), capacitances between the energy storage capacitors ( = capacitances between the screen and the case (46 pF), and capacitances between the screens (30 pF). Besides, and are, respectively, the inductance of the capacitors ( 1 50 nH), the inductance of the leads = = 1 50 nH), and the stray inductance (0.45 f.!H). In the main spark gaps with identical gaps, G 1 and G2 , the voltage is initially distributed fifty­ fifty between them. The trigger spark gap, for the extension of the triggering range and shortening the jitter, is made three-gap and in the charging mode, the potentials at electrodes 1-4, in the direction from the ground, are, respectively, zero, Vo/4, Vo/2, and V0 • The gaps Go and SG0 of the trigger spark gap are equal to a half of the gap G 1 or G2 of the spark gaps of the

Vdc I

Vdc,

Ccouph C, Ct . C2, C3, C4

C1 C2

L, Lt. L2, L0

(L1 L2

MARX

GENERATORS

241

middle stages. The additional discharge switch serves for preliminary illumination of the trigger spark gap. The capacitors of the are charged from a high-voltage source of de voltage + through the voltage divider cables and charging resistors

S0

Lo ... L2,

R1 • V0

MG

Rd,

Figure 13.4. Circuit diagram of the GM of the Gamma accelerator: Rct voltage divider (50 Q); Rshh Rsh2• Rsh3 - shunting resistors; L2 - Vof4 line; SGtr - trigger spark gap; Ctr = 750 pF - trigger capacitance; R = I MQ; R5 1 0 ill; R1oad - load resistance; L1oad - load inductance (other symbols are described in the text) -

=

The resistors (5 1 0 Q) and ( 1 kQ) serve to decouple the circuits on triggering and R4 (5 1 Q) serves to protect the cable (line with voltage against the voltage wave reflected from the load of the By means of the trigger spark gap pulses of amplitude and 1 0%-90% rise time tr ::::; 30 ns for triggering and illumination of the spark gap are formed in the cables and (line with voltage and trigger line). As the trigger pulse arrives at the gaps and of the trigger spark gap, the voltage across these gaps can increase three times compared to its initial value. The overvoltage across the gap increases more rapidly than across the gap This just determines the sequence in which the gaps in the first (trigger) spark gap are broken down: and After the operation of the first spark gap, the voltage across the gap 0 1 of the second spark gap can be tripled compared to its initial value. For the gap of the second spark gap broken down, the voltage across the capacitor Ccoupi i is determined by the formula

R2 R3 L0 MG. SGtr, Vo/2 So L1 L3 G2 SG0 Vo/2 02 SG0. G2, SG0, Go. 01 -

Vo)

242 Vccoupll (t) Vo [o. 5 - Ccoupln.S/C + 1 (1 =

{

]

Chapter 13 (13.2)

cos rot) ,

[

]}

05

where ro = CCcoupn / C + 1) / Ccoupll (L + Lt + �) ' , obtained in view of the initial conditions J!;; (O) = (0) = From (13.2) it follows that for Ccoupll « C the voltage is a maximum: ; that is, in an ideal case, the voltage across the gap 02 of the second spark gap can be increased fivefold. This provides low-jitter operation of the first stages of the MG. The voltages across the gaps of the first spark gap are increased less resulting from the than three times because of the decrease in potential triggering resistances and the final resistance of the channel.

-Vo, Vccoupn Vo/2V .coupn :.:::: -2.5Vo c V0

1

2

3

4

Al_ I'r+---H---+---

5 M---+--- 6 _-tk:----t- 7

9 10

Figure 13. 5. Schematic diagram of a voltage pulse generator: 1 - auxiliary spark gap; 2 charging resistors; 3 spark gap column; 4 auxiliary electrode of the first spark gap; 5 coupling capacitor; 6 duralumin screen; 7 capacitive energy store; 8 load; 9 tank with transformer oil; 10 stack; 11 spark gap electrodes -

-

-

-

-

-

-

-

-

MARX GENERATORS

243

The design of the generator is shown in Fig. 1 3.5. Depending on specific purposes, 6-, 1 2-, 20-, and 33-stage versions of the generator were realized. The design feature is that all spark gaps 3 are placed in common case 9, and so their mutual irradiation is attained. To reduce the voltage gradients, the generator is screened stage by stage with ring screens 6, which are connected to the middle electrodes of the spark gaps. The spherical electrodes 40 mm in diameter are made of duralumin, and the case of the spark gaps is fabricated from a polyethylene tube 140 mm in diameter. Dry air is fed to the spark gaps. To increase the lifetime of the spark gaps, the air in the case was completely renewed after each operation of the generator. Charging resistors 2 are fabricated from polyethylene tubes inserted into the ring terminals of the electrodes of spark gaps 3 and filled with water. For contact to water, stainless steel rods are used. For a 1 2-stage section of the MG, stack 1 0 and all power supply utilities are mounted on the cover of tank 9 of diameter 1 .2 m and height 3 m, filled with transformer oil. The load of the MG during its testing and adjustment was either a piece of double-wound Nichrome wire or a water resistor. It should be noted that because of the stage-by-stage screening, additional elements are involved in the circuit shown in Fig. 1 3.4: the ground capacitances of the screens, C3, and the capacitances between two adjacent screens, Figure 1 3.6 presents the general view of a 33-stage section of an MG with open screens. The energy storage capacitors are located on a chassis made of delta wood. Each screen can be opened, providing an easy approach to stage elements in wiring. Sockets for power supply, control, and trigger cables can be seen which are located on the front metal flange. On the other end face, the output high-voltage terminal is placed.

c4.

Figure 13. 6. General view of the Gamma generator module with the screens open

244

Chapter

13

The design of the section admits its operation in both the vertical and the horizontal position. Its rectangular shape in plan allows a section assembly with a minimum clearance. A megajoule pulse generator intended for powering the Gamma accelerator (Bastrikov was developed and built at IHCE. The generator consisted of simultaneously operating sections, each containing stages. The sections were assembled in a metal tank shaped as a truncated pyramid and filled with transformer oil. The MG had a system of oil feeding and dumping, a system of preparation of air and its feeding into the spark gaps units of the sections, and a fire-prevention system. The management of the MG and all systems was carried out from a control panel. The MG capacitance with the capacitors connected in series was J.!F and its inductance was H. With the maximum charge voltage V0 = kV, an output voltage of MV, a stored energy of MJ, a volumetric energy density kJ/m3, and a mass energy density of kJ/t. were obtained. A more of detailed description of this Marx generator can be found in the monograph by Kremnev and Mesyats Numerical methods for simulating the processes in the MG types described above are given elsewhere (Heilbronner, Koval'chuk and Kremnev, Sigorsky and Petrenko, Meek and Craggs,

22et a/. , 1982)

33

0.264 1.04 8.2

1.7x10-6 2.8 9.2 1976;

5.

(1987). 1971; 1953).

85

1987;

HIGH-POWER NANOSECOND PULSE DEVICES WITH MARX GENERATORS

The Marx generators described above are primary charging devices of high-power nanosecond pulse generators (Fig. An MG charges a primary energy store (capacitor or line) within about J.!S. The pulsed charging of an energy store enables one to use nonconventional liquids for insulation of MG's, such as water and glycerin, and not just transformer oil. Besides, it is possible to work with much stronger electric fields, allowing one to reduce the overall dimensions of the device and to use a nontriggered spark gap as the main switch. The primary energy store is discharged through the main switch into a pulse-forming line, which in turn is discharged through a peaker into a transmission line. The transmission line is connected to a load through another peaker. The load can be the diode of an accelerator of electrons or ions, a gas laser, the resonator of a high-power microwave generator, a z-pinch shell, the diode of a high-power x-ray generator, etc. The circuit in Fig. is a generalized one, since, depending on the parameters of the pulse and its purpose, some or other elements can be

13.7). 1

13.7

MARX GENERATORS

245

absent. In particular, the second peaker, as a rule, is used not only to shorten the pulse rise time, but also to reduce the amplitude of the prepulse. The latter, if an electron diode is used as a load, results in the occurrence of premature explosive electron emission and undesirable filling of the diode with plasma before the arrival of the main pulse. Therefore, in some circuits where the prepulse does not play a role, the second peaker may be absent. The transmission line can serve simultaneously as an impedance converter, for example, an exponential strip or coaxial line. In some generators, there is no peaker at all, and the pulse, after pulse-forming line, arrives immediately at the load.

Figure 13. 7. Elements of the unified circuit for the production of nanosecond high-power pulses: 1 Marx generator, 2 capacitive energy store, 3 pulse-forming line, 4 transmission line, 5 load, 6 main switch, 7 - first peaker, 8 second peaker -

-

-

-

-

-

-

Let us consider a circuit with a Marx generator as a charging device in the historical aspect. Mesyats ( 1 962) proposed to charge a low-inductance generator from a Marx generator to eliminate the effect of the inductance of its discharge circuit on the rise time of the pulse. A generator that was capable of producing 1 50-kV pulses with a current of 5 kA is described elsewhere (Vorob' ev and Mesyats, 1 963; Vorob'ev et a/. , 1 963), The generator was powered by pulses from an MG. The pulse-forming and transmission lines were fabricated from coaxial copper tubes insulated with transformer oil. The spark gap was in a sealed chamber under an air pressure of 1 0 atm. Pulses of rise time no more than 1 ns with a flat top (20 ns) appeared across the load of the generator. The generator involved elements 1, 2, 3, 5, and 6 of the circuit given in Fig. 1 3.7. This idea was further developed in nanosecond generators capable of producing 0.5 and 1 MV of peak voltage (Vorob'ev and Rudenko, 1 965; Vorob'ev et al. , 1 968), in which a Marx generator charged a noninductive capacitor insulated with transformer oil. This capacitor, through a spark gap immersed in compressed nitrogen, was discharged into a coaxial line filled with transformer oil. The load was the device designed to investigate the development of electrical discharges in dielectrics (see Fig. 1 3 .5). By properly choosing the inductance of the Marx generator and the capacitance of the energy storage capacitor and using a load with R1oad » Zo, it is possible to multiply the pulse voltage two times: first, due to the oscillatory charging of the capacitor from the

246

Chapter 13

Marx generator and, second, due to doubling the voltage across the load. With such a generator, pulses of rise time ns and amplitude MV were produced. In first high-power nanosecond pulsed electron accelerators (Link, coaxial oil-filled lines were charged from a Marx generator and then discharged, through a spark gap immersed in compressed gas, into an electron diode. Thus, these accelerators involved elements 1, 2, 5, and 6 of the unified circuit (see Fig. The book edited by Martin et al. contains a review by Goodman who described the x-ray generators developed in at AWRE (Aldermaston). Earlier, no information on these generators appeared in the literature. In these generators, strip and coaxial lines were charged from an MG to a voltage of MV and then discharged into x-ray tubes. Hence, they contained elements 1, 2, 5, and 6 of the unified circuit. All subsequent systems with pulsed charging from a Marx generator harnessed this principle. These were Hermes II (Martin, Aurora (Bernstein and Smith, PULSERAD (Clauser et al. , Gamble (Levine and Vitkovitsky, and other. The generator of the PBF A II system (Turman et al. , contained all elements of the circuit given in Fig. Marx generator 1 was discharged into water capacitor 2, which was discharged through laser-triggered multielectrode gas switch 6 into lines 3 and 4. Peakers 7 and 8 immersed in water were used to compress the pulse and increase the peak voltage. Then the pulse arrived at a coaxial-strip adapter, an inverter of polarity, and two strip lines, which transferred the pulse energy to vacuum diode 5. As a result, pulses of voltage MV with a power of TW appeared across the load. The PBF A II accelerator was insulated with four types of dielectric: transformer oil, gas, water, and vacuum. In the first zone, Marx generators were disposed, in the second one a laser-triggered multielectrode gas spark gap, in the third one water pulse-forming and transmission coaxial-strip lines with multichannel water spark gaps; in the fourth zone there were an inductive energy store, a voltage multiplier, and a plasma opening switch for final shortening of the pulse rise time. We shall discuss other types of Marx­ charged high-power pulse generators when considering high-power pulsed electrons and ion accelerators, lasers, pulsed x-ray generators, etc. Here we should only note that one of the major problems in developing Marx generators is to reduce the pulse rise time from o-6 s, as achieved by now, to o-7 s. This would allow one to considerably simplify the design of high-power generators and, in some cases, to get rid of additional energy stores and switches. In particular, for direct electron pumping of excimer lasers, electron accelerators were developed in which a Marx generator with a voltage of kV was discharged immediately into a vacuum diode with explosive electron emission. The electron current in an accelerator of this

1

1

1967),

13.7).

(1996)

1964-1968

0.2-4

1969), 1978),

1973), 1971), 13.7.

25

1985)

100

1

1

600

MARX GENERATORS

247

type was 700 kV and the rise time to its maximum was 2 · 1 0-7 s (Abdullin et al. , 1 993). The Marx generator consisted of twelve sections triggered simultaneously to within 1 o-s � · The sections operated under the conditions of vacuum isolation, and the spark gaps were located in an insulating tube filled with a mixture of SF 6 (30%) and air under a pressure of 1 .5 atm. 4

5

Figure 13.8. Schematic diagram ofthe SYRINX/GSI Marx generator

In another version of Marx generator used in the SYRINX system designed for the purposes of radiography, a current rise time of 6 · 1 0-7 s was achieved with the peak current equal to 700 kA and the voltage -1 MV (Koval' chuk et al., 1 997). The design of a 1 0-stage section of the Marx generator is shown in Fig. 1 3 .8. Stage capacitors 1 are stacked on dielectric bars 2, which are fastened to vertical dielectric plates 3. These plates hang on carrier arms 4 built in the cover of tank 5. Each capacitor is supplied with spark gap 6, which, with the help of box-shaped trunks 7, is connected to the outer electrode of coaxial line 8. The inner electrode of this line is connected on one side to load 9 and on the other to the output electrode of the spark gap of the last stage. The diameters of the inner and outer conductors of the coaxial line are 1 60 and 200 mm, respectively. The electrode gap of the

248

Chapter 13

coaxial line is insulated with a solid insulator (polyethylene pipe). Each section is located inside its own tank. The internal spaces of tank 1 0 and has a height of 4.8 m, length load 9 are filled with transformer oil. The tank .. of 1 .7 m, and width of 0.9 m. The parameters of the section are: capacitance 3 .95 )..lF , inductance 1 0 nH, voltage 90 kV, and pressure of dry air in the spark gap 2.5 atm.

REFERENCES Abdullin, E. N., Bugaev, S. P., Efremov, A. M., Zorin, V. B., Koval'chuk, B. M., Kremnev, V. V., Loginov, S. V., Mesyats, G. A., Tolkachev, V. S., and Schanin, P. M., 1993, Electron-Beam Generators Based on Vacuum-Insulated Marx Generators, Prib. Tekh. Eksp. 5: 1 3 8- 1 42. Babykin, M. V. and Bartov, A. V., 1972, Methods for the Production of Limitingly High Electric Powers in Short Pulses (in Russian), Preprint. l. V. Kurchatov IAE, Moscow. Bastrikov, A. N., Bugaev, S. P., Vorob'yushko, M. 1., Dulzon, A. A., Kassirov, G. M., Koval'chuk, B. M., Kokshenev, V. A., Koshelev, V. 1., Manylov, V. 1., Mesyats, G. A., Novikov, A. A., Podkovyrov, V. G., Potalitsyn, Yu. F., Sukhushin, K. N., Timofeev, M. N., and Yakovlev, V. P., 1 989, "Gamma", a High-Current Electron Accelerator, Prib. Tekh. Eksp. 2:36-4 1 . Bastrikov, A . N., Koval'chuk, B. M., and Kokshenev, V . A., 198 1 , A Low-Jitter High-Power Voltage Pulse Generator, Ibid. 6: 1 0 1 - 1 04. Bastrikov, A. N., Vorob'yushko, M. 1., Koval'chuk, B. M., et a!. , 1 982, A Voltage Pulse Generator for Pulsed Power Systems. In Proc. 2nd All- Union Conf on Engineering Problems ofThermonuclear Reactors (in Russian), Vol. 3, pp. 1 52-1 59. Bernstein, B., and Smith, 1., 1 973, "Aurora", an Electron Accelerator, IEEE Trans. Nucl. Sci. 20:294-300. Bolshakov, E. P., Velikhov, E. P., and Glukhikh V. A., 1982, The "Angara-5" System Module, At. Energ. 53: 14- 1 8 . Broadbent, T . E . , 1 960, New High-Voltage Multistage Impulse Generator Circuit, J. Sci. Instrum. 37:23 1 -236. Charbonnier, F. M., Barbour, J. P., and Brenegter, I. L., 1967, Intense Nanosecond Electron Beams, IEEE Trans. Nucl. Sci. 14:789. Clauser, M. J., Baker, L., McDaniel, D. H., Stinnett, R. W., and Toepfer, A. J., 1978, Magnetic Implosion of Plasmas with Short Pulse, High Power Generators, Bull. Amer. Phys. Soc. Ser. II 23:822. El'chaninov, A. S., Zagulov, F. Ya., Koval'chuk, B. M., and Yakovlev, V. P., 1974, Nanosecond-Jitter Generator of Electron Beams. In Nanosecong High-Power Pulsed Sources of Accelerated Electrons (in Russian, G. A. Mesyats, ed.), Nauka, Novosibirsk, pp. 123-127. Fitch, R. A., 1971, Marx and Marx-Like High Voltage Generators, IEEE Trans. Nucl. Sci. 18: 1 90- 1 96. Graybill, S. E. and Nablo, S. V., 1 967, The Generation and Diagnoses of Pulsed Relativistic Electron Beams above Watts, IEEE Trans. Nucl. Sci. 14:782-788. Gygi, E .. and Schneider, F., 1 964, A Nanosecond Pulse Generator of 200 kV Amplitude, Sci. Rept. CERN. AR64:46.

lOll

MARX GENERA TORS

249

Heilbronner, F., 1 97 1 , Firing and Voltage Shape of Multistage Impulse Generators, IEEE Trans. Pow. App. Syst. 90:2233-2238. Keller, L. P. and Walschon, E. G., 1 966, Simple Marx High Voltage Pulse Generator for Wide Gap Spark Chambers, Rev. Sci. Instrum. 37: 1 258. Koval'chuk, B. M. and Kremnev, V. V., 1 987, Arkadiev-Marx Generators for High-Current Accelerators. In Physics and Technology of Pulsed Power Systems (in Russian, E. P. Velikhov, ed.), Energoatomizdat, Moscow, pp. 1 65- 1 79. Koval'chuk, B. M., Kokshenev, V. A., Novikov, A. A., and Yakovlev, V. P., 1989, A 1-MV Module for High-Power, High-Current Pulse Generators, Prib. Tekh. Eksp. 1 : 1 37-139. Koval'chuk, B. M., Kremnev, V. V., Kim, A. A., and Manylov, V. 1., 1 997, A Fast Primary Energy Store Based on a Marx Generator, Izv. Vyssh. Uchebn. Zaved. , Fiz. 12: 1 7-24. Kremnev, V. V. and Mesyats, G. A., 1 987, Methods ofMultiplication and Transformation of Pulses in High-Current Electronics (in Russian). Nauka, Novosibirsk. Levine, L. S. and Vitkovitsky, I. M., 1 97 1 , Pulsed Power Technology for Controlled Thermonuclear Fusion, IEEE Trans. Nuc/. Sci. 18 (Pt 2): 1 05- 1 1 2 . Link, W . T . , 1 967, Electron Beams from 1 0 1 1 - 1 0 1 2 Watt Pulsed Accelerators, IEEE Trans. Nucl. Sci. 14:777-78 1 . Lockwood, G. J., Ruggles, L . E., Neyer, B . T, and Scheider, L . X., 1 985, Photon Diagnostics Leading to an Improved Marx, Proc. V IEEE Pulse Power Conf, Arlington, VA, pp. 784-787. Martin, T. H., Guenther, A. H., and Kristiansen, M., eds., 1 996, J. C. Martin on Pulsed Power. Plenum Press, New York. Martin, T. H., 1 969, Design and Performance of the Sandia Laboratories "Hermes-II'' Flash X-Ray Generator, IEEE Trans. Nucl. Sci. 1 6 (Pt 1 ):59-63. Meek, J. M. and Craggs, J. D., 1 953, Electrical Breakdown of Gases. Clarendon Press, Oxford. Mesyats, G. A., 1 962, A Voltage Pulse Generator, USSR Inventor's Certificate No. 1 56 6 1 6. Mesyats, G. A., 1 960, Production of Short-Rise-Time High Voltage Pulses. In High- Voltage Test Equipment and Measurements (in Russian, A. A. Vorob'ev, ed.), Gosenergoizdat, Moscow, pp. 379-393. Prestwich, K. B. and Johnson, D. L., 1 969, Development of an 1 8-Megavolt Marx Generator, IEEE Trans. Nucl. Sci. 16:64-70. Schering, H. and Raske, W., 1 935, Ein kleiner Steilwellengenerator for 500 kv, ETZ. Elektrotechnische Zeitschrift zentralb/attfor Elektrotechnik. 56:75 1 . Schneider, L . X. and Lockwood, G . J., 1 985, Engineering High Reliability, Low-Jitter Marx Generators, Proc. V IEEE Pulse Power Conf, Arlington, VA, pp. 780-783. Sigorsky, V. P. and Petrenko, A. 1., 1 976, Algorithms for Analysis of Electronic Circuits (in Russian). Sov. Radio, Moscow. Smirnov, S. M. and Terentiev, P. V., 1 964, High Voltage Pulse Generators (in Russian). Energia, Moscow-Leningrad. Smith, W. A., 1 958, An Improvement to the Multistage Impulse Generator, J. Sci. Instrum. 35:474. Sterligov, A. A., Usov, Yu. P., Tsvetkov, V. 1., and Shatalov, A. A., 1 976, A 1 35-kJ Voltage Pulse Generator, Prib. Tekh. Eksp. 6:7 1 -73. Turman, B. N., Martin, T. H., Neau, E. L., et a/., 1 985, PBFA-II, a 1 00 TW Pulsed Power Driver for the Inertial Confinement Fusion Program. In Proc. V IEEE Pulse Power Conf, Arlington, VA, pp. 1 55- 1 6 1 .

250

Chapter 13

Vorob'yushko, M. 1 . , Koval'chuk, B. M., Kokshenev, V. A., et a/. , 1 977, Development and Investigation of Marx Generator Sections for Pulsed Power Systems. In Proc. 1st All­ Union Conf. on Engineering Problems ofThermonuclear Reactors, Vol. 3, pp. 160- 167. Vorob'ev, G. A. and Mesyats, G. A., 1963, Techniques of Formation of Nanosecond High­ Voltage Pulses (in Russian). Gosatomizdat, Moscow. Vorob'ev, G. A. and Rudenko, N. S., 1965, A 500-kV Nanosecond Pulse Generator, Prib. Tekh. Eksp. 1 : 1 09- 1 1 1 . Vorob'ev, G. A., Mesyats, G. A., Rudenko, N. S., and Smimov, V. A., 1963, Generator of 1 5 0-kV Short-Rise-Time Pulses, Ibid. 6:93-94. Vorob'ev, G. A., Rudenko, N. S., Batin, V. V., and Tsvetkov, V. 1., 1968, A 1-MV Nanosecond Pulse Generator, Ibid. 1 : 1 26- 1 27. Woolston, T. L. and Ives, H. C., 1985, Marx Generator Engineering and Assembly Line Technology for the PBFA II Accelerator. In Proc. V IEEE Pulse Power Conf., Arlington, VA, pp. 788-79 1 .

Chapter 1 4 PULSE TRANSFORMERS

1.

INTRODUCTION

In the previous chapter, we considered nanosecond high-power pulse generators with pulse-forming lines charged from a Marx generator. A system of this type has a number of drawbacks that prevent its wide use in pulsed power technology, for instance, the presence of a great number of spark gaps, making the system short living and little suited for repetitive operation, and the need in electrical insulation of all capacitors of the generator. In this respect, pulse transformers are preferable. Many types of transformer, such as Tesla transformers, autotransformers, line transformers, transformers based on long lines, etc., are now in use (El'chaninov and Mesyats, With the help of Tesla transformers or autotransformers, it is possible to Hz create systems repetitively operated at pulse repetition rates of up to and voltages over MV. Such systems are compact since the transformer can be built in the energy storage line (SINUS series). In particular, Tesla transformers were used in compact pulse generators, accelerators, and x-ray generators (Tsukerman Line transformers (Mesyats, allow more efficient voltage multiplication than Marx generators. In particular, in the Hermes III accelerator, a voltage of MV was achieved (Ramirez due to multiplication of the voltage of primary generators based on Marx-generator­ charged energy storage lines. Thus, the use of pulse transformers allows one to attain high pulse repetition rates, to design very compact systems, and to obtain efficient voltage multiplication. We shall consider these generators in more detail.

1987).

103

1

eta/. , 1971). 1979) 20

eta/. , 1987)

252

Chapter

14

GENERATORS WITH TESLA TRANSFORMERS.

2.

AUTOTRANSFORMERS

The principle of operation of a Tesla transformer was considered above (see Section 2 of Chapter 1 ). Recall that this is a resonant transformer consisting of two inductively coupled circuits with equal natural oscillation frequencies, i.e., with = so that with the choice = the voltage across the capacitor can be multiplied times.

C1L1 CLC2 C2L2,

C1 n2C2

c1

n

L1 L3

4

ET

2

TT

Lz

1

5

3

Figure 14. 1. Circuit diagram of a Marx generator: 1 triggering of spark gap SG�o 2 triggering of spark gap SG2, 3 voltage control, 4 charging device, 5 control board, MD ­ matching device of resistance R; TT - Tesla transformer; ET - electron tube -

-

-

-

A repetitive nanosecond pulse generator was developed (Mesyats 1 969) for the operation with an electron accelerator. The voltage pulse amplitude was controlled within the limits 50-500 kV; the pulse duration ranged from 1 0 to 40 ns and was controlled by a chopping spark gap (Fig. 14. 1 ). If the capacitor is charged, as the spark gap S1 operates, oscillations are induced in the circuit and transferred, due to inductive coupling, to the circuit and vice versa. The capacitance of the coaxial line serves as If we neglect the active resistance of the transformer windings, we obtain that the voltage across the line will have the form of = being the beatings with the second half wave peaking at initial voltage across the capacitor The transformer developed had the = 2 J..LH, following parameters: = 0.23 J..LF , = 370 pF, = 1230 J..LH ; the primary and secondary windings contained, respectively, 6 and 230 turns. The transformer was designed as two coaxial cylinders (the outer cylinder being made of bakelite and the inner one of polyethylene). The secondary winding was wound on the inner cylinder by a Nichrome wire of ohmic resistance 50 n and immersed in transformer oil. The pulse repetition

et al. ,

L1

C2•

C1 L1 C1 L2C2

C1

L1 C1L1). VhC2 2 .Jc1/C2 V0L2(V0

253

PULSE TRANSFORMERS

rate was 200 Hz. A Tesla transformer was also used in the RIUS-5 pulsed electron accelerator operating in the megavolt range (Abramyan et a/. , 1984). The transformer charged a coaxial line placed in the same case in the environment of a mixture of 50% SF6 and 50% nitrogen. The primary capacitive energy store C1 was located outside the case.

-

-

Figure 14.2. Schematic of a Tesla transformer built in a coaxial pulse-forming line: 1 primary winding; 2 secondary winding; 3, 4 PFL central and outer electrodes, respectively, which serve simultaneously as the magnetic circuit of the Tesla transformer; 5 pulse-forming line. cline - capacitance of the line

In the above generators, the coupling coefficient of the circuits was therefore, the maximum voltage was achieved only within the second half wave. This made the generators unreliable in operation, since the Tesla transformer, the line L" and the switch S2 were under the full charge voltage for a long time (-1 0 J.l.S) before the operation of the main switch S2 • To get around this difficulty, it was proposed (El'chaninov et a/., 1 974) to use transformers for which k = 1 due to the open ferromagnetic core. Usually, such a transformer is built directly in the coaxial pulse-forming line of the accelerator. For example, in the transformer shown in Fig. 14.2 (El'chaninov and Mesyats, 1 987; El'chaninov et a/. , 1 979), the magnetic circuit simultaneously serves as the conductor of the pulse-forming line. An important characteristic of this type of transformer is the ratio of the effective stray inductance to the magnetizing inductance, both reduced to the = + (see Fig. 1 .5). For a coaxial primary circuit, transformer (see Fig. 14.2) (El'chaninov and Mesyats, 1 987; El'chaninov et a!., 1 979; El'chaninov et a/. , 1 983), we have

k = 0.6;

LJLll (Ls Ls1 Ls2 )

( )2

b._ = 3.n2 1_

L"tJ.

3

lk

(213 + 1)(13 - l)ln 13 ,

( 1 4. 1 )

where 13 = r1/r2 ; r 1 and r2 are, respectively, the external and the internal radius of the coaxial pulse-forming line, and lk is the length of the transformer winding. The ratio determines the efficiency 11 and

LJLll

254

Chapter

coupling coefficient Mesyats

14

of the transformer. According to El'chaninov and

(1987), k 2 ] 1-a(2-n/2)+a 1(14.2) =� [ � 2 2 1+a Lll- (l +a) • L2Ls ' k=1-(14.3) a=(14.1)-(14. L1 C1/L2C2.3) LsfLJJ. « 1 0.8-0.k 9. 1, 2-3 r11h = 0.05-0. 1 (1987). eta/., 1969) eta/. , 1979). 11

J1.

where From it follows that for we have � and for �= and the efficiency will be Detailed information on designing transformers of this type is given by El' chaninov and Mesyats Used as switches in the primary circuit of Tesla transformers are spark gaps (Mesyats and thyristors (El'chaninov The use of the latter enables one to power accelerators directly from industrial supply lines. The SINUS-4 machine, one of the first repetitively operated high-current electron accelerators, was based on a Tesla transformer with an open ferromagnetic core, built in a pulse-forming line (Fig. and had the following parameters: the electron energy keV, the beam current 8 kA, the pulse duration ns, the pulse repetition rate Hz, the voltage across the primary winding of the transformer V; � � em, and the time of charging of the pulse-forming line The magnetic circuit was made of electrotechnical steel (stacks of 8-J..Lm-thick strip). The primary energy store consisted of thirty capacitors and the primary switch contained thirty thyristors. The average power of this electron accelerator was about kW (El'chaninov The parameters of four pulsed accelerators of the SINUS series are given in Table In these accelerators, a transformer-oil-insulated energy storage line is connected to a load through a gas-flow switch filled with nitrogen compressed to atm. In studying the operation of this type of switch, it was revealed that the parameters of the pulses across the load were unstable (El 'chaninov This turned out to be related to the fact that the discharge channel in the gas-discharge switch changed its position in the cathode-anode gap (Fig. To remedy this flaw, the gas flow velocity in the switch should be high enough to remove the plasma of the previous discharge, but not so high that the cathode surface be strongly cooled and the sites of enhanced electron emission be eliminated. Thus, there is an optimal gas flow velocity v0, which depends on pulse repetition rate. This effect is well illustrated by Fig. ·

400 100 14.2), V1 = 340 = r1/35J.r2 S.L . 3.3; 1 00-J.F.L et al. , 1979).

25

h = 100

10

14.1.

10 et al. , 1979). 14.3).

14.3.

PULSE TRANSFORMERS

255 (a)

( b)

Figure 14.3. Oscillograms of the pulsed voltage across the load of the Sinus generator (on the right) and the respective photographs of the discharge channel in the switch (on the left) with the gas flow velocity v > v0 (a) and v "" v0 (b). The photographs were taken at a peak voltage of600 kV, a current of 5 A, a pulse duration of 25 ns, and a pulse repetition rate of 1 00 Hz Table 14. 1. Parameters of some Eulsed accelerators ofthe SINUS series Beam current, Electron Pulse duration, kA energy, keY ns

Accelerator version

Pulse repetition rate, Hz

SINUS-4

400

8

25

1 00

SINUS-5

700

7

10

1 00

SINUS-6

400

5

25

1 000

SINUS-7

2000

20

40

1 00

Tesla transformers are also widely used in compact nanosecond high­ voltage pulse generators intended for the production of electron beams and pulsed x rays (Tsukerman ). High-efficiency devices of this type are systems of the Radan series (Shpak in which a coaxial line filled with transformer oil is charged from a built-in Tesla transformer Switching of the current in the primary circuit of the transformer (Fig. is performed with the help of thyristors at a voltage equal to the voltage of the supply line. The switch on the high-voltage side is a dismountable high­ pressure spark gap, which operates in the environment of nitrogen at atm. The general view of a Radan accelerator is given in Fig. The Radan accelerators are widely used for pumping gas and semiconductor lasers, for the production of x rays and microwaves of wavelength mm and pulse power MW, for sterilization of medical devices, and for other purposes. Martin and Smith proposed to produce voltage pulses of up to MV with the use of a pulse autotransformer with metal foil windings. The characteristic feature of this type of transformer is that it is insulated with paper impregnated with high-s dielectric (water). This has the result that the

et a/., 1971 eta/., 1993)

14.4).

14.5. 40 2-10

10-60

1

(1968)

Chapter 14

256

electric field at the foil edge levels off. The configuration of one of the windings of such a transformer is shown in Fig. 14.6. Contacts D and C are the terminals of the primary winding and A and B are the ends of the secondary one. Before the foil is turned in a spiral, it is coated with insulating polyethylene or Dacron tape and the cutouts are filled with adsorbing paper whose thickness is chosen equal to the thickness of the foil. Then the foil tape with the imposed insulation is wound on a cylinder. Figure 1 .7 shows a circuit diagram and the equivalent circuit of an autotransformer. The primary voltage can be applied not necessarily to the bottom turns, but also to the central ones. 6

� ..

II+•

320 mm

-----+!

----' -'--'-'--'-

-

4

3

2

1

5

·-8---

Figure 14.4. Block diagram of a Radan-type accelerator: 1, 2 primary and secondary windings; 3, 4 - outer and inner windings of the Tesla transformer; 5 - gas-gap switch; 6 load; 7, 8 - capacitive voltage divider; A 1 -A4 - timers; B1 -B4 - pulse dividers; D - driver -

Figure 14.5. General view of a Radan-type system. Voltage 30-300 kV, line wave impedance 45 n, pulse duration 4 ns, pulse rise time 1 ns, maximum pulse repetition rate 25 Hz, mass 28 kg, average required power 250 W

PULSE TRANSFORMERS

Figure 14. 6. Configuration o f a foil winding with an applied insulation: 1 2 foil ribbon

257

-

insulating layer;

-

Several pulsed electron accelerators were developed in which a pulse­ forming line was powered from an autotransformer. Bugaev et a/. ( 1979) reported on the development of the SINUS- I accelerator that produced an electron beam of energy 500 keV, current 10 kA, and pulse duration 25 ns. The pulse-forming line was charged by a pulse autotransformer with an open ferromagnetic core. The pulse-forming element was a coaxial line of wave impedance 8 Q filled with glycerin. The accelerator is schematically shown in Fig. 1 4.7. A metal tube 2 incorporates a pulse transformer 4, an energy storage element 5 made as a coaxial line segment, chamber 6 with high-pressure spark gaps, and an acceleration tube. Originally, energy is stored in a charging capacitor 1 which is located outside the tube and is connected to the transformer winding by a strip line. The capacitor 1 is switched into the transformer winding by an air spark gap 3. In the pulse transformer, an open armored core made of electrotechnical steel is used because the magnetic flux has no time to be distributed throughout the core. The absence of a closed core facilitates the service of the transformer having a coaxial configuration. The winding is designed like that of an autotransformer and has the shape of a wedge (narrowing from the beginning to the end). The turns are interlaid with polyethylene film. The necessity of fast charging of the energy storage line (0.5 J.!S) with the high charging capacitance places rigid requirements on the inductance of the charging circuit. This problem is solved by using a transformer of small dimensions with the least possible spaci:::.g between the turns and by making the inductance of the transformer primary circuit as low as possible. With this purpose, the energy supply from the primary capacitive energy store to the transformer is realized with the help of a low­ impedance strip line, which passes the shortest way inside the transformer core. The top part of tube 2, where the transformer is located, is filled with transformer oil. In the bottom part of the tube, a coaxial energy storage line 5 with glycerin as dielectric is located. For shortening the rise time of the pulse across the load, a spark gap 7 is used which operates in the environment of nitrogen compressed to 1 2 atm, and a necessary pulse duration is specified by a chopping spark gap 8, since with no chopping spark gap, because of the incomplete match of the line to the load, afterpulses appear.

258

Chapter 14

Figure 14. 7. Schematic drawing of an accelerator: 1 charging capacitor, 2 tube, 3 spark gap, 4 pulse transformer, 5 energy storage unit, 6 spark gap chamber, 7 peaking spark gap, 8 chopping spark gap, 9 cathode, 10 anode -

-

-

-

-

1

-

-

-

-

-

2

3

Figure 14.8. Schematic diagram of the Sinus-2 accelerator: 1 energy input from primary storage capacitors, 2 secondary winding, 3 autotransformer core, 4 and 5 double pulse­ forming line, 6 electron beam extraction foil, 7 explosive-emission cathode, 8 charging inductor, 9 and 10 capacitive voltage dividers, 11 gas switch, 12 window for inj ection of electrons into the gas gap -

-

-

-

-

-

-

-

-

-

PULSE TRANSFORMERS

259

An autotransformer was also incorporated in the design of the SINUS-2 accelerator that produced electron beams of energy MeV, current 30 kA, and pulse duration ns (Bugaev et al. , (Fig. Foil autotransformers are successfully used in charging high-power water energy stores. The advantages of foil transformers for the above purpose are realized at best in the accelerator described by Fedorov et a/. The use of high-strength film insulation impregnated with conducting water solution, the realization of parallel operation of transformers, and the increase in tum voltage by connecting the primary energy store to a section of the transformer primary tum enabled the authors of the cited work to transform kJ of energy from a kV voltage level to MV within o-6 s.

11974)

40

50

20

3.

1

14.8). (1978).

1

LINE PULSE TRANSFORMERS

For the production of megavolt pulses of microsecond duration with an energy of up to J and more, linear pulse transformers (LPT' s) are used (Mesyats, As mentioned in Chapter an LPT consists of single­ tum transformers with a common secondary winding. The secondary winding is a metal rod on which toroidal inductors with the primary winding are put on. A capacitor or line is discharged into all primary windings simultaneously through a triggered fast spark gap switch. The equivalent circuit of an LPT and the mechanism of voltage multiplication were considered above (see Chap. 3). Mesyats described the Modul pulse generator designed for the production of hot plasmas by the method of MHD implosions, developed at IHCE. This machine, with kJ of stored energy, generated pulses of current up to MA, duration s, and voltage 2 MV. The generator consisted of a charging device, water energy storage and transmission lines, and appropriate switches. The charging device in this system was a linear pulse transformer (Fig. The pulse transformer 2 had a low internal inductance since the secondary winding is made as one tum 2a. Owing to the low internal inductance, LPT's can be used for fast charging of high-voltage energy stores with high-energy storage capabilities, including water stores. The LPT was designed as a set of twelve identical sections. Each section consisted of two transformers with single-tum primary and secondary windings. The secondary windings were connected in series. The primary circuit of the transformer consisted of two oppositely charged capacitors 3 H, V), six parallel-connected transmission cables, (3 · -6 F, and two gas switches 4. The primary tum was formed by the cores of the transmission cables. The transformation factor of the LPT, reduced to the charge voltage of the capacitor, was equal to The cores of the magnetic

106 1979).

1,

(1979) 2

N

100 10-7

14.9).

10 40·10-9 50·103

48.

260

Chapter 14

circuits were made of electrotechnical tape covered with lacquer and glued with epoxy. This made the cores mechanically strong and simplified their processing. The final internal and external diameters of the cores were, respectively, and mm; the filling factor was and the weight of mm one core was kg. Two cores mounted in a case with a gap of between them formed one magnetic circuit of cross-sectional area cm2• For the reduction of the cross section of magnetic circuits, provision was made for pulsed magnetic reversal To connect the capacitors to the LPT primary winding, triggered spark gaps were used which, in the voltage range kV, operated with a jitter less than ns. The secondary turn of the LPT was formed by the case and the central core made of a tube of diameter mm To insulate the tube from the magnetic circuit, polyethylene film I 0 impregnated with glycerin was applied on the tube. The internal space of the transformer was also filled with glycerin. The choice of glycerin as dielectric instead of water was dictated by the presence of steel magnetic circuits. In testing the film-glycerin insulation with single V and duration the insulation was pulses of peak voltage broken down at a field of V/cm; at V/cm breakdown occurred after pulses. With the maximum design parameters, the field inside the transformer was V/cm.

25075 515

0.8,

2303-4 C1

(5, 11).

25-45

80

1.1.5·15 ·061 06 0.5 · 1 06

10-15

10 2a

.

1.2· 1061.8 · 1o-6

2000 mm

5500 mm

2000 mm

1

§

0

8 N

Figure 14. 9. Schematic diagram of the Modul system: 1 trigger generator; 2 - line pulse transformer; 3 48 capacitors; 4 - spark gaps; 5 remagnetization capacitor; 6 6 water pulse-forming lines; 7 - peaking spark gaps; 8 - transmission line; 9 - load; 10 - glycerin­ impregnated film insulation; 1 1 remagnetization inductor; 12 insulators; 13 transmission line -

-

-

-

-

-

-

PULSE TRANSFORMERS

261

The use of an LPT for charging an energy store can be illustrated by the SNOP-2, SNOP-3, and MIG systems developed and built at IHCE (El'chaninov and Mesyats, 1 987; Kovsharov et a/., 1 987; Luchinsky et a/. , 1 997). The SNOP-3 generator (Fig. 14. 1 0) (Kovshsarov et a/., 1 987), intended for studying the dynamics of imploding wire arrays, produces a power of 1 TW and provides in a 30-nH inductive load a current of 2.2 MA with a rise rate of 4 · 1 0 1 3 A/s. The generator consists of a primary energy store (capacitor bank), a line pulse transformer, an intermediate capacitive energy store, a pulse-forming line, and a transmission line. The switching between these elements is accomplished by triggered and nontriggered water spark gaps. The quest for short charging times for low-resistance water­ insulated lines forces one to use transformers with a minimum stray inductance. 4

6

7

8 9 10

13

11 12

Figure 14. 1 0. Schematic diagram of the SNOP-3 generator: 1 - 24 inductors; 2 - inner conductor; 3 film-glycerin insulation; 4 - bushing insulator; cl - 48 capacitors; s 49 spark gap switches; 5 L and C2 - separating inductor and the capacitor of the demagnetization circuit; 6 intermediate capacitive energy store; 7 - support insulators; 8 water insulation; 9 triggered multichannel spark gap; 10 pulse-forming line; 1 1 nontriggered multichannel switch; 12 - transmission line; 13 - capacitive voltage pickups; 14 - current pickup; 15 - load unit; 16 - vacuum insulator -

-

-

-

-

-

In the SNOP-3 machine, an LPT is used for charging an intermediate capacitive energy store of resistance 1 .3 Q and electric length 7 5 ns. The voltage increases to a maximum of 2 MV within 1 .3 f..l.S . The energy store 6 (see Fig. 14. 1 0), switch 9, and pulse-forming line 1 0 form an circuit with the time of voltage rise to a maximum equal to 300 ns. The energy transfer from the store to the pulse-forming line occurs in the resonance manner: two runs of an electromagnetic wave from the switch to the end of the store and back (�300 ns) correspond to its four runs from one end of the line to another (�300 ns). The pulse-forming line is discharged into a transmission

LC

262

Chapter 14

line 12 of the same wave impedance through a nontriggered multichannel switch 1 1 . At the end of the transmission line, there is a load unit 15. Further development of the ideology of the Modul and SNOP systems was realized in the MIG multi-purpose machine (Luchinsky et a/. , 1 997). This system is intended for the generation of pulses of peak voltage up to 6 MV and current up to 2.5 MA with a power of 2.5 TW. The load resistance ranges from a few ohms to several hundreds of ohms since the load is generally a z-pinch or an electron beam. In this machine, to produce a voltage of 6 MV across a load, plasma and exploding-wire opening switches are used. The Hermes III accelerator (Corley et a/. , 1 987; Johnson et a/. , 1 987; Pate et a/. , 1 987) built at SNL is the most powerful LPT-based system in the world. It is capable of generating a beam of current 800 kA and pulse duration 40 ns at an accelerating voltage of 20 MV and is intended for experimentation under the conditions of high-doze irradiation. This machine is capable of producing doze rates of 5 · 1 0 1 2 R/s in a cylindrical volume of base area 500 cm2 and height 1 5 em. The main distinguishing feature of the accelerator is the use of a magnetically insulated vacuum coaxial line to sum up the voltages of 20 inductor sections of the LPT. The magnetically insulated line is formed by the cathode holder and the internal cylindrical surfaces of the sections enclosing the holder. An electromagnetic pulse is supplied to the line through the ring slots cut in the internal surfaces of the inductor sections. The latter contain transmission lines and magnetic cores providing high­ voltage insulation due to inductance. With this system design and the 20-MV accelerating voltage, there are difficulties, first, with the insulation of the energy storage sections and, second, with the reduction of the leakage currents resulting from the electron emission from the cathode holder. The first problem is solved by using metglas magnetic cores, providing an inductive isolation of the sections from the total voltage. The second difficulty is overcome by that the cathode holder serves simultaneously as an element of the magnetically insulated vacuum line that operates in a self­ consistent mode and provides the transportation of the "electron layer", formed by leakage electrons in the diode. It has made it possible to create an accelerator with small losses. The Hermes III accelerator (Ramirez et a/. , 1 987) contains ten Marx generators, twenty intermediate energy stores, twenty laser-triggered multielectrode gas switches, eighty water pulse-forming and transmission lines, and twenty LPT's (inductively insulated storage ring sections) that switch energy into the voltage summation system (magnetically insulated vacuum coaxial line) that delivers energy to an electron diode (radiation converter). The energy storage system consists of a primary store and an

PULSE TRANSFORMERS

263

intermediate store. The primary store incorporates ten 1 56-kJ, 2.4-MV Marx generators. The generators are placed in two tanks, five in each, on two sides of the accelerator. The intermediate store consists of twenty 1 9-nF cylindrical water capacitors. Under optimal conditions, each capacitor is charged to 2.2 MV within 950 ns. As the voltage peaks, the gas switches switch energy from the intermediate store into the pulse-forming lines. Twenty spark gaps filled with SF6 are responsible for synchronous operation of the all units of the accelerator. The switches are immersed in transformer oil. They are similar in design to the switches used in the PBFA II. They also have two sections: one section is laser-triggered and the other, where the voltage it is distributed over ten gaps, is nontriggered, The jitter of the operation of the laser­ triggered spark gaps is not over 2 ns. Such a switch ensures reliable operation of the system up to 2.5 MV. To trigger the spark gaps, a pulsed KrF laser (A. � 248 nm) with pulse duration of 20 ns and energy of 900 mJ is used. The optical system, which contains 20 fiber channels that bring the radiation to the switches, controls, with the help of mirrors, the pulse delay time within 5 ns.

Figure 14. 11. Schematic and circuit diagrams of a stage ofthe LTD-1 00 transformer

264

Chapter 14

Koval'chuk et al. ( 1 997) of iHCE developed a series of pulse generators with LTD-type line transformers. Figure 1 4. 1 1 presents the schematic and simplified electric circuit diagrams of a capacitor-based stage of the LTD1 00 transformer with the parameters: 1 00 kV, 40 nF, 25 nH, and 270 mO. The stage contains eighteen capacitors subdivided into nine identical pairs (2); the capacitors of each pair are oppositely charged to ± 1 00 kV. The circuit of a pair contains a series spark gap 1 that connects the capacitors of the pair to load 5. High-voltage insulation is provided by polyethylene insulators 3 and transformer oil filling the internal space of the stage. The core of the stage is wound of steel tape. It consists of six rings of total cross section 53 cm2 • The stage is intended for the operation into a load of resistance R = (L/C) 1 12 - 0.4 0. Capacitors C+

Dry air inlet/outlet

Capacitors CCharging resistors

Starting resistors

Starting voltage lead

Figure 14. 12. Side view ofthe LTD- 100 stage

Figure 1 4. 1 2 gives a side view of the module. It has the shape of a disk of diameter 1 350 mm and height 200 mm; nine pairs of capacitors are arranged evenly in a circle. The charging resistors are -1 kO liquid (water solution of CuS04) resistors; the triggering resistors of the same resistance are made of conducting rubber. Five cables are connected to the module: two cables for the charge voltage, two cables for the current biasing the cores, and one

PULSE TRANSFORMERS

265

triggering cable. The bleed-in and effluent of dry air from the spark gaps is performed through a common sleeve. In the short-circuit mode with the inductance of the coaxial output equal to nH, the time of conversion of the energy stored in the capacitors into the energy of a magnetic field is ns at a peak current of kA. By mere addition of transformer stages of this type, it is possible to design pulse generators with parameters ranging over wide limits.

3

125

380

4.

TRANSFORMERS USING LONG LINES

In the technology of nanosecond high-power pulses, besides the above transformers with lumped parameters, transformers based on long lines (see Chapter are also used. Figure presents a high-voltage pulse generator proposed by Lewis and developed by Pavlovsky and The generator consisted of three basic elements: a pulse­ Sklizkov forming line (PFL), a spark gap, and a transforming line (TL). The pulse­ forming line consists of five cable pieces, each m long, connected in parallel, and was charged to kV. As the spark gap operated, a rectangular pulse of duration J..lS , rise time over ns, and amplitude kV was generated across the PFL. The transforming line also consisted of five cable pieces. The input resistance of the TL was equal to the wave impedance of the PFL. At the output of the TL, all cables were connected in series. The electric length of the TL was chosen equal to the pulse duration. The cable pieces in the TL were formed into coils that were offset by no less than em from each other and from the surrounding massive metal units. The coils were placed on a bakelite tube em in diameter. The high­ voltage ends were carefully insulated and, together with the load, immersed in oil to prevent a crown. A spark gap of coaxial geometry operating at a pressure of several atmospheres was used. When matched to the load, the generator produced a rectangular pulse of amplitude kV and duration J..lS . For a load with kn, a pulse of amplitude kV and rise time ns was obtained. For the production of high-voltage (up to kV) pulses of duration ns with a rise time of ns, a two-stage pulse-forming line and a transformer based on cable pieces can be used (Nasibov et al. , described a transformer circuit based on pieces of coaxial Nasibov lines wound on a ferromagnetic core. The windings consist of three pieces of coaxial cable. The beginnings and the ends of the cable piece braids are connected in parallel and form the primary winding of the transformer. The cores of the cable pieces are connected in series and form the secondary winding. The transformation factor is equal to the number of cable pieces.

2) (1962).

(1955)14.13

0.25 70

10-20

25

5

35

30

Rtoad 2 20

0.25 50 250

160 300

=

(1965)

300

1965).

266

Chapter 14

To increase the inductance of the winding, the cables are wound on a ferromagnetic core. For the case of short pulses, the best choice of the core material is ferrite.

l O cm

Rectifier

Figure 14. 13. Schematic diagram of a 300-kV nanosecond pulse generator

To load

Figure 14. 14. Current pulse transformer with a coaxial cable wound in spiral: 1, 2 - inner and outer conductors of the cable; 3 - collecting bars; 4 - cut in the cable enve10pe

PULSE TRANSFORMERS

267

Designs of the step-down air transformer are known in which coaxial cable turns are used as windings. A similar principle is used in the transformers intended for the production of pulsed voltage. In these transformers, the cable core and conducting envelope are utilized as windings, which improves the frequency characteristic of the transformer (Gaaze and Shneerson, 1 965). A step-up current transformer with a coaxial cable spiral winding was described by Latushkin and Yudin ( 1 967) (Fig. 14. 14). On each tum of the spiral, a small portion of the conducting envelope of the cable is cut off. The cuts are located one above the other, and their edges are connected with busbars to the load. The cable is connected through a switch to a capacitor bank. When the capacitors discharge, a current flows through the cable core, envelope ends, busbars, and load. In the tum envelope, an emf is induced, and, therefore, the total current of all coils passes through the load.

REFERENCES Abramyan, E. A., Alterkop, B. A., and Kuleshov, G. D., 1 984, Intense Electron Beams: The Physics, Technology and Applications (in Russian). Energoatomizdat, Moscow. Bugaev, S. P., El'chaninov, A. S., Zagulov, F. Ya., Koval'chuk, B. M., and Mesyats, G. A., 1 970, A High-Current Pulsed Electron Accelerator, Prib. Tekh. Eksp. 6 : 1 5- 1 7. Bugaev, S. P., El'chaninov, A. S., Zagulov, F. Ya., Koval'chuk, B. M., Mesyats, G. A., and Potalitsyn, Yu. F., 1 974, A High-Power Electron-Beam Pulse Generator. In High-Power Nanosecond Pulsed Sources of Accelerated Electrons (in Russian, G. A. Mesyats, ed.}, Nauka, Novosibirsk, pp. 1 1 3-1 1 9. Corley, J. P., Johnson, D. L., Weber, B. V., et al. , 1 987, Development and Testing of the "Hermes III" Pulse Forming Transmission Lines. In Proc. VI IEEE Pulse Power Conf, Arlington, VA, pp. 486-489. El'chaninov A. S., Zagulov F. Ya., and Koval'chuk B. M., 1 974, A short-electron-beam generator with a high-voltage source built in a line. In High-Power Nanosecond Pulsed Sources of Accelerated Electrons (in Russian, G. A. Mesyats, ed.), Nauka, Novosibirsk, pp. 1 1 9-123. El'chaninov, A. S. and Mesyats, G. A., 1 987, Transformer Power Supply Circuits for High­ Power Nanosecond Pulse Generators. In Physics and Technology ofPulsed Power Systems (in Russian, E. P. Velikhov, ed.}, Energoatomizdat, Moscow, pp. 1 79-1 88. El'chaninov, A. S., Zagulov, F. Ya., Korovin, S. D., and Mesyats, G. A., 1 979, Electron Beam Accelerator with High Pulse Recurrence Frequency. In Proc. III Intern. Conf on High Power Electron and Ion Beam Research and Technology, Novosibirsk, USSR, pp. 1 9 1 - 1 97. El'chaninov, A. S., Zagulov, F. Ya., Korovin, S. D., Landi' , V. F., Lopatin, V. V., and Mesyats, G. A., 1 983, High-Pulse-Repetition-Rate, High-Current Electron Beam Accelerators. In High-Current Pulsed Electron Beams in Technology (in Russian, G. A. Mesyats, ed.), Nauka, Novosibirsk, pp. 5-2 1 .

268

Chapter 14

Fedorov, V. M., Scheglov, M. A., and Semenov, E. P . , 1978, A Compact 1-MV Transformer. In Proc. All-Union Workshop on Engineering Problems of Thermonuclear Reactors (in Russian), Res. Inst. of Electrophysical Apparatus, Leningrad, p. 62. Gaaze, V. B. and Shneerson, G. A., 1 965, A High-Voltage Cable Transformer for the Production of High Pulsed Currents, Prib. Tekh. Eksp. 6 : 1 05- 1 1 0. Johnson, D. L., Ramirez, J. J., Huddle, C. W., et a/. , 1987, "Hermes III" Prototype Cavity Tests. In Proc. VI IEEE Pulse Power Conf, Arlington, VA, pp. 482-485. Koval'chuk, B. M., Vizir, V. A., Kim, A. A., Kumpyak, E. V., Loginov, S. V., Bastrikov, A. N., Chervyakov, V. V., Tsoi, N. V., Monjaux, P., and Choi, P., 1 997, A Fast Primary Energy Store Based on a Line Pulse Transformer, Izv. Vyssh. Uchebn. Zaved., Fiz. 12:25-37. Kovshsarov, N. F., Luchinsky, A. V., Mesyats, G. A., Ratakhin N. A., Sorokin, S. A., and Feduschak, V. F., 1 987, "SNOP-3", a Pulse Generator, Prib. Tekh. Eksp. 6:84-89. Latushkin, S. T. and Yudin, L. l., 1967, A Short Current Pulse Generator, Ibid. 4:1 1 0- 1 14. Lewis, I. A. D., 1 955, Some Transmission Line Devices for Use with Millimicrosecond Pulses, Electr. Eng. 27:332. Luchinsky, A. V., Ratakhin, N. A., Feduschak, V. F., and Shepelev, A. N., 1997, A Transformer-Type Multipurpose Pulse Generator, Izv. Vyssh. Uchebn. Zaved., Fiz. 12:67-75. Martin, J. C. and Smith, I. D., 1 968, U.S. Patent No. 1 1 14 7 1 3 . Mesyats, G . A., 1979, Pulsed High-Current Electron Technology, Proc. 2nd IEEE Intern. Pulsed Power Conf, Lubbock, TX, pp. 9- 16. Mesyats, G. A., Khmyrov, V. V., and Osipov, V. V., 1969, A 500-kV Nanosecond Rectangular Pulse Generator, Prib. Tekh. Eksp. 2 : 1 02- 1 04. Nasibov, A. S., 1 965, A Pulse Transformer with Coaxial-Cable Windings, Elektrichestvo. 2. Nasibov, A. S., Lomakin, V. L., and Bagramov, V. G., 1 965, A Short, High-Voltage Pulse Generator, Prib. Tekh. Eksp. 5: 1 33-1 36. Pate, R. C., Patterson, J. C., Dowdican, M. C., et a/. , 1 987, Self-Magnetically Insulated Transmission Lines (MITL) Systems Design for the 20-Stage "Hermes III" Accelerator, Proc. VI IEEE Pulse Power Conf., Arlington, VA, pp. 478-48 1 . Pavlovsky, A. I . and Sklizkov, G . V., 1962, Production of Rectangular High Voltage Pulses, Prib. Tekh. Eksp. 2:98. Ramirez, J. J., Prestwich, K. R., Burgess, E. L., et a/. , 1987, The Hermes III Program, Proc. VI IEEE Pulse Power Conf, Arlington, VA, pp. 294-299. Shpak, V. G., Shunailov, S. A., Yalandin, M. I., and Dyad'kov, A. A., 1993, RADAN SEF303A, a Compact High-Current Pulse Generator, Prib. Tekh. Eksp. 1: 149- 1 55 . Tsukerman V. A., Tarasova L. V . , and Lobov S. I . , 1 9 7 1 , New X-Ray Sources, Usp. Fiz. Nauk. 103:3 1 9-337.

PART 6 . GENERATORS WITH PLASMA OPENING SWITCHES

Chapter 1 5 PULSE GENERATORS WITH ELECTRICALLY EXPLODED CONDUCTORS

1.

INTRODUCTION

The generators of high-power nanosecond pulses described in the previous sections are based on capacitive energy storage (CES) followed by voltage multiplication with the help of Marx generators or transformers. In devices of this type, the extraction of energy occurs on the microseconds time scale. To attain nanosecond times, it is necessary to use intermediate energy stores (capacitors or lines) and one or several peaking switches. This makes the devices with CES, especially megajoule systems, very bulky and costly. Now the designs of CES devices feature high perfection, especially those where many Marx generators operate in parallel. However, even in these systems, the energy density is not above 5 kJ/m3 at an output voltage of 3 MV. The energy density is roughly in inverse proportion to the output voltage V: for V - 1 07 V it is :::: 0.5 kJ/m3 (Aurora). The low energy density results in a significant inductance of the CES discharge circuit that limits the output power to Pmax = 1-3 TW and the average power rise rate to about 3 TW/J.ls. In other words, CES devices provide the rise time of power at the load tr - 0.5-1 J.lS. However, the expanding research and engineering applications demand powers above 1 013 W with tr < I o-7 s. In some cases, for example, in systems intended for the production of high-power hard x rays and microwave radiation, inductive energy stores are employed in which the current is cut off by electrical explosion of conductors (EEC). This method has long been known (Early and Martin, 1 965; Maisonnier et al. , 1 966). However, it came in nanosecond pulse technology only in the 1 970s when it became clear that to increase the

272

Chapter

15

resistance rise rate in an opening switch, it is necessary to use not a foil, but a set of parallel-connected conductors (Koval'chuk 1 974). In this case, the generator operates as follows (Fig. 1 5 . 1): as the switch S closes, the current flows from the energy store of capacitance charged to a voltage V0 through the inductor L and exploded conductors EC. The load R is connected through the spark gap SG. If the cross section of a conductor is small, it is heated by the current it carries; its resistance increases and causes an increase in the rate of energy absorption by the conductor. As the energy becomes high enough, the conductor fuses and explodes. As this takes place, a jump is observed in the voltage waveform (Fig. 1 5 .2); the fused conductor is heated up to some point in time at which it starts exploding, i.e., quickly expanding with dispersion and partial evaporation of the metal. As this takes place, the conductor resistance increases by several orders of magnitude, the current abruptly decreases, and a voltage pulse is generated across the circuit inductor. If the electric strength of the EEC products is higher than the pulse peak voltage, the current is completely cut off (time in Fig. 1 5 .2). This is - t3) whose duration is determined by followed by a no-current interval the voltage remaining across the capacitor bank and by the velocity of expansion of the EEC products. However, if the spark gap SG (Fig. 1 5 . 1 ) is tuned so that it is broken down by the voltage generated on explosion, the inductor current I will be switched into the load and the voltage across the load may become several times greater than the charge voltage of the capacitor bank. The circuit shown in Fig. 1 5 . 1 is referred to as one-stage since it uses only one opening switch. If one more inductive energy store and an EEC switch are used as a load for the first stage, the circuit is referred to as two-stage. Generators with circuits consisting of thee and more stages are feasible. The studies performed have shown that EEC opening switches are capable of reducing the power rise time by an order of magnitude and increasing the power (mainly due to an increase in voltage) by an order of magnitude as compared to the direct discharge of a CES into a load. In this case, the energy density in the source increases due to the decrease in CES output voltage and absence of pulse-forming lines.

dR/dt,

et al., C

t1

(t2

Figure 15.1. Circuit diagram of a pulse generator with an EEC opening switch

t2

Figure 15.2. EEC current (top) and voltage (bottom) waveforms

PULSE GENERATORS WITH EEC'S

273

CHOICE OF CONDUCTORS FOR CURRENT

2.

INTERRUPTION

It is well known that if a high current pulse (with the current density reaching 1 06- 1 09 A/cm2), generally produced by discharging a capacitor (Fig. 1 5 . 1 ), is passed through a thin metal conductor, there occurs an electrical explosion of the conductor. As this takes place, the liquid metal, because of its inertia, is overheated throughout its volume or in some regions and evaporates as intensely as if exploded. During evaporation, the metal conductivity of the conductor quickly decreases, resulting in current cutoff in the discharge circuit and a voltage pulse across the circuit inductor whose amplitude is given by

L

v,

L L didt ' =

(15.1)

where I i s the current in the circuit. If the voltage does not result in breakdown of the gap in which the exploding conductor is located, there comes a no-current interval (NCI). As the metal vapors expand, the pressure in the channel falls and, when the voltage remaining across the capacitor becomes equal to the breakdown voltage of the metal vapors, an arc discharge is initiated. If the voltage arising across the circuit inductor upon current cutoff is higher than the breakdown voltage, the conductor is shunted by the discharge even earlier than the explosion is complete. For fixed discharge circuit and conductor parameters, an increase in conductor length increases the NCI duration, while its decrease results in shunting of the conductor by the arc discharge. The conductor length at which there occurs complete current cutoff with a zero NCI is called the critica1 1ength. When using EEC to interrupt a current, the choice of the conductor material, shape, and dimensions and the parameters of the discharge circuit should ensure prescribed parameters of the pulse to be generated across the load. Though the mechanism of EEC remains obscure in many respects and there is no mathematical model for the calculation of its characteristics, the available experimental data allow one to choose the conductor material, cross-sectional area, and shape and to estimate its length necessary for a current pulse of specified amplitude be generated across the load. First, we restrict the spectrum of suitable metals by their boiling temperature and work function. If of the conductor metal is high enough, a shunting discharge develops over the conductor surface due to thermoemission even before the explosion, and the circuit is not broken. As revealed in experiment, an explosion followed by a no-current interval cannot be realized under normal conditions for tungsten, molybdenum,

VL

Tb

Tb

274

Chapter et a/. ,

15

tantalum, and zirconium (Sobolev, 1 947; Kvartskhava 1 956). Therefore, the metals whose work function is lower than the sublimation energy are not suitable for opening switches. To attain high efficiency of the energy transfer from a primary to an inductive energy store, obviously low-resistivity materials should be used. To transfer energy from an inductive energy store to a load, it is necessary to heat an exploded conductor (EC) to Tb and evaporate it. Since the energy losses for the heating and evaporation of the EC reduce the efficiency of the whole of the system, it is desirable to have a material with a low specific heat of evaporation. If we take into account that the temperature factors of resistance of high-conductivity materials are approximately identical, the product of resistivity X by sublimation energy e5 can be taken as a criterion in judging if the material is suitable · for an opening switch (Kotov 1 974). Table 1 5 . 1 lists the characteristics of the metals showing the lowest values of the product of x by e5• It can be seen that Ag, Au, Al, Zn, and Cu have the most suitable characteristics. Since gold is expensive and its characteristics are worse than those of silver, four metals remain that should be checked up experimentally. It should be noted that Maisonnier ( 1 966) and Janes and Koritz ( 1 959), who used more intricate comparison methods, arrived at the conclusion that the above metals, except zinc, should have the best opening characteristics.

et al. , eta/.

Table 15.1. Metal

x· I 07 !.1·m

Es I Q-9 J·m-3

X . Es Q·J·m-2

Silver

0. 1 66

27.6

457

Gold

0.24

1 9.5

470

Aluminum

0.32

23

736

Zinc

0.61

1 2.5

762

Copper

0. 1 78

47.5

845

Tin

1.13

1 0.2

1 1 50

Lead

2.08

1 1 .2

2330

Platinum

1.10

5 8.5

6440

Note: x is the resistivity at 1 8°C and e. is the sublimation energy.

Experiments with exploding Ag, Cu, and Al wires (Mesyats, 1 974) have shown that silver has better opening characteristics then copper and aluminum. Thus, under identical experimental conditions, for Ag and Cu wires the peak interrupted current, Imax, appears to be approximately the same, while for Al wires it is a factor - 1 .3 lower. Besides, a gap with an aluminum wire has a lower electric strength than a gap with a copper or silver wire. Therefore, an exploded Al wire is shunted by the arc discharge

PULSE GENERATORS WITH EEC'S

275

within a shorter time than copper and silver wires, resulting in a lower peak voltage. Silver wires, compared to copper ones, owing to the lower specific heat of evaporation of silver, provide generation of a pulse of higher amplitude and longer duration, the gap electric strength being the same. Silver, however, is much more expensive than copper; therefore, copper conductors are more usable. Let us pass to the choice of the shape and dimensions of exploded conductors. If for two differently shaped conductors identical in cross­ sectional area, the energy density immediately prior to the explosion is the same, the initial velocity of propagation of the evaporation wave will also be the same (Bennett, 1 967). For this case, it can be shown that the shape of the conductor cross-section affects the rate of current interruption.

(a) � (b)

�• .. u s u s

�

0 00 N

(c)

_)

•• = • ••

f

Figure 15.3. Voltage waveforms for copper conductors of the same cross-sectional area in air connected in a circuit with C 2.6 J.LF, V0 37 kV, L 2.2 J.LH: a foil of cross-section 0.0 147x4 mm and length 580 mm a wire of diameter 0.28 mm and length 1 90 mm (b), and 1 2 parallel wires of diameter 0.08 mm and length 350 mm. The voltage scale is the same for all traces. The calibration frequency is 12.5 MHz =

(a);

=

=

An opening switch made of parallel thin wires provides a shorter opening time and a considerably higher power (Fig. 1 5.3) than a single cylindrical or foil conductor of the same cross-section does. It is should be noted that the chosen conductor lengths ensured the highest voltage (power), and the energy absorbed by the opening switches was approximately the same. Therefore, in subsequent experiments and developments, opening switches made of parallel thin wires were used. It should be noted that in switching currents of - 1 06 A, foil opening switches may appear to be more technological (Bakulin et a/. , 1 976). The overall dimensions of a switch can be reduced by arranging the conductors in a zigzag (Kotov et a/. , 1 976).

Chapter 15

276 3.

THE MHD METHOD IN DESIGNING CIRCUITS WITH EEC SWITCHES

In magnetohydrodynamic (MHD) calculations, the coordinate-dependent current density, the electric and magnetic field strengths, the density, temperature, pressure, and mass velocity of the material, and the radiation field in the material (if this field is significant) are determined at each point in time. Simultaneously, the calculation gives the time dependences of currents and voltages for every element of the electric circuit. As a rule, calculations of this type are based on solving numerically one-dimensional MHD equations in the one-temperature approximation taking into account electronic heat conductivity. The radiation transfer to the material is described in the spectral diffusion approximation. The system of equations in Lagt:angian coordinates for the case of cylindrical symmetry is given by Kotov et al. ( 1 987). In calculations of this type, it is of critical importance that the properties of the material, equations of state, relations of the electric and heat conductivities on the state of the material, and spectral coefficients of absorption of radiation be described adequately. The description of the properties of a material over a wide range of states, including the metal-to­ plasma transition region, is an independent and rather intricate physical problem. In calculations of an EEC, various methods for such a description are used. For example, Bakulin et a/. ( 1 976), used the equations of state derived based on the Thomas-Fermi model (Kalitkin and Kuzmina, 1 978) for the high-temperature region (T > 1 eV). To specify the coefficients of electrical and heat conductivities, interpolation formulas constructed with the use of a semiclassical theory of transfer were applied. The spectral radiation field over which the absorption coefficients were averaged was determined by solving the equations of spectral diffusion of radiation (Kotov and Luchinsky, 1 987). The absorption coefficients were set either by tables, obtained from detailed quantum-mechanical calculations, or by analytic formulas (Zel'dovich and Raizer, 1 963). The procedure of averaging was carried out in a certain number of time steps. The values of hydrodynamic quantities at the boundary of the mixed phase region calculated from thermodynamic relations as functions of the relative density of the material are presented in Fig. 1 5 .4. The critical point is characterized by 8 0.322 and Er 5.28 kJ/g. Within the mixed phase region, the hydrodynamic quantities were estimated by interpolation with respect to the concentration of one of the phases between the values of these quantities at the boundary. To find the dependence of the electrical conductivity on the state of the material, a calculation-experimental method was applied in which the electrical conductivity was chosen so that the

=

=

277

PULSE GENERATORS WITH EEC'S

calculations would describe with a reasonable accuracy a number of "reference" experiments on the explosion of conductors that had been carried out under conditions considerably different from each other. For fixed values of f:T below the critical value, the resistivity abruptly increases with decreasing 8 near the 8 values corresponding to the boundary of the mixed phase region and has a maximum at a density below the critical density. This circumstance plays an important role and largely determines the increase in metal resistance during an electrical explosion and the switching capabilities of electrically exploded conductors. 10 20

8

1 5 '2 e:.

bil 6

g .... w

w

4

10

2

5

0.2

0

0.4

0

0.6

600

50

500

40

400

� 30

� 300

20

200

......

:::...

10

1 00

0

0

l:l..

0.8

Figure 15.4. Time variations of pressure p, specific internal energy energy ET at the boundary of the phase mix region for copper

60

"" 0

&,

and specific thermal

I = 27 em

3 2 t [J.I.S]

4

0

1 2 t [J.I.S]

3

Figure 15.5. Voltage and current waveforms for single wires of different length exploded in air at V0 = 1 40 kV, Co = 1 .5 J.I.F, L = 3 J.I.H, r = 0.0 1 4 em

278

Chapter 15

The calculation method described was checked by comparing the calculation results with the data of numerous experiments among which there were two-stage explosions of copper and aluminum conductors in air, water, oil, and epoxy compound (Kotov and Luchinsky, 1 987). In all cases, the difference between the calculated and experimentally determined peak currents and voltages was not over 1 0%. The calculations described rather adequately the dependences of the current and voltage on time and on the characteristics of the wires and electric circuits. Some calculation results and experimental data are compared in Fig. 1 5 .5. The solid and dashed lines represent, respectively, the measured and calculated current /(t) and voltage V(t) With this method, calculations of the pulsed currents and voltages generated by systems of the IGUR type (Kovalev et a/. , 1 98 1 ) were carried out, the parameters of the systems were chosen, the operation of the circuits was analyzed, and the modes of operation were selected. .

4.

THE SIMILARITY METHOD IN STUDYING GENERATORS WITH EEC SWITCHES

The MHD method allows one to calculate all characteristics of a circuit with an EEC opening switch operating into a load. At the same time, these calculations are rather cumbersome and call for special computer facilities. The alternative is similarity theory that enables one, with a minimum of information on the mechanism of a phenomenon, to reduce the number of variables, to establish the form of the dependence of the sought-for quantities on similarity criteria, and to extend the dependences obtained to the whole class of similar phenomena. Calculations of EEC with the use of similarity criteria allows an engineer to optimize a circuit for a chosen parameter with an accuracy sufficient for designing and to predict the basic characteristics of the circuit, such as the amplitude and duration of current and voltage pulses, the energy transferred to the load, the time to explosion, etc. (Kotov et a/. , 1 974; Kotov and Luchinsky, 1 987). The factors that substantially affect the behavior of an LC circuit with an EEC switch (without a load), are the capacitance C and charge voltage V0 of the capacitor bank, the inductance of the discharge circuit, L, the diameter d, length /, and number n of the parallel wires used, and some characteristic values of resistivity xo, specific energy e0, and rate of destruction v0 of the conductor material. It is supposed that v0 is a function of only e0• According to the similarity theory, the eight dimensional factors, which are described with the help of five independent dimensions (the dimensions of length and diameter in the given description of the phenomenon are considered independent) (Kline, 1 965), can be combined in three

PULSE GENERATORS WITH EEC'S

279

dimensionless complexes. When doing this, it is desirable that the complexes be physically meaningful. We write these complexes as

CVo2 - Vo JLC xol -1 - nd2.JLIC' -2 - n2d4E0.JLIC' d ' Z = JLC; il 2 Eo), v0 x , Eo, (15.2) n

n

n

(15.2)

3-

where II 1 describes the attenuation of oscillations in the circuit, i.e., characterizes the ratio of the active resistance of the conductors to the wave impedance of the circuit describes the specific action of the circuit current for conductors of the chosen section (the product of il 1 by the and il describes the ratio of the time ratio of the stored energy to 3 constant of the circuit to that of the explosion of the conductors. If we investigate one metal, the constants and that describe the metal in can be omitted, and then we obtain three dimensional parameters:

For convenience, we assume that the initial factors have the following dimensions: l and [mm], [�F], [�H], [kV], and [�s]. The investigations performed by Kotov and Sedoi have shown that all characteristics of an circuit with EEC can be modeled by the parameters with an error no more than over a wide range of initial values of the circuit characteristics:

d C L V0 JLC (1976) LC (15.3) 20% Von ==1-80, 1-500 dC== 0.0.1-2000 L = 0. 4 -50 04-1 = 4-2600 mm. A.=E = (0.18-20)· (0.07-2)·1041 06 J/(mm4· -' · -0' ), v= 10-190 �F, mm,

kV,

�H,

l

The parameters were varied within the following limits: n

mm

1

�s/mm,

thus covering the entire spectrum of the operation characteristics of EEC opening switches. Prior to the onset of an explosion, the characteristics depend only on f.. and (Azarkevich, For example, the normalized circuit current is given by

E

Ym

1973). = I�� = A(E ·10-6A_ll3 )a ' Ia

(15.4)

(where is the peak current) and the normalized time it takes for the current to reach a maximum is

280

Chapter 15 (1 5.5)

In ( 1 5 .4), A = 0.9 and a = -0.25 for copper conductors and A = 0.78 and a = -0.3 1 for aluminum conductors. In ( 1 5.5), B = 0.9 and � = -0.3 1 for copper conductors and B = 0.9 and � = -0.3 for aluminum conductors. Similar expressions have been obtained for the energy absorbed by a conductor to the moment the current reaches a maximum and for silver conductors. If a characteristic also describes the stage of explosion, for example, the peak voltage across the conductor, Va, it depends on all the three parameters that enter in ( 1 5 .3). It was revealed (Kotov et a!. , 1 974) that the highest rise rates of resistance of an exploded conductor are reached if the conductor length is close to its critical value, fer, that provides, with other things being equal, a no-current interval of zero duration. To simplify the expressions for the characteristics under investigation, the dependence of the parameter Acr on E and v was found for l = lcr (Fig. 1 5.6) and all other dependences were determined for the critical length. For example, the normalized peak voltage (overvoltage) K = VP /V0 was obtained for Acr as a function cf E, v, energy absorbed by the conductor explosion delay time, voltage pulse duration, etc. (Fig. 1 5.7) (Sedoi, 1 976; Kolganov et a!. , 1 976). Analysis of these dependences allowed the conclusion that silver conductors have characteristics very similar to the characteristics of copper conductor, while aluminum conductors, for the production of the same power, demand a lower inductance of the circuit and should have larger cross sections and lengths in comparison with copper, i.e., in technological and constructive requirements they are exceeded only by copper conductors. Therefore, the latter were used in the subsequent research and development work. q

I

20

"'

�

�.

10 8 's .§.. 6

0

4 2

o,.,

� :31--'

....

4

1"1

�

-

�'-' �

� . �� ..

. ....1":.---

6 8 10

EV

20 40 60 1 00 · 1 06 ((J·JlS)/(Q·mm5)]

200

400

Figure 15.6. Parameter A cr as a function of E and v for aluminum, silver, and copper conductors (from top to bottom). The regions above and below each plot are associated with an explosion with and without a no-current period, respectively

PULSE GENERATORS WITH EEC'S

0

20

40

v

60 80 [J.!slmm]

281

1 00

1 20

140

Figure 15. 7. Normalized peak voltage across an EEC as a function of simulation parameters: the solid, dot-and-dash, and dashed curves correspond to copper, silver, and aluminum, respectively; the numbers at the curve denote the respective values of the parameter 1 0-6 e ·

Based on the relations described, the power supplies of now operative six direct-action accelerators were designed. The power supplies provided an output voltage ranging from to MV, currents from to kA, and pulse durations from to ns. Some of them were described by Mesyats Kotov et and Kotov and Luchinsky Azarkevich et used similarity criteria and an experimentally revealed dependence of the resistance of a copper wire on the conditions of its explosion to describe the operation of a circuit with an EEC opening switch by a system of equations and designed a code for solving these equation to find the circuit parameters. In contrast to the MHD model, this one is substantially simpler. Moreover, it is applicable to any circuit containing an EEC switch (e.g., line transformer) and any type of load, including a nonlinear one (vacuum diode, variable inductor, etc.) if this load can be described by some equation, to obtain current and voltage waveforms for given points of the circuit. Earlier we used an engineering method that was applicable only to circuits with the diode replaced by an invariable resistor and allowed calculations of the peak voltage and current only.

(1974),

0. 3 2. 5 50 700 al.al.(1976), (1990)

4 55 (1987).

LC

5.

DESCRIPTION OF PULSE DEVICES WITH EEC SWITCHES

Pulse generators with inductive energy storage usually operate by the following scheme: A Marx generator, which serves as a primary energy store, is discharged into an inductor. As the inductor current reaches a

282

Chapter

15

maximum, an opening switch operates that cuts off or abruptly reduces the current. This results in an emf generated in the inductor. After the operation of a closing switch, this emf is applied to the diode of an accelerator, giving rise to explosive emission of electrons and their acceleration. The opening switch is a basic element of this type of system. This can be a switch based on exploding wires, a plasma erosion opening switch, and a semiconductor switch. In one of the first studies performed at IHCE, a Marx generator was discharged into an inductive energy store (Koval'chuk Thin electrically exploded conductors were used as an opening switch (Fig.

et al. , 1974).15.8).

L

SG

� �,

EEC

- -

..------ 2 3

-

-

-

Figure 15.8. Schematic diagram of an electron accelerator: 1 multipoint cathode, 2 metal foil anode, 3 Faraday cup, 4 Marx generator with capacitance C1 C/n (n being the number of stages), R shunt for measuring current =

If the resistance of an openin switch increases by the linear law R = with the load resistance R1oad » LIC1 (L being the inductance of the circuit and the capacitance of the Marx capacitors connected in series), a voltage pulse of duration fp = JiJb and amplitude

J

C1

bt

(15.6) where V0 is the voltage at the MG output, will appear between the switch terminals. Hence, to produce a pulse of large amplitude and short duration, it is necessary to increase the rate of rise of the switch resistance. For opening switches with exploding conductors, the highest resistance rise rate can be obtained, as shown above, by using a large number of parallel-connected thin conductors (Koval'chuk If we assume that the conductivity of a conductor falls during the propagation of the evaporation wave, we have that at the time zero

et al. , 1974).

( dR ) = 16xlv3 -;Jt

t=O

nnd '

(15.7)

PULSE GENERATORS WITH EEC'S

283

where X is the resistivity; n, I, and d are the number of conductors, their length and diameter, respectively, and v is the velocity of propagation of the evaporation wave. Thin multiwire opening switches were used in two types of electron accelerator and x-ray source: Puchok and VIRA. In an electron accelerator of the Puchok type (Kotov et al., 1 976), an additional inductor, a vacuum insulator, a peaking and a chopping spark gap were mounted in a common case (Fig. 1 5.9) filled with nitrogen at 1 0 atm. The opening switch was made of parallel copper wires fastened in a zigzag fashion on an insulating support. Since the inductor, being a source of current, was switched into the diode, the accelerating voltage was determined by the resistance of the diode and by the switched current and could be considerably greater than the output voltage of the MG. Used as a cathode was a steel hollow truncated cone with an exit diameter of 60 mm; the anode was made of copper foil. The peak current was 45 kA and the peak voltage was 1 .75 MV. These results were obtained at V0 = 390 kV and = 12.5 ).!H with 62 wires of diameter 0.06 mm and length 2.5 m. The pulse was chopped by the discharge initiated in the gap of the opening switch. In contrast to conventional circuits, in the accelerator under consideration the power supply was matched to the load merely by varying the wave impedance of the circuit and the parameters of the opening switch. For this accelerator, the ratio of the total energy of the beam to the volume of the system ( 1 . 5 kJ/m3 ) was much greater than for conventional systems with capacitive energy storage for which it ranges between 0.04 and 0.4 kJ/ m3 • The parameters of several nanosecond electron accelerators of the Puchok series are given in Table 1 5.2.

L

LC

Table 15.2. Accelerator

V0, kV

Puchok-0.6

350

12

6.1

0.6

C, pF

L, JlH

V, MV

I, kA 5 .2

tp,

ns

1 00

t.. ns 20

50

2500

4. 1

0.32

8

70

15

Puchok-0.6A

1 70

1 700

3.6

0.65

42

50

15

Puchok-2

390

520

12.5

1 .75

45

1 00

20

Puchok- I B

300

320

14

1 .5

23

80

8

Puchok-0.3

The VIRA series of generators have been created at IEP. One of them had the following parameters (Kotov et al. , 1 990): voltage 1 .5 MV, current 30 kA, and pulse duration of about 1 00 ns. The Marx generator, which was discharged into an inductor of inductance 5 .3 J.!H, had a voltage of 400 kV and a capacitance of 0.3 ).!F. The opening switch consisted of 30 copper conductors of diameter 0.08 mm and length 1 .6 m.

284

Chapter 15 To oscilloscope

CT

Figure 15.9. Schematic diagram ofthe Puchok accelerator with an inductive energy store and a multiwire opening switch: CT - current transformer in the opening switch circuit, Lso1 solenoid inductance, EC - exploded conductors, VI - section vacuum insulator, C - cathode, A - diode anode, VD - voltage divider, SG1-SG2 - spark gap switches

To develop an accelerator with an EEC opening switch, two approaches can be used: an MHD method and calculations based on similarity theory. Typical representatives of systems designed by applying the similarity method are the Puchok and VIRA machines considered above. The method of mathematical modeling was used to design systems of the IGUR type, developed at the Scientific Research Institute of Applied Physics (Kovalev et a/. , 1 98 1 ). The IGUR- 1 system has the following parameters: voltage 3 . 1 MV, current 44 kA, and pulse duration 1 00-500 ns, and the IGUR-2 system, respectively: 3 .7 MV, 70 kA, and 1 00-500 ns (Kovalev et a/., 198 1). In the IGUR- 1 generator producing short pulses of braking radiation (Fig. 1 5 . 1 0), the primary energy store is a twelve-stage Marx generator with the following parameters: C = 0.29 J..I.F , V0 = 0.96 MV, and L = 12 f.!H. The generator is charged by a voltage of ±40 kV. The spark gap SG 1 is intended to start the Marx generator; the spark gaps SG and SGch protect the Marx generator and the acceleration tube from being overvolted. The system as a whole is made in open version; the high-voltage insulation is air. The acceleration tube consists of a steel container, two porcelain insulators of maximum internal diameter 43 and height 350 em, and a steel rod that is terminated with a cathode. As the spark gap SG 1 in the first stage operates,

PULSE GENERATORS WITH EEC'S

285

the Marx generator is started and a current flows through the opening switch made of parallel-connected copper conductors. On explosion of these conductors, a voltage is applied to the acceleration tube through the spark gap SGpeak· In the optimum mode, the output voltage was 3.2 MV, the current 44 kA, and the pulse duration 1 00-500 ns. Rsh

Ro

Ro

Ro

SG 1 3

L

Figure 15. 10. Circuit diagram of the IGUR- 1 accelerator: R0 and C - MG resistors and charging resistor, SG2-SG 12 - GM spark gaps, SG1 - trigger spark gap, capacitors, Rsh SG1 3 - switch, rEEc EEC switch, L - inductor, SGpeak - peaking spark gap, DT - discharge tube, SGch - chopping spark gap, Sh - shunting spark gap -

-

The IGUR-2 accelerator (Diankov et al. , 1 995) is designed as a two-stage system. As the capacitive energy store is discharged into the inductive unit and the conductors explode, the spark gap in the first stage operates to switch on the second stage. The acceleration tube is connected, with the help of the spark gap of the second stage, in parallel with the second EEC switch during its explosion. Such a circuit allows the voltage pulse to be peaked additionally. Considerably greater pulse parameters have been attained with the IGUR-3 system (Diankov et al. , 1 995). The high voltage pulse is produced with the help of an inductive energy store and an EEC opening switch. The primary energy store consists of two 1 .4-MV Marx generators capable of storing 300 kJ of energy. Each Marx generator is placed in a tank of height 1 .2 m and diameter 7.5 m. Along its axis, a container of height of 8.5 m and diameter 2 m is located. In this container, there are a storage inductor, an EEC unit, an oil peaking spark gap, and an acceleration tube with explosive electron emission, which serves as a load. The EEC unit consists of 1 5 pipes of diameter 1 1 0 mm. All units of the accelerator are immersed in transformer oil. Several operation modes of the generator were tried out with the production of braking radiation and an electron beam on the nanosecond and microsecond scales. The greatest doze rate of braking radiation at a distance of 1 m from the diode window, 1 0 1 0 R/s, was obtained at a load voltage of

286

Chapter 15

6 MV, a current of 55 kA, and a pulse duration of 25 ns. Besides, a mode was worked out in which two successive pulses are generated by the Marx generators. In the electron acceleration mode, an electron beam with a current of up to 3 0 kA, a duration of 3 0 ns, and an average electron energy of 2.5 MeV was obtained. The next system of this series is the EMIR-M machine (Diankov et al. , 1 995). This is a combination oftwo high-voltage pulse devices. The first one is a pulsed electron accelerator consisting of a Marx generator, an inductive energy store, an EEC opening switch, a switch connecting the accelerator to a load, and an acceleration tube. The second one incorporates a high-voltage pulse generator and a system generating an electromagnetic field. The devices are grouped in such a manner that they can create, separately or simultaneously, a pulsed flux of gamma photons or electrons and an electromagnetic field in the test zone. In addition, the design of the Marx generator and its configuration in two independent units makes it possible to use one acceleration tube to produce two successive radiation pulses with an adjustable time interval. The general view of the EMIR-M system is given in Fig. 1 5. 1 1 (Koval'chuk and Kremnev, 1987). The Marx generator with bipolar charging consists of twenty four independent modules grouped by twelve in two independent units. In each unit, the module outputs are combined by a collector. Each collector is connected to the EEC unit through its own inductor.

Figure 15.1 1. Schematic diagram of the EMIR-M system: 1 channels; 3 test zone; 4 electromagnetic field generator; 5 switch of the diode; 7 EEC unit container -

-

-

-

MG container; 2 EEC insulator of the diode; 6 -

-

-

The EEC unit is a device providing technological conditions for mounting a set of conductors, exploding the latter, and removing the explosion products. It is designed as a set of ten airtight polyethylene pipes (channels) of diameter 1 3 0 mm and length 4 m in which cartridges with

PULSE GENERATORS WITH EEC'S

287

conductors are placed. Immediately prior to the operation, the channels are filled with air compressed to a pressure of up to 3 atm. In operating conditions, the set of conductors involves approximately 1 00 copper wire pieces of diameter 0. 1 mm and length 4-6.5 m. The acceleration tube (diode) is structurally similar to a number of devices of this type. Its basic element - a vacuum insulator - is a set of alternating insulating and grading rings. The insulating and grading rings are made of caprolon and aluminum alloy, respectively. The number of insulating rings is nineteen at a height of 1 00 mm or forty six at a height of 40 mm. The grading rings are figured to provide shielding of the vacuum surface of the insulator. The internal diameter of the insulator is 1 080 mm. The electrodes of the diode are designed as two coaxial cylinders of length 700 mm The diameters of the inner and outer cylinders are 1 00 and 500 mm, respectively. Depending on the operation mode, the face part of the outer electrode is furnished with a tantalum target (for the production of braking radiation) or a titanium foil window (for the extraction of an electron beam). The EMIR-M system was also operated as an electromagnetic field generator. It has been shown (Luchinsky et al. , 1 997) that a pulsed voltage of up to 5 MV can be produced with the use of a line transformer as an inductive energy store and electrically exploded conductors as an opening switch (the MIG system). The compactness of the line pulse transformer, EEC unit, and storage inductor and the possibilities to vary the pulse voltage, rise time, and duration over wide limits make the system very convenient for physical research at small laboratories. .

REFERENCES Azarkevich E. 1., 1 973, Application of Similarity Theory to the Calculations of Some Characteristics of Electrically Exploded Conductors, Zh. Tekh. Fiz. 43: 14 1 - 1 45. Azarkevich, E. 1., Goryainov, G. M., and Zherlitsyn, A. G., 1 990, Formation of Relativistic High-Current Electron Beams from Low-Voltage Energy Sources. In Proc. VIII Int. Conf on High-Power Particle Beams (BEAMS '90), (July 2-5, 1990), Novosibirsk, USSR; World Scientific. 1 990. Vol. 2, pp. 854-859. Bakulin, Yu. D., Kuropatenko, V. F., and Luchinsky, A. V., 1 976, Magnetohydrodynamic Calculations of Exploding Wires, Zh. Tekh. Fiz. 46: 1 963-1 969. Bennett, F. D., 1 967, High Temperature Exploding Wires. In Progress in High Temperature Physics and Chemistry (C. A. Rouse, ed.), Pergamon Press, Oxford, Vol. 1 . Diankov, V. S., Kovalev, V. P., Kormilitsyn, A. 1., and Lavrentiev, B. P., 1 995, High-Power Generators of Braking Radiation and Electron Beams Based on Inductive Energy Stores, Izv. Vyssh. Uchebn. Zaved. , Fiz. 12:84-92. Early, H. C. and Martin, F. J. , 1 965, Method of Producing a Fast Current Rise from Energy Storage Capacitors, Rev. Sci. Instrum. 36: 1 000-1 003.

288

Chapter 15

Janes, G. S. and Koritz, H., 1 959, High-Power Pulse Steepening by Means of Exploding Wires, Ibid. 30: 1 032-1 037. Kalitkin, N. N. and Kuzmina, L. V., 1 978, Tables of Thermodynamic Functions of Matter at High Energy Densities: ?reprint. Inst. Appl. Mathematics ofthe USSR AS, Moscow. Kline, S. J., 1 965, Similitude and Approximation Theory. McGraw Hill, New York. Kolganov, N. G. and Kotov, Yu. A., 1 976, Switching of an LC Circuit into an Active Load with the Use of Electrically Exploded Conductors. In Development and Application of Intense Electron Beam Sources (in Russian, G. A. Mesyats, ed.), Nauka, Novosibirsk, pp. 9-75. Kotov, Yu. A. and Luchinsky, A. V., 1 987, Amplification of the Power of a Capacitive Energy Store by an Opening Switch Based on Exploded Conductors. In Physics and Technology of Pulsed Power Systems (in Russian, E. P. Velikhov, ed.), Energoatomizdat, Moscow, pp. 1 89-2 1 1 . Kotov, Yu. A. and Sedoi, V . S., 1976, Similarity in an Electrical Explosion of Conductors. In Development and Application of Intense Electron Beam Sources (in Russian, G. A. Mesyats, ed.), Nauka, Novosibirsk, pp. 56-59. Kotov, Yu. A., Kolganov, N. G., and Sedoi, V. S., 1 974, Formation of High-Voltage Pulses with the Use of Exploded Conductors. In High-Power Nanosecond Pulse Sources of Accelerated Electrons (in Russian, G. A. Mesyats, ed.), Nauka, Novosibirsk, pp. 83-96. Kotov, Yu. A., Kolganov, N. G., Sedoi, V. S., Koval'chuk, B. M., and Mesyats, G. A., 1976, Nanosecond Pulse Generators with Inductive Storage, Proc. I IEEE Intern. Pulsed Power Conf, Lubbock, TX, pp. ( 1 A)1 - 1 1 . Kotov, Yu. A., Sokovnin, S . Yu., and Filatov, A. L., 1990, VIRA- 1 .5 M, a Compact Generator of Braking Radiation, Prib. Tekh. Eksp. 2 : 1 49- 1 53. Koval'chuk B. M., Kotov, Yu. A., and Mesyats, G. A., 1 974, A Nanosecond High-Current Electron Accelerator with an Inductive Energy Store, Zh. Tekh. Fiz. 44:2 1 5-2 17. Koval'chuk, B. M. and Kremnev, V. V., 1 987, Arkadiev-Marx Generators for High-Current Accelerators. In Physics and Technology of Pulsed Power Systems (in Russian, E. P. Velikhov, ed.), Energoatomizdat, Moscow, pp. 165-1 79. Kovalev, V. P., Kormilitsyn, A. 1., Luchinsky, A. V., Martynov, V. 1., and Pekhterev, I. A., 1 9 8 1 , IGUR- 1, an Electron Accelerator with an Inductive Energy Store and Exploded Conductors, Zh. Tekh. Fiz. 51: 1 865-1 867. Kvartskhava, I. F., Bondarenko, V. V., Plyutto, A. A., and Chemov, A. A., 1956, Oscilloscopic Determination of the Energy of an Electrical Explosion of Wires, Zh. Eksp. Teor. Fiz. 31 :745-75 1 . Luchinsky, A . V., Ratakhin, N . A., Feduschak, V . F., and Shepelev, A. N., 1 997, A Transformer-Type Multipurpose Pulse Generator, Izv. Vyssh. Uchebn. Zaved. , Fiz. 12:67-75. Maisonnier, Ch., Linhardt, J. G., and Gourlan, C., 1966, Rapid Transfer of Magnetic Energy by Means of Exploding Foils, Rev. Sci. Instrum. 37: 1 3 80- 1388. Mesyats, G. A., 1 974, Generation of High-Power Nanosecond Pulses (in Russian). Sov. Radio, Moscow. Sedoi, V. S., 1 976, Some Regularities in an Electrical Explosion of Conductors, Zh. Tekh. Fiz. 46: 1 707- 1 7 1 0. Sobolev, N. N., 1 947, Study of the Electrical Explosion of Thin Wires, Zh. Eksp. Teor. Fiz. 17:986-997. Zel'dovich, Ya. B. and Raizer, Yu. P., 1963, Physics ofShock Waves and High-Temperature Hydrodynamic Phenomena (in Russian). Fizmatgiz, Moscow.

Chapter 1 6 PULSE GENERATORS WITH PLASMA OPENING SWITCHES

1.

GENERATORS WITH NANOSECOND PLASMA OPENING SWITCHES

A major trend in pulsed power is the development of systems with inductive energy storage and plasma opening switches (POS's). The use of POS 's enables one to solve several problems: to increase the power of pulse generators, reduce the pulse duration, eliminate prepulses, and create compact and low-cost pulse generators and accelerators. In general, a POS operates as follows: Near the load of the pulse generator, a plasma bridge forms between the grounded and the potential electrode. The current of the generator originally flows through this bridge; as this takes place, energy is partially (or completely) delivered from the capacitive to the inductive energy store. Under certain conditions, the conductivity of the plasma bridge abruptly decreases, a vortical emf is generated, and the energy stored in the inductor is switched into the load. As prototypes of POS's, plasma-filled diodes can be considered that were used by Plyutto and co-workers (Suladze et al. , 1 969; Mkheidze, et al. , 1 97 1 ) in their experiments on the production of high-power electron beams for collective acceleration of ions. The experimental arrangement is given in Fig. 1 6. 1 . The plasma generated by a spark plasma source 1 flew into an acceleration gap 2 of width 2 em. The accelerating field, which was sustained by a capacitor of capacitance C2 = 0.4 J.lF, was applied to the gap filled with plasma (n � 1 0 1 3 cm-3) with a delay of � 1 -2 J.lS. A distinctive feature of the formation of an electron beam in an acceleration gap prefilled with plasma is that at the initial stage of the current passage, the gap is

290

Chapter

16

short-circuited by plasma and the gap voltage is low. As the current reaches some critical value, the resistance of the gap increases, the electron current is cut off, and the potential difference across the gap abruptly increases to a value exceeding the initial voltage of the power supply. At the stage of cutoff of the total current, an electron beam is formed in the plasma a significant part of which passes through the anode grid and is measured by a Faraday cup. In the experiment under consideration, the critical current increased with plasma density and reached 2 · 1 04 A. The beam current reached 1 04 A with a pulse duration of 3 · 1 0-7 s. The electrons had a broad energy spectrum, and their maximum energy reached 3eV0 (Vo being the voltage applied to the gap). 3

2

1

L

Figure 16. 1. Sketch of the experimental arrangement: 1 - spark source, 2 - acceleration gap, 3 - acceleration electrode, SGt. SG2 - spark gaps, L - inductance of the capacitor C2 and discharge circuit

The next step in the development of this technology was the experiment carried out on the Proto I system at SNL (Mendel 1 976, 1 977). A plasma source was built in an explosive-emission diode to eliminate prepulses that arise during the operation of a Marx generator and a main switch due to the displacement current flowing through the self-capacitances of switches and peakers. Such a prepulse creates plasma in the diode before the arrival of the main pulse, disrupting the operation of the electron accelerator because of the decrease in diode impedance. Since the prepulse current is low compared to the main pulse current, the plasma bridge initially operates in the short-circuit mode, and the resistance abruptly increases during the rise time of the main pulse. In the diode of the Proto I accelerator (Mendel 1 976), the cathode of diameter -2.5 em was grounded and the anode was under a pulsed potential of -2 MV. The main switch consisted of two switches, each composed of several plasma guns evenly arranged in a circle. These two

et al. ,

eta/. ,

PULSE GENERATORS WITH PLASMA OPENING SWITCHES

291

circles were coaxial with respect to the cathode. The anode plate, made of copper, aluminum, or carbon, had a thickness of 1 .2 or 0.6 em. The cathode was mounted on the plate of the switch. The plate contained two series of round holes through which the switch plasma flew toward the anode plate. The switch operated as a diode with a rapidly varying anode-cathode gap. The variation of the gap was because the significant current caused so intense losses of ions in the cathode plasma layer that this plasma decayed more rapidly than the flowing plasma could replace it. This criterion of plasma flow balance gave the threshold current for the switch to operate as an opening switch. The POS performed only one function: It reduced the prepulse in the Proto I accelerator. Because of the rapid increase in voltage, a prepulse of amplitude to 30 kV passed through the capacitance of the switch to the diode. This prepulse created a plasma of density - 1 0 1 3 cm-3 at the cathode, which was a handicap to z-pinch experiments. In the presence of a plasma switch, the prepulse amplitude decreased and its subsequent fluctuations were eliminated. Because of the short rise time of the diode voltage, it became possible to make the anode-cathode gap as small as 2 mm at a voltage of -2 MV. On the Proto I accelerator with the switch described, the current rise rate at the cathode reached -3· 1 013 A/s, and the rise rate of the voltage across the anode-cathode gap was as high as 1 0 1 5 V/s. The accelerator current equal to -75 kA was switched to the anode-cathode gap within 5 · 1 o-9 s. An important step in the development of the POS technology was the experiment performed by Stringfield and co-workers (Stringfield et a/. , 1 9 8 1 ) on the Python system. The plasma switch passed a current of 1 MA and substantially shortened the rise time of the current in the load (the diode of an accelerator) due to the nonlinear resistance of the plasma. Thus, the POS played the role of a peaker for the pulse leading edge. Meger et al. ( 1 983), in experiments on the Gamble I system at NRL, have demonstrated the possibility of using a POS (Fig. 1 6.2) both as a peaker for the pulse leading edge and as an opening switch to increase the peak power and shorten the pulse across the load in systems with inductive energy storage (Fig. 1 6.3). In all these and subsequent experiments with POS 's carried out at the laboratories of the United States, high-power pulse generators based on water lines were used. The characteristic time of the closed state of the POS was -1 0-7 s and the duration of the current cutoff phase was -1 o-s s. Therefore, we refer to this type of POS as a nanosecond POS. The early work with systems of this type was reviewed by Weber et al. ( 1 987) and Guenther et al. ( 1 987).

I0

Chapter 1 6

292

Plasma sources

Vaccuum inductive store region 1 00-200 nH

Figure 16.2. Schematic o f a POS built i n a coaxial transmission line 300

� ....,

(a)

>

(b)

�

200

": I

::::...

1 00

0

2

20

40

60 80 1 00 1 20 t [ns]

1

0

20

40

60 80 1 00 120 t [ns]

Figure 16.3. Experimental data obtained on a generator with a POS: (a) shortening of the pulse rise time with a short-circuited load; (b) 1 - voltage across a matched load without a POS; 2 - voltage across the load with the use of an inductive energy store and a POS (a)

(b)

-..-

/E:?£=<8): --

��0��0 000�00 ��0��� 000000 ��0��0 �00�00 ��0��0 000000 �

�00�00

I

S cm

...__ '--

Copper Insulator

I

Figure 16.4. Plasma sources used in plasma opening switches: a - coaxial plasma gun; b plasma source with dielectric surface discharge, c - plasma expansion from the source

-

PULSE GENERATORS WITH PLASMA OPENING SWITCHES

293

To understand the operation of plasma opening switches, we consider the designs of plasma sources. As a rule, two types of source are used: coaxial guns and multielectrode guns with a discharge over the surface of a dielectric (Fig. 1 6.4) (Weber et a/. , 1 987). These guns are usually charged from capacitors through gas spark gaps. The current varies by a damping sinusoid with a period of several microseconds.

2.

GENERATORS WITH MICROSECOND POS'S

The shortening of a pulse duration from 1 o-7 to 1 o-s s with the use of a POS failed to simplify the design of nanosecond high-power pulse generators because this did not eliminate the complex system of pulse transformation between the Marx generator (MG) and the load that included an intermediate coaxial capacitive energy store, bushing insulators, fast high­ power switches, etc. It was anticipated that a POS could be used to transform the microsecond pulse produced by an MG directly into a pulse of duration 1 0-7 s with many times increased power. This idea was first realized at IHCE (Abdullin et al. , 1 986). Therefore, we consider the operation of microsecond POS 's using the works performed at IHCE as an example. Preliminary experiments were carried out on the Gamma system (Abdullin et al. , 1 986). This was an electron accelerator intended for the production of high-power microsecond electron beams with an MG discharging into an explosive-emission electron diode. A schematic diagram of the experimental setup is shown in Fig. 1 6.5, a. The primary energy store was an MG with a capacitance of 0.26 �-tF and an inductance of 2.5 J..lH. An electron diode with a graphite cathode of diameter 1 40 mm and a hollow cylindrical anode through which plasma was injected into the cathode-anode gap served as a load. Plasma was generated with the use of eight coaxial plasma guns into which capacitors of capacitance 3 J..lF and voltage 20 kV were discharged. The period of fluctuations of the discharge current was 20 J..lS , and the delay time between the start of the MG and the operation ,of the plasma guns could be varied in the range 0-200 J..lS. Typical diode current and voltage waveforms obtained without and with a plasma opening switch are given in Fig. 1 6.5, b and c, respectively. With no plasma, the power in the diode was 5· 101 0 W, and in the presence of plasma, which appeared 1 8-23 J..lS before the start of the MG, it was 3 · 1 0 1 1 W. Thus, a sixfold increase in power took place. Within 300 ns, about 60% of the energy generated by the MG were transferred to the load. The voltage across the load almost doubled. Thus, it was proved that a POS could be operated in the mode of microsecond pulse rise times and durations. We refer to opening switches of this type as microsecond plasma opening switches (MPOS 's).

Chapter 1 6

294

The next very important step in the development o f MPOS's was the proposal of Koval'chuk and Mesyats (1985) to use a vacuum coaxial line with magnetic self-isolation (MIVL) as an inductive energy store. This simultaneously solved the problems of energy storage and its transfer to the load. In addition, the conditions for designing were considerably improved since there was no need in a bushing insulator between the opening switch and the load (electron diode, ion diode, x-ray diode, etc.). (a)

(b)

I

(c)

v

, ....... ,., ....... _ ....... - I 1 00 I I ,...., 0 d f""----'---7---1

200

200 1 00 0

0.5

1 .0 1 .5 t [).LS]

2.0

Figure 16.5. The Gamma electron accelerator with an MPOS: a - schematic diagram of the accelerator (I - Marx generator, 2 - diode, 3 - plasma guns); b - current and voltage waveforms for the diode not filled with plasma; c - current and voltage waveforms with the diode filled with plasma

The circuit of such a generator is shown schematically in Fig. 1 6.6. With the MPOS closed, a capacitor bank or a Marx generator is discharged into a line, which stores an energy Lnnel2 /2 . As the current reaches I = V0 .JCii , where L = Lnne + LMa (Lnne and LMa being the respective inductances of the line and MG) the energy stored in the line will be a maximum. If at this moment the current is cut off by the opening switch, a pulse will appear across the load Ztoad· The Marina machine, a nanosecond high-power pulse generator, incorporated a vacuum energy storage line, an MPOS, and a load with a line segment built in between the two last components (see Fig. 16.6) (Koval'chuk and Mesyats, 1 985; Mesyats et al. , 1 987). The Marx generator had the following parameters: voltage V0 up to 960 kV, capacitance C = 0.4· 1 0-6 F, and inductance Lg = 0.8· 1 0-6 H. The vacuum line was 4 m long. Its wave impedance was 60 Q and the inductance Lune. including the inductance of the bushing insulator, was 1 . 3 · 1 0-6 H. An inductor (closed vacuum line segment) of inductance L1oad = 0.2 · 1 o-6 H, an explosive­ emission vacuum diode producing an electron beam, or an opening switch were used as a load. The opening switch contained eight plasma injectors.

PULSE GENERATORS WITH PLASMA OPENING SWITCHES

295

An investigation of the operation of the opening switch as the load of the generator showed that its resistance reached 1 6 Q at a rise rate of 1 09 Q/s. The switch was in the open state for 1 o-6 s. The voltage across the switch increased within 25 ns to 2.5 MV, which was a factor of 3 .4 greater than V0•

Figure 16. 6. Schematic diagram of a pulse generator with a vacuum line and a POS (a) and its equivalent circuit (b)

A developed version of a generator with an MPOS and an MIVL is the GIT-4 system (Koval'chuk and Mesyats, 1 990). It comprises four multimodule Marx generators with vacuum bushing insulators through which the generators are connected to a common MIVL (Fig. 1 6.7, a). The plasma opening switch and the load are mounted at the far end of the vacuum energy store relative to the generator. Used as plasma sources are coaxial plasma guns or surface plasma sources. The discharge current in the plasma sources is oscillatory or aperiodic with the rise time to a maximum equal to - 1 J.lS and the amplitude ranging between 1 0 and 1 5 kA. The shift of the onset of current passage in the guns relative to the main current is provided by a timing circuit. The total energy storage capability of the Marx generators is 2 . 1 6 MJ, their inductance is = 0. 1 J.lH and capacitance = 4.8 J.lF. The equivalent circuit of the GIT-4 generator is given in Fig. 1 6.7, b. Here, and are the MG capacitance with its capacitors connected in series and the MG inductance, respectively, and is the inductance of the vacuum insulator and MIVL up to the opening switch; the element Z replaces the opening switch - load system. To perform a z-pinch experiment, the generator was operated with radial MPOS' s (Fig. 1 6.8). Sixty four guns of the capillary type were mounted in the outer cylinder of an MIVL. The central conductor was shaped as a cylinder; the outer one was composed of rods of diameter 1 0 mm. The central conductor was shorted to the end face of the coaxial line through an indium gasket. The switched current was measured by an integrating coil placed at the end face of the system.

LMa

CMG

CMa LMo

Lv

296

II (a)

:r: :r: :r: :r: :r: :r: :r: :r:

:r:

I�

1 = :

Chapter 1 6

I 1 1 3 =1: =- · = I

_2-

lf ! fl . �� �

I

(b)

Figure 16. 7. Schematic diagram of the GIT-4 system (a) and its equivalent circuit (b): 1 Marx generators, 2 coaxial vacuum line, 3 connection of the unit incorporating an MPOS and a load. Each Marx generator contains 36 sections

-

-

-

..l t.wo ns

3 TW

Figure 16.8. The POS in the GIT-4 system (a) and the output parameters of GIT-4 in idle run at the end of the vacuum line load ( VMa = 600 kV, /1 2 MA, Pz = 3.4 TW) (b) =

With the diameters of the outer and the central conductor equal to 560 and 480 mm, respectively, the current was 2.8 MA at a generator voltage of 720 kV. The switched current was 2.4 MA. The current rise rate within a period of 1 00 ns between zero and 2.1 MA was 2. 1 · 10 1 3 A/s. As the generator voltage was increased from 480 to 720 kV, the peak current increased from 1 .8 to 2.8 MA. The magnetic field intensity at the cathode at a peak current was 1 .85· 1 06 Aim. To enhance the magnetic field at the cathode, the conductors of the opening switch were reduced in diameter. With the generator idling, the central conductor terminated in a hemisphere (the dashed line in Fig. 1 6.8, a). The z-pinch load was simulated by a solid metal cylinder placed at the center. The switched current was measured by a Rogowski coil and magnetic loops. In the short-circuit mode at a generator voltage of 720 kV, the maximum cutoff current was 2.6 MA and the switched current amplitude and rise rate

PULSE GENERATORS WITH PLASMA OPENING SWITCHES

297

were, respectively, 2.3 MA and 2.5 · 1 0 1 3 A/s. As the voltage of the generator was increased from 480 to 720 kV, the current increased from 1 .67 to 2.6 MA. The intensity of the magnetic field at the cathode at maximum currents was �2.6· 1 06 Aim. In the idling mode, the equivalent resistance of the switch-load system was about 1 n. At a generator voltage of 480 kV, the cutoff current was 1 .74 MA, the voltage across the opening switch was 1 .4 MV, and the power was 2 TW. At a generator voltage of 600 kV, the cutoff current was 2 MA, the voltage across the opening switch was 1 . 7 MV, and the output power was 3 .4 TW (Fig. 1 6.8, b). On the GIT-4 system, the operation of a two-stage circuit, i.e., a circuit with two POS' s was tested. The geometry of the vacuum part of the experimental arrangement is presented in Fig. 1 6.9. The cathode of the first stage, POS 1 , was 280 mm in diameter. The anode was made as a squirrel cage of diameter 350 mm. Sixty four guns were arranged in a circle of diameter 480 mm. The second stage, POS2, was a coaxial line segment with a diameter ratio of 2 1 0/40 (mm). Thirty two plasma guns were located on the anode.

32 plasma guns

Figure 16.9. Schematic diagram of the GIT-4 generator with two plasma opening switches

With the voltage of the Marx generator equal to 480 kV the current in POS 1 reached 1 . 7 MA within 1 .2 J..lS . As POS2 opened, a voltage pulse of amplitude 1 MV was generated. This made it possible to obtain a 0.6-MA current in POS2 within 1 00 ns. To measure the voltage generated on operation of POS2, a short-circuited coaxial vacuum line segment of length 3 m was used, and the current was measured by integrating Rogowski coils. The voltage increased thirteen times compared to that produced by the Marx generator. Downstream of POS2, the pulse FWHM was 20 ns. Thus, microsecond plasma opening switches have made it possible to considerably simplify and reduce the price of the pulse generators operating

Chapter 1 6

298

in the megajoule, megaampere, and megavolt ranges. Experimental studies of generators with MPOS 's were also performed by Commisso et al. (1992), Goodrich and Hinshelwood (1993), Sincemy et al. (1995), and Weber et al. (1 992). We shall speak of some of them below, when discussing megajoule systems with MPOS 's. Here, we consider one more research system, the HAWK. machine (Commisso et al. , 1 992). It included an oil-insulated Marx generator ( 1 J.!F, 640 kV, 225 kJ) terminated in an MIVL. The current amplitude and rise time were, respectively, 720 kA and 1 .2 J.!S. The anode of the MPOS consisted of twelve rods located on the surface of a cylinder of radius 7.5 em. A variety of configurations of the inner electrode (cathode) could be used. In the majority of experiments, plasma sources with a dielectric surface breakdown were employed. Besides, the system contained twelve coaxial guns (Commisso et al. , 1 992) each made as a cut of a coaxial cable. In some experiments, four gas valves were used that operated 400-500 J.!S before the start of the system. The gas discharge was initiated by discharging a capacitor. The working gases were H2 , Ar, and He. The results obtained were similar to those obtained with conventional plasma sources. The plasma density in the POS was -10 1 5 cm-3 • Experimental studies of the operation of POS' s and MIVL' s in the conduction and current cutoff phases are described by Ottinger et al. (1984), Mosher et al. (1 987), Golovanov et al. (1988), Weber et al. (1990), and Bystritskii et al. ( 1992).

3.

NANOSECOND MEGAJOULE PULSE GENERATORS WITH MPOS'S

In Section 2 of Chapter 1 6 we already spoke of some pulse generators with MPOS 's that were used basically for studying the physical processes occurring in plasma opening switches. In this section, we consider nanosecond pulse generators with MPOS 's that serve to meet special goals such as to study the properties of z-pinches, to produce high-power x-ray pulses, to irradiate materials in various technological processes, etc. The GIT series of generators has been developed at IHCE. We spoke of one of them, the GIT-4 machine (see Section 2 of Chapter 1 6) (Koval' chuk and Mesyats, 1 990). Now we consider the GIT-16 machine (Bugaev et al. , 1 997). This electrophysics system is a current pulse generator with an intermediate inductive energy store and an MPOS-based opening switch. The system is intended for experimentation with high-temperature plasmas generated by gas puff and wire array implosions. It has a modular configuration. The modules are arranged in a circle of diameter 22 m (Fig. 1 6. 1 0).

299

PULSE GENERATORS WITH PLASMA OPENING SWITCHES

Figure 16. 10. General view ofthe GIT-1 2 facility

The use of a system composed of eight modules (GIT-8, 50% of the energy storage capability) in experiments with a POS and a z-pinch load since 1 992 showed that damping resistors must be connected in the circuit of each module to protect the energy storage capacitors against the backward voltage wave. As this was done, experiments could be performed with currents of -4 MA (70 kV charge voltage of MG) at an acceptable level of failures of the capacitors in the course of operation. In 1 996, four modules were added (GIT- 1 2), and now the system is capable of storing 5 MJ of energy with the current in the circuit increasing to -6 MA within - 1 .7 J..t.S . The main parameters of intermediate versions of the system are given in Table 16. 1 . 16 1 . parameters of GIT- 12 depend'mg on the number of moduIes Parameters Configuration

T.able

.

With no damping resistor

With damping resistors

GIT-8

GIT-8

GIT-1 2

Current rise time tmax• !lS

1 .67

1 .69

Charge voltage, kV

50.0

50

70

50

70

Stored energy, MJ

1 .73

1 .73

3.38

5

tmax• MA

4.43

3.04

4,26

2.59 4.4

0.8tmax, MA

4.20

2.93

4. 1 0

4.24

5.94

POS current at t POS current at t

=

=

1 .74

6.2

Each module (Fig. 1 6. 1 1 ) consists of a primary energy store (set of Marx generators), a vacuum bushing insulator 6, and a vacuum transmission line 7.

Chapter 16

300

The primary energy store is an assembly of nine parallel sections 2 connected as a 1 2-stage Marx generator and placed in a metal tank 1 . The damping resistor 5 is made of stainless steel foil that forms a bifilar winding insulated with electrotechnical cardboard and transformer oil. The capacitance of the primary energy store of each module is 1 .2 11F and its inductance is -440 nH. The inductance of the bushing insulator, damping resistor, and 4-m transmission line is, respectively, -200, 250, and 179 nH. The active resistance of the damping resistor is 0.42 0. 2

3

5

Figure 16. 1 1. Schematic diagram of the GIT module: 1 - tank with transformer oil; 2 - Marx generators; 3, 4 - systems for starting and timing of the Marx generators; 5 - resistor; 6 bushing insulator; 7 vacuum line -

The transmission lines 1 converge from the twelve modules to the central unit (Fig. 1 6 . 1 2) that is a vacuum coaxial line segment of length 0.6 m with the shell diameter equal to 1 .6 m. The main collector 2 is 1 .5 m in diameter. It leans on the short-circuited vacuum line 3 whose wave impedance is 60 Q and electric length 6. 7 ns. On the top flange of the shell, which is 30 mm apart from the inner high-voltage electrode, the POS unit is located. The POS' s subject to investigation were axially symmetric systems with the anode-to-cathode diameter ratio Did = 3801320 (mm). The anode was solid or transparent as a squirrel cage, made of thirty two rods of diameter I 0 mm . The cathode was solid, with a spherical adapter to a short-circuited load with Did = 70140 {mm). To create an initial conducting medium, plasma was injected in the POS region within a time td � (2 -1 0) !lS prior to the operation of the Marx generators. Used as plasma injectors were highly reliable, long-lifetime guns. The discharge current in each gun was oscillatory (with a period of 4.8 !lS and a damping decrement of 1 .6); the amplitude of the first current maximum was -9 kA.

PULSE GENERATORS WITH PLASMA OPENING SWITCHES

301

The GIT- 1 2 megajoule system is one of the world's largest pulse generators in which the idea of direct pumping of an inductive energy store from Marx generators and energy delivery to a load with the help of a microsecond POS is realized. In the course of z-pinch experiments, the basic mechanisms of the operation of microsecond POS 's with currents on the level of several megaamperes have been revealed and the factors interfering the improvement of switching characteristics have been determined. It has been shown that during the conduction stage the current channel propagates in the MPOS zone in the direction from the generator to the load. In this case, if the plasma density in the switch zone is too large, some part of this plasma is drawn into the load region, breaking the match of the generator to the load and can promote the occurrence of backward breakdown of the MPOS. Optimization of the MPOS-load adapter has made it possible to increase the z-pinch current and the x-radiation power not increasing the plasma density and current in the MPOS. Experiments with a combined MPOS have shown the possibility of going to larger currents, with the total amount of the injected plasma preserved, due to a proper distribution of the plasma density over the MPOS region.

Figure 16. 12. Central unit of the GIT- 12: 1 - coaxial vacuum transmission line, 2 - main collector, 3 - base vacuum line

One more electrophysics system with an MPOS is the DECADE machine (Sincemy et a/. , 1 995). This is a multimodule system operating into x-ray explosive-emission diodes. It produces 20 krad of x radiation in a pulse at a distance of 1 3 em from the diodes over an area of 1 m2 at a pulse duration of 40 ns and a voltage of 1 .8 MV. Within the framework of this program, the DRM l and then DMl and DM2 modules have been built. The DM2 system operates with a magnetically triggered plasma opening switch.

Chapter 1 6

302

The DM l module consists of an oil Marx generator capable of storing of energy, an intermediate energy storage capacitor, a water line, a vacuum line with an MPOS, and a diode. As the MPOS is short-circuited, the current increases to 1 .8 MA within 300 ns. The Marx generator consists of six modules, each containing twelve stages (85 kV per stage). The output voltage of the Marx generator is 1 MV at a capacitance of 1 . 1 �-tF. The intermediate energy storage capacitor has a capacitance of 400 nF. It is discharged through six parallel triggered gas (SF6) gaps that operate with a jitter � 5 ns. The plasma sources are coaxial cable guns that produce a plasma density of -1015 cm-3 • The radius of the inner electrode (cathode) is 4.4 em. The anode consists of two parts closed through the plasma. The anode on the generator side ("upstream anode") is a cylinder of radius 9 em. The anode on the side load ("downstream anode") is made as a ring with an internal diameter of 1 6.5 em. For the MPOS of standard configuration, the maximum voltage is 1 .2 MV at a conduction time of -300 ns. For the "plasma anode", a maximum voltage 2.3 MV has been achieved for the longest investigated conduction time equal to 550 ns. The ACE-4 megajoule system, developed by the Maxwell company, contains a Marx generator, an oil line, a vacuum line, a coaxial or radial (disk) MPOS, and an electron diode (Thompson et a/. , 1 994). The opening switch is subdivided into two identical POS 's with their cathodes facing each other. Experiments have shown that the opening times of the top and the bottom POS differ insignificantly. The principal parameters of some operation modes of the ACE-4 system are given in Table 1 6.2.

570 kJ

Table 16.2. POS type

V0, kV

I., MA

to, f..lS Vpos, MV 8 1 .3 0.3 3.7 0.87 520 1 .0 360 2.1 1 .05 1 .2 Here, t0 is the time to the current cutoff in the MPOS, Rc is the radius of the MIVL cathode, V0 is the output voltage of the Marx generator, and Is is the MPOS current.

Radial Coaxial, Rc = 9 em Coaxial, Rc 6 em =

The ACE-4 system is capable of storing 4 MJ of energy (Thompson et a!. , 1 994). The Marx generator consists of twenty four generators placed in four oil tanks. In the case of a radial MPOS, the plasma sources were placed on two disks of internal and external radii 40 and 60 em, respectively, located outside the MPOS. Plasma entered the MPOS region through a transparent anode. The data given in Table 1 6.3 refer to the case where the load was an electron diode with an impedance of 0.25 n. The inner electrode of the coaxial MPOS has a negative polarity. The anode consists of sixteen longitudinal rods. Around of the anode, fifteen plasma sources are located. The load was an inductor of inductance 200 nH. ·

PULSE GENERATORS WITH PLASMA OPENING SWITCHES

303

According to interference measurements, the electron density in the MPOS was 1 0 1 5 cm-3• Along with the conventional MPOS 's considered above, there exist magnetically triggered POS ' s that can operate both on the nanosecond and the microsecond scale. In conventional plasma opening switches, the triggering delay time can be varied by selecting the operation mode of the plasma sources, by varying the delay between the injection of plasma and the onset of current passage through the POS, etc. The technology of magnetic POS' s, according to the intention of their developers (SNL), should simplify the control of the opening time due to the application of external magnetic fields (Mendel et a/. , 1 992; Savage et al. , 1 992, 1 994, 1 997). The elements of a POS of this type operate in the following sequence: 1 . An external magnetic field is created in the POS by a "slow" coil. 2. The plasma source fills the anode-cathode gap with plasma. 3. An additional plasma source creates plasma in the trigger POS. 4. The current of the generator flows successively through the trigger POS, cathode, and main POS. 5. As the trigger POS opens, the current is switched into a coil producing a fast magnetic field, which is directed opposite to the external magnetic field. 6. The change in magnetic field configuration initiates the opening process in the main POS. Thus, at the first stage, the problem becomes simpler: the opening process is realized not in the main POS, but in the trigger one, at a substantially lower voltage. However, first, it is necessary to choose initial conditions for the trigger MPOS. Second, for the operation of the magnetic POS to be efficient, it is required that the trigger switch in the POS remained open until all processes in the main POS are complete.

4.

OTHER TYPES OF GENERATOR WITH MPOS'S

A number of systems with MPOS 's operating in the pulse repetition mode were developed at I. V. Kurchatov Institute of Atomic Energy (Barinov et al., 1 997). They were used in electron accelerators and x-ray pulse generators and had the following: voltage up to 1 MV, current up to 1 00 kA, average power up to 20 kW, pulse repetition rate 1-4 Hz, pulse duration -1 0-7 s, and efficiency 20-30%. The MPOS technology was combined with the operation of a line transformer (Bastrikov et al., 1 999). The major factor that limits the efficiency of the current switching from inductive energy stores with the help of microsecond POS 's is their rather low resistance in the open state. It

304

Chapter 16

reaches, as a rule, �2 Q at a current of � 1 MA. The low resistance limits the rate of energy extraction from the energy store and increases the time of current switching into the load. The use of a line transformer as a generator in a circuit with series­ connected opening switches makes it possible to solve the problem of increasing the current rise rate in an inductive load. In this circuit, in several stages of the transformer a plasma opening switch is connected in the primary circuit. As the POS operates, a voltage pulse appears at the output of the primary circuit. The amplitude of this pulse is determined by the POS resistance and by the current in the primary circuit at the instant the POS operates. Summation of the voltages of several circuits makes it possible to increase the output voltage of the generator. To realize the scheme proposed, it is necessary that at the stage of charging the load be isolated from the generator circuit with the help of a spark gap. The feasibility of the circuit with a nontriggert;d spark gap operated due to a surface discharge over a dielectric, which was connected upstream of the load was checked in experiments on the GIT-4 machine (Koval'chuk and Mesyats, 1 990). As a result, a spark gap with the required switching characteristic has been developed. The GIT-4 consists of three sections, each containing five steps of a line transformer. Between the sections, opening switches with sixteen plasma gun injectors are connected. The vacuum part of the primary circuit of each section is formed by coaxial conductors with a diameter ratio of 200/160 (mm). The distance between the end of one and the beginning of the other electrode of the vacuum coaxial line of the transformer primary circuit is 40 mm. The electrodes of a vacuum coaxial line with a diameter ratio of 1 55/1 30 (mm) form an additional inductor of the lead to the load. Originally, the primary circuits of the transformer sections are short-circuited by the plasma opening switches connected in a break of the outer electrode of the transformer vacuum coaxial line. The cathodes of the opening switches are fixed on the electrodes. To prevent the current passage in the load before the operation of the opening switches, a nontriggered spark gap with a surface discharge over a dielectric is used. The spark gap is connected in a break of the central electrode of the load. It should be broken down upon operation of the opening switches. The charge voltage was 90 kV. The opening switches and the switching spark gap operated with a delay of 0.8 J.!S. The generator current at this moment was �760 kA. The residual current in the opening switches was � 1 00 kA and the load current was �400 kA. The peak voltage maximum the MPOS was �1 .4 MV, the voltage across the load reached 2.6 MV, and the peak power delivered to the load was 430 GW. The corresponding values for the transformer consisting of fifteen steps with one opening switch at the

PULSE GENERATORS WITH PLASMA OPENING SWITCHES

305

output were 1 .5 MV and 1 60 GW. Thus, the circuit proposed allows one to increase the output voltage by a factor of 1 . 7 and the power by a factor of 2. 7. An even greater gain in voltage can be obtained by decreasing the inductance between the central conductor of the transformer and the is reduced to 50 or 30 nH, the voltage across plasma opening switch. If the load will increase to 3 or 3 .5 MV, respectively.

Ls

Ls

REFERENCES Abdullin, E. N., Bazhenov, G. P., Kim, A. A., Koval'chuk, B. M., and Kokshenev, V. A., 1 986, A POS with Microsecond Times of Energy Delivery to an Inductive Energy Store, Fiz. Plazmy. 12: 1 260-1 264. Barinov, N. U., Belenky, G. S., Dolgachev, G. 1., Zakatov, L. P., Nitishinsky, G. 1., and Ushakov, A. G., 1 997, Repetitive Plasma Opening Switches and Their Use in the Technology of High-Power Accelerators, Izv. Vyssh. Uchebn. Zaved , Fiz. 12:47-55. Bastrikov, A. N., Zherlitsyn, A. A., Kim, A. A., Koval'chuk, B. M., Loginov, S. V., and Yakovlev, V. P., 1 999, Increasing the Power of a Line Transformer with a Series­ Connected POS, Ibid. 9- 14. Bugaev, S. P., Volkov, A. M., Kim, A. A., Kiselev, V. N., Koval'chuk, B. M., Kovsharov, N. F., Kokshenev, V. A., Kurmaev, N. E., Loginov, S. V., Mesyats, G. A., Fursov, F. 1., Khuzeev, A. P., 1 997, GIT- 1 6, a Megajoule Pulse Generator with a Plasma Switch for Z-Pinch Loads, Ibid 38-46. Bystritskii, V. M., Mesyats, G. A., Kim, A. A., Koval'chuk, B. M., Krasik, Ya. E., 1 992, Microsecond Plasma Opening Switches, Fiz. Elem. Chastits At. Yadra. 23:20-57. Commisso, R. J., Goodrich, P. J., Grossman, J. M., Hinshelwood, D. D., Ottinger, P. F., and Weber, B. V ., 1 992, Characterization of a Microsecond-Conductive-Time Plasma Opening Switch, Phys. Fluids. B4 (Pt 2):2368-2376. Golovanov, Yu. P., Dolgachev, G. 1., Zakatov, L. P., and Skoryupin, V. A., 1 988, Use of Plasma Opening Switches in Inductive Energy Stores for the Creation of Terawatt Generators with High Energy Capabilities, Fiz. Plazmy. 14:880-885. Goodrich, P. J. and Hinshelwood, D. D., 1 993, High Power Opening Switch Operation on "HAWK". In Proc. IX IEEE Intern. Pulsed Power Conf, Albuquerque, TX, pp. 5 1 1-5 1 5 . Guenther, A., Kristiansen, M., and Martin, T., eds., 1 987, Opening Switches. Plenum Press, New York. Koval'chuk, B. M. and Mesyats, G. A., 1 985, Nanosecond Pulse Generator with a Vacuum Line and a Plasma Opening Switch, Dok/. AN SSSR. 284:857-859. Koval'chuk, B. M. and Mesyats, G. A., 1 990, Superpower Pulsed Systems with Plasma Opening Switches. In Proc. VIII Intern. Conf on High-Power Particle Beam Research and Technology, Novosibirsk, USSR. Vol. 1 , pp. 92- 103. Meger, R. A., Commisso, R. J., Cooperstein, G., and Goldstein, S. A., 1 983, Vacuum Inductive Store I Pulse Compression Experiments on a High Power Accelerator using Plasma Opening Switches, App/. Phys. Lett. 42:943-945. Mendel, C. W., Goldstein, S. A., and Miller, P. A., 1 976, The Plasma Erosion Switch. In Proc. I IEEE Pulsed Power Conf, Lubbock, TX, pp. ( 1 C2) 1 -6. Mendel, C. W., Goldstein, S. A., and Miller, P. A., 1 977, A Fast Opening Switch for Use in REB Diode Experiments, J. Appl. Phys. 48: 1 004- 1 006.

306

Chapter 1 6

Mendel, C. W., Jr., Savage, M . E., Zagar, D . M., Simpson, W . W., Grasser, T . W., and Quintenz, J. P., 1 992, Experiments on a Current-Toggled Plasma-Opening Switch, Ibid 71 :373 1-3746. Mesyats, G. A., Bugaev, S. P., Kim, A. A., Koval'chuk, B. M., and Kokshenev, V. A., 1 987, Microsecond Plasma Opening Switches, IEEE Trans. Plasma Sci. 15:649-653 . Mkheidze, G . P., Plyutto, A . A., and Korop, E . D., 1 97 1 , Acceleration o f Ions during the Passage of a Current through Plasma, Zh. Tekh. Fiz. 41:952-963. Mosher, D., Grossmann, J. M., Ottinger, P. F., and Colombant, D. G., 1 987, A Self-Similar Model for Conduction in the Plasma Erosion Opening Switch, IEEE Trans. Plasma Sci. 15:695-703. Ottinger, P. F., Goldstein, S. A., and Meger, R. A., 1984, Theoretical Modeling of the Plasma Erosion Opening Switch for Inductive Storage Applications, J. App/. Phys. 56:774-784. Savage, M. E., Hong, E. R., Simpson, W. W., and Usher, M. A., 1 994, Plasma Opening Switch Experiments at Sandia National Laboratories. In Proc. X Intern. Conf. on High­ Power Particle Beams, San Diego, CA, pp. 4 1 -44. Savage, M. E., Simpson, W. W., Cooper, G. W., and Usher, M. A., 1 992, Long Conduction Time Plasma Opening Switch Experiments at Sandia National Laboratories. In Proc. IX Intern. Conf on High-Power Particle Beams, Washington, DC, pp. 621 -626. Savage, M. E., Simpson, W. W., Mendel, C. W., et a/., 1 997. In Proc. Intern. POS Workshop, (April 1 997), Gramat, France. Sincemy, P., Ashby, S., Childers, K., Goyer, J., Kortbawi, D., Roth, 1., Stallings, C., Denpsey, J., 1 995, Performance of Decade Module No 1 (DM 1) and the Status of the Decade Machine. In Proc. X IEEE Intern. Pulsed Power Conference, Albuquerque, TX, pp. 405-4 1 6. Stringfield, R., Schneider, R., Genuario, R. D., Roth, 1., Childers, K., Stallings, C., and Dakin, D., 1981, Plasma Erosion Switches with Imploding Plasma Loads on a Multiterawatt Pulsed Power Generator, J. Appl. Phys. 52: 1 278-1284. Suladze, K. V., Tskhadaya, B. A., and Plyutto, A. A., 1 969, Features of the Formation of Intense Electron Beams in Confined Plasmas, Pis'ma Zh. Eksp. Teor. Fiz. 10:282-285. Thompson, J., Coleman, P., Gilbert, C., Husovsky, D., Miller, A. R., Rauch, J., Rix, W., Robertson, K., and Waisman, E., 1 994, ACE 4 Inductive Energy Storage Power Conditioning Performance. In Proc. X Intern. Conf on High-Power Particle Beams, San Diego, CA, pp. 12- 1 6. Weber, B. V., Boller, J. R., Commisso, R. J., Goodrich, P. J., Grossman, J. M., Hinshelwood, D. D., Kellogg, J. C., Ottinger, P. F., and Cooperstein, G., 1 992, Microsecond-Conduction­ Time POS Experiments. In Proc. IX Intern. Conf on High-Power Particle Beams, Washington, DC, pp. 375-384. Weber, B. V., Commisso, R. J., Cooperstein, G., Goodrich, P. J., Grossman, J. M., Hinshelwood, D. D., Kellog, J. C., Mosher, D., Neri, J. M., and Ottinger, P. F., 1990, Plasma Erosion Opening Switch Operation in the 50 ns - 1 JlS Conduction Time Range. In Proc. VIII Intern. Conf. on High-Power Particle Beam Research and Technology, Novosibirsk, USSR, pp. 406-4 13. Weber, B. V., Commisso, R. J., Cooperstein, G., Grossman, J. M., Hinshelwood, D. D., Mosher, D., Neri, J. M., Ottinger, P. F., and Stephanakis, S. J., 1987, Plasma Erosion Opening Switch Research at NRL. In IEEE Trans. Plasma Sci. 15:635-648.

Chapter 1 7 ELECTRON-TRIGGERED GAS-DISCHARGE SWITCHES

1.

INTRODUCTION

In this chapter, we consider high-pressure discharge devices (the right branch of Paschen's curve) with full triggering. This implies that these devices are able not only to pass a current due to the application of a trigger pulse, as spark gaps or thyratrons, but also to stop passing the current when the trigger pulse is complete or an additional blocking pulse is applied. In this respect, they have properties similar to those of electron tubes or triggered semiconductor devices. A feature of the switches to be considered here is that the physical processes occurring in them have been rather well investigated in the physics of gas discharges (see Section 5 of Chapter 4). In this respect, they have an advantage over EEC switches and POS's. However, these devices are not capable to switch powers of 1 01 2 W and greater as the mentioned switches do. At the best, the pulse power is 1 0 1 0 W. However, an important advantage of these devices is that they can operate in the repetitive pulse mode, and in a burst mode the pulse repetition rate can reach 1 06 Hz. The central place in this chapter is occupied by injection thyratrons (IT's). Their operation is quite understandable. Imagine a conventional thyratron that, as the heat circuit of the cathode is rapidly broken, will cease to pass a current. However, this process will be long because the cathode cooling is a sluggish process. In IT's, instead of the electron emission from a hot cathode, direct injection of electrons into gas is used. For the first time, this type of discharge was realized by the team of Mesyats at IHCE (Koval'chuk et a!. , 1 97 1 a, 1 976; Mesyats et a!., 1 972). However, originally

308

Chapter 1 7

the effect of injection of electrons into high-pressure (> 1 atm) gas in the presence of an electric field was utilized in high-power gas lasers. A fundamental property ofiT's (Koval'chuk et al. , 1 976) is rapidly rising plasma resistance in the gas discharge column as a result of recombination of charge carriers and attachment of electrons to gas molecules. This occurs when the injection of an electron beam into the gas is rapidly terminated. This effect can be harnessed for current interruption in generators with inductive energy storage. Besides, an IT can serve merely as a switch to interrupt kiloampere currents. An IT can also be operated in the closing mode, as a conventional thyratron. In the closing and opening mode, an IT can serve as a repetitively pulsed device. A serious disadvantage of IT's is the radiation background that is created by an electron beam with an electrons energy > 1 00 keV (electrons with lower energies cannot be injected into the gas volume of an IT because of the presence of the metal foil separating the vacuum and gas chambers). Another disadvantage is that these devices are bulky because of the presence of the electron accelerator. The third one is the short lifetime of IT's resulting from the fact that the foil is broken after a certain number of pulses. We do not consider the triggered devices that operate in modes corresponding to the distant left branch of the Paschen curve, such as tacitrons and crossatrons. They are seldom used in the technology of high­ power nanosecond pulses as basic devices but can play an auxiliary role in the first stages of compression of high-power pulses.

2.

TRIGGERING OF AN INJECTION THYRATRON

The problem of full triggering can be solved by using a non-self­ sustained discharge and injecting pre-accelerated electrons into the gas-filled gap. The device called an injection thyratron consists of two chambers (Fig. 1 7. 1 ): gas chamber 1-2 and vacuum chamber 2-3, separated by a thin metal foil 2. Cathode 3 emits electrons, which are accelerated and then pass through foil 2 into the gas chamber. The accelerated electrons ionize the gas, and, if voltage is applied to the gas gap, a current will flow in the circuit. Under certain conditions, it is possible to interrupt this current by terminating the injection of electrons (Koval'chuk et al. , 197 1 a). Thus, we have a fully triggered device. The effect of full triggering by the discharge current was demonstrated in early injection electronics experiments (Koval'chuk et al. , 1 97 1 b; Mesyats et al. , 1 972).

ELECTRON-TRIGGERED GAS-DISCHARGE SWITCHES

309

1 2 3

t

t

t

Figure 1 7. 1. Sketch of an injection thyratron and its connection circuit (Ca - storage capacitance of the accelerator; C, R - capacitance and resistance of the pulse generator)

To analyze the operation of an IT, we transform the system of equations

(4.29)-(4.36) to obtain dne = \jl dt

-

R ne

p

2

- 11 N,ne '

(17. 1 )

j = enve ,

(17. )

2

where ne is the electron density in the gas, m-3 ; is the electronegative gas molecule density, m-3 ; is the probability of attachment of one electron to an electronegative gas molecule in 1 s; is the recombination coefficient, m3/s; is the number of electrons generated by the beam electrons in 1 m3 in 1 s; Ve is the drift velocity of electrons, m/s; e is the electron charge, C, and j is the electron current density, A/m2• Let us consider a mode with V « Vdc ( V being the voltage across the gap and Vdc the de breakdown voltage). This allows us to neglect the term describing impact ionization in equation ( 1 7 . 1 ) Hereinafter, we assume that the voltage across the gas gap varies in time. To const, const, and const. For the simplify the analysis, we put closing mode, the exact solution of (17. 1 ), in view of the above assumptions, has the form

N

11

�

'I'

.

'I' =

lo/ [1 - exp (-th:)] , fj3 1 + exp (-tit)

a a2 a 0.5�112N2

n=

�=

(17.3)

0.5nN �) [112((11N'1')2�t141\jl2 ,�Jo.s .

; 't = I( /\jl � + 4 where = assume that there is no electron attachment, for t < density in the plasma will be

ne(t) = \jlt .

11 = +

If we the electron

(17.4)

For a linear approximation of the drift velocity of electrons, Ve, as a function of Elp, we can write Ve = k0VIpd , where ko/p is the mobility of electrons in the gas and p is the gas pressure. In this case, the discharge current at the initial stage can be expressed as

310

Chapter 1 7 ( 1 7.5)

where S is the cross-sectional area of the discharge column, which is equal to the area of the region from which the beam is injected, A, = Se\jfk0 /pd . Using this formula, we can calculate the current as a function of time for various pulse circuits. For a pulse generator with a discharging energy storage line (Fig. 1 7.2, a), the current during the pulse rise time will vary by the law

l(t)

=

Vo 'A.t 1 + RA.t

,

( 1 7.6)

and for a pulse generator with a discharging capacitor (Fig. 1 7 .2, b) by the law

( )

l(t) = V0A.texp -

A.t2 , 2C

(1 7.7)

where R is the resistance of the load plus the wave impedance of the line. Let us estimate the pulse parameters for both generator circuits. When a line is discharged, the current tends to its peak value Ia = V0 /R . The time it takes for the current to reach a level of 0.9Ia (pulse rise time) is given by ( 1 7.8) For a discharging capacitor, the peak current is Ia = Vo (A.C/e)1 12 ,

( 1 7.9)

where e is the natural logarithmic base, and the time in which the current reaches a maximum is

fmax = (C/'A.)1 12 (a)

( 17 . 1 0)

•

� � Rch Vo

L--+Q+-----+0� _L IT

-

f

R�

T.___c

---+

_ _

Figure 1 7. 2. Connection circuits of an injection thyratron line; b with an energy storage capacitor

(IT): a - with an energy storage

ELECTRON-TRIGGERED GAS-DISCHARGE SWITCHES

311

The most important characteristic of any switch is the current rise rate of during switching, di/dt. As follows from ( 1 7.6) and ( 1 7.7), at the initial stage of current passage we have di/dt oc A. The parameter A increases with the current of injected beam electrons, Ib, and with the parameters 'i' and k0• Thus, high current rise rates can be attained by increasing these three parameters. In experiments with the switch of the SINUS-2 pulsed accelerator, for the production of a volume discharge, a 2-kA electron beam was used which was injected into nitrogen at a pressure of 1 0 atm (Koval'chuk et al. , 1 972). At a voltage of 700 kV across the switch the discharge current was 40 kA. In this case, the current rise rate was three times greater than that attained in the spark mode of operation of the switch. The ionization cross section cr increases as the energy of the injected electrons is reduced. However, it is difficult to take advantage of this effect to increase di/dt, since a reduction of the electron energy is interfered, on the one hand, by the presence of a separating foil, which should be shot through by the electrons, and, on the other hand, by the requirements that thermalized electrons be present in small numbers and the gas be uniformly ionized over the gap width to avoid electric field enhancement and discharge constriction. From formula ( 1 7.3) it follows that, as in a steady state we have dneldt = 0 , the electron density will be determined by the formula -

( 1 7. 1 1 ) The time dependence of the electron density in the discharge column for the case the charged particles are lost due to recombination, is described by expression (4.39), and for the case the electrons decrease in number due to attachment to atoms and molecules of an electronegative gas it is given by the formula ( 1 7. 1 2) where 11 is the electron attachment constant and nimp is the concentration of the electronegative impurity in the main gas. Introducing the resistance of the discharge gap by Rg = pd/Sen(t)k0 , we can easily obtain the time-varying load current:

I-

Vo Rload + [pd/Seko n(t)] ·

( 1 7. 1 3)

From this formula it follows that the maximum current is achieved at a steady-state electron density in the discharge, and this current can be

Chapter 1 7

312

increased by reducing Rg, which for the recombination and the attachment mode is given, respectively, by

dr:t l / 2 ( " 8_ ) Rg - P p e.�b crp 1 / 2 ko

(17. 14)

_

and by

Rg =

pdnimpll ko fbcrp '

(17. 1 5)

where cr is the average ionization cross section. Since, as the parameter pd is kept constant, the voltage V0 remains almost unchanged, the current flowing through the device increases with increasing beam current, electrode area, and gas pressure and also with the use of gases having high mobility k0• Among gases of this type, of particular interest is methane for which breakdown voltages are about the same as for N2 and C02 , and the drift velocity, for very low Elp [1-1 .5 V/(m·Pa)], is greater by an order of magnitude (Fig. 1 7.3 ) . For the first time, methane was used in an injection thyratron by Hunter (1 976). 12

8

......, "'

10

� 8

"' I 0 "'

6 4 2 0

2

3 4 5 6 7 8 (Eip)· l .33 [V/(m · Pa)]

9

10

Figure 1 7. 3. Electron drift velocities in nitrogen (1) and methane (2)

Efremov and Koval' chuk (1 982) investigated the electrical characteristics of a non-self-sustained discharge triggered by an electron beam. The electron beam was produced by a gun with a directly heated cathode and was injected, through a window of diameter 1 .6 em sealed off with titanium foil of thickness 20 J.Lm, into the discharge chamber. The energy of the accelerated electrons was 135 keY and the current density downstream of the foil was 14 mA/cm2 • The beam current pulse had a rectangular waveform; its

ELECTRON-TRIGGERED GAS-DISCHARGE SWITCHES

313

duration was 8 J.lS and the rise time and fall time were less than 1 0 ns. One of the electrodes was sectioned, i.e., made of concentric rings varied in diameter. Therefore, there was an opportunity to measure the peak current passed through each ring and the total discharge current. In the course of the experiment, probe measurements of the distribution of the potential across the gap were carried out. The probe, made as an array of tungsten wires stretched parallel to the cathode, was placed some distance from the cathode. The discharge was photographed from the screen of an image amplifier with the camera shutter open. The current-voltage characteristics (CVC's) measured for the injection of electrons through the cathode and through the anode are shown in Fig. 1 7 .4. In both cases, the CVC's have breaks in the region of small currents. Figure 1 7 .4, where the initial portions of the characteristics are gtven, pictorially demonstrates the possibility to increase the amplitude of the discharge current in methane in comparison with nitrogen. 80

+

(a)

70

35

+

60

� .......

�

50

.......

40

25 20

30

15

20

10

10

5

0

2

4

6

v

0

8 1 0 12 14 [kB]

± v

2 [kB]

3

Figure 1 7. 4. Current-voltage characteristics of a discharge in methane with an electron beam injected through the anode (+) and cathode ( ) (a) and the initial portions of these characteristics (b). For comparison, CVC ' s for a discharge in nitrogen are given (±) -

An investigation of the dependence of the discharge current on the applied voltage for various cross sections of the cathode and anode has shown that an increase in anode current is observed in all cross sections. At the cathode, the area through which the discharge current passes increases with applied voltage, the current flows first through the central part and then through the peripheral regions. The total discharge current is observed to saturate when there comes saturation in all ring areas of the cathode. In the central region, saturation of the discharge current takes place at lower voltages than in the peripheral regions. At fields over 7-8 kV/cm, the discharge gap was broken down within some tens of milliseconds after the

Chapter 1 7

3 14

passage of the electron beam. The typical waveform of the discharge current for electrons injected through the anode is shown in Fig. 1 7.5, a. For an injected beam of current density 1 5 mA/cm2 , the time of current rise and fall is 3-5 J..lS , and the current amplification factor, i.e. the ratio of the discharge current to the beam current, is equal to 1 03 at average fields of 500 V/cm. At higher fields, initially the pulse waveform is distorted (Fig. 1 7 .5, b), and then self-sustained high-frequency fluctuations appear (Fig. 1 7.5, c). The percentage of modulation reaches 1 0%, and the period of fluctuations weakly depends on the parameters of the external LC circuit and is approximately equal to T � dl Ve, where d is the electrode separation and Ve is the drift velocity of electrons. In the case where fluctuations of the discharge current were observed, the probe fixed fluctuations of the plasma potential. < �

80 r-------� c 60 40 20

�� o ��L_L_L_�� 8 16 20 0 4 12 t [J.Lm]

Figure 1 7.5. Current waveforms for a discharge in methane for V0

=

2 (a), 3 (b), and 8 kV (c)

In weak fields, before the break in the eve, a luminous film appears on the cathode. As the field is increased, the current increases abruptly and bright luminous spots appear on the cathode due to the occurrence of emission centers. When electrons are injected through the cathode, spots, as well as breaks in the eVC' s, appear at lower voltages than this takes place when injection is performed through the anode. Spots arise in the central region of the cathode and, with increasing voltage and, consequently, current, they cover the cathode surface, forming a ring structure. Fluctuations of the discharge current and probe potential at fields higher than 500 V/cm are due to the nonmonotonic dependence of the drift velocity of electrons on reduced field (see Fig. 1 7.3). A similar dependence for semiconductors, such as GaAs, results in the phenomenon known as the Gunn effect (Levinshtein et a/. , 1 975). As this takes place, a high field domain appears near the cathode and then moves toward the anode with a velocity approximately equal to the drift velocity of electrons. The formation, movement, and disintegration of the domain are accompanied by fluctuations of the current flowing through the semiconductor. A similar effect was observed in non-self-sustained discharges in mixtures of argon

ELECTRON-TRIGGERED GAS-DISCHARGE SWITCHES

315

with molecular gases (Lopantseva et al. , 1 979). In the experiment under consideration, the domain instability was testified by fluctuations of the discharge current and probe potential. Thus, the use of a non-self-sustained discharge triggered by an electron beam in methane allows one to obtain high discharge currents at rather low electric fields. Breakdown of the discharge gap is observed at fields over 7-8 kV/cm. Let us consider the use of an IT as a closing switch in repetitive pulse generators that are capable of producing a pulse power of the order of 10 1 0 W with a pulse duration of -100 ns and a pulse repetition rate of 104 Hz (burst mode). An example of such a system is the ETAIATA generator (Vitkovitsky, 1 987). The electron beam injector of this type of switch generates a short-rise-time pulse, and the working gas is quickly ionized. Figure 1 7.6 shows two circuits of electric generators using an IT as a closing switch. In both generators, the switch S operates to charge energy storage lines. Usually, direct charging of the capacitor C0 from a Marx generator (Fig. 1 7.6, a) occurs within about 1 f..LS . The use of a voltage step­ up transformer (Fig. 1 7 .6, b) gives a number of advantages. For example, the switch S can be a semiconductor thyristor. The charging time increases to several microseconds. The IT should provide a peak pulse power of 4· 1 09 W delivered to the load. At a pulse repetition rate > 1 0 kHz (pulse interval < 1 00 f..LS) the average output pulse power is 1 06 W. The power transfer through the switch results in some dissipation of energy in the switch. The amount of dissipated energy, which depends on the pulse duration, current, and fall voltage across the switch in the conduction phase, is less than the energy delivered to the load. In the open state, the conductivity of the switch is negligible in all cases considered here. Additionally, the switch inductance must be limited to -100 nH.

(b)

V,

�� cr p

iT

1Rload

Figure 1 7. 6. Circuit diagrams illustrating the use of an IT as a closing switch. The energy required for the production of output pulses is stored in a capacitor and then transferred to an intermediate pulse-forming line either immediately (a) or through a step-up transformer (b). The output pulse of the pulse-forming line is controlled by the IT

316

Chapter 1 7

Other applications of IT's in nanosecond pulse power technology and the engineering methods of designing generators with IT's operating as closing switches can be found in reviews by Mesyats ( 1 982), Koval'chuk et al. ( 1 979), Vitkovitsky ( 1 987), and Guenther et a/. ( 1 987).

3.

THE CURRENT CUTOFF MODE

As the electron injection is quickly terminated, the electron density in the plasma, ne, starts rapidly decreasing and the resistance of the IT abruptly increases. For the pure recombination mode where the attachment of electrons to electronegative gas molecules is negligible, the time dependence of ne is given by ( 17. 1 6) For the mode where electron attachment plays the dominant role in the deionization of the plasma, we have ( 1 7. 1 7) where nimp is the concentration of the electronegative impurity in the basic gas and ne0 is the plasma density in the discharge column immediately prior to the termination of electron injection. Let us now find the characteristic current cutoff time, t0• If we assume that it is equal to the time in which the electron density in the plasma decreases to one tenth, we have for the recombination mode ( 17. 1 8) and for the electron attachment mode ( 1 7. 1 9) Electron attachment very strongly affects the rate of fall of plasma density and reduces the current cutoff time. However, it should be borne in mind that the steady-state electron density, i.e., the current amplification factor of the device, decreases as well (Fig. 1 7.7) (Koval'chuk et al., 1 979). The influence of the electronegative gas impurity on the current cutoff time is evident from relationships simulated on a computer (Fernsler et a/., 1 979). A 20-0 resistor was connected to a 200-kV voltage source through an injection thyratron filled with nitrogen at 1 0 atm. An electron beam of energy 1 5 0 keY, current 1 kA, and duration 1 00 ns was injected through an area of 1 03 cm2 into a 2-cm gap. For the initial portion of the curve, the

ELECTRON-TRIGGERED GAS-DISCHARGE SWITCHES

317

rising current is described by formula ( 1 7 .5) from which it follows that the current does not depend on � and 11 and, hence, on the impurity content. After the termination of injection, the current cutoff time was determined by the oxygen concentration in nitrogen. For pure nitrogen, the current cutoff time was 1 o-7 s, while with an admixture of 1 % oxygen it was 1 o-6 s. 10

� 8 C:< a

�

:::::-:-

6

("')

,.e. � "'! ......

.-..

4 2

0

50

1 00

1 50

200

250

300

j [mA/cm2]

Figure 1 7. 7. Current-voltage characteristics of a quasi-stationary discharge sustained by electron beam: I - pure nitrogen; 2 - nitrogen + 3% 02 ; 3 - air

an

Koval'chuk and Mesyats (1976) proposed an IT for use as an opening switch in generators with inductive energy storage. The resistance of an opening switch operating in the recombination mode increases by the law

(17 .20) where Rn = pd�112 /ek0 S\JI 1 12 • If a source of voltage V0 and an inductor L are connected in a circuit with such an opening switch (Fig. 1 7 .8), a pulsed voltage will appear across the inductor as a result of current cutoff:

Vr = V0 (l + A-r)exp [ - (-r + 0.5A-r2 ) ] ,

where 't = t/9 ; time given by

(17.21)

9 = LSek0 (pdt 1 (\J,II�)112 ; A = \JILSk0 (pdt 1 • At a moment of

L(A 1 12 - 1) A.Rn

fmax = ----'----'the voltage across the inductor reaches a maximum of

(1 7.22)

318 VL

max

= Vo A 1 1 2 exp

Chapter 1 7

(2A 1-A) .

(1 7.23)

A preliminary experiment with measuring the current cutoff time was carried out by Koval'chuk and Mesyats (1 976) in the discharge chamber of a high-power C02 laser with an active volume of 300 l. A mixture of C02 :N2 :He = 1 : 1 :3 at atmospheric pressure was used. At an injected electron current of 1 5 kA (beam current density jb = 1 .5 A/cm2) the injection of electrons was terminated in 2· 1 o-6 s by removing voltage from the diode of the accelerator. In this case, the cutoff time for a current of 1 50 kA was -2 · 1 0-7 s.

2

- -

-

-5 -

1 Vo ' 5

--

-

Figure 1 7. 8. Circuit diagram showing the connection of an injection thyratron to a pulse generator with inductive energy storage: 1 current source, L inductive energy store, 2 hot cathode, 6 grid for electron-beam control, load, 3 electron beam, 4 foil anode, S switch connecting the energy store L to the load

It should be noted that opening switches of this type are most promising for the operation in compressed gases (p = 1 0 atm and more). In this case, 1 first, the opening time decreases, since t oc p 12 , and, second, the electric strength of the switch increases in the course of opening. Let us consider some applications of IT's in pulsed power technology. Efremov et al. (1991) used an IT for fast interruption of a 5-kA current that flew during 1 00 J.l.S. The current in the IT was cut off within -1 0 J.l.S by means of a cylindrical IT with an electron beam of cross section 1 .2 m2 • An accelerator with a plasma cathode made as a mesh cylinder (Fig. 1 7.9) was used. Plasma was injected into the cylinder during the discharge of an artificial line into a coaxial plasma gun. As the injection of plasma was terminated (in 1 J.LS), the emission of electrons through the mesh into the acceleration region stopped. For acceleration of electrons, a 300-kV Marx

-

ELECTRON-TRIGGERED GAS-DISCHARGE SWITCHES

319

generator was used. The current of accelerated electrons was 1 0 A, and as the electrons left behind the cylindrical window covered with foil, it was 6 A. The accelerator was enclosed in a metal cylinder filled with methane at atmospheric pressure. The gap between the foil electrode and the main cylinder was 1 0 em, and the electric field was 5 kV/cm. The discharge current was amplified almost 103 times. The capacitor bank of capacitance 103 JlF could store up to 1 MJ of energy at a voltage of 50 kV. Thus, the possibility of fast cutoff of a current > 4 kA flowing for a rather long time has been demonstrated (Efremov et al. , 1 99 1 ). Oscillograms illustrating the operation of the injection thyratron are given in Fig. 17. 10.

- Vch PFL Figure 1 7. 9. Schematic diagram of an electron accelerator for an injection thyratron: 1 electron extraction window, 2 - case of the power supply, 3 - mesh electron emitter, 4 pulse-forming line, 5 - Marx generator, 6 - section cylinder, 7 - hollow anode of the plasma emitter, 8 - insulators, 9 - plasma guns, 10 - auxiliary electrodes, 1 1 - Teflon bushing insulators

320

Chapter 1 7 (a)

� �

(b)

� .......

(c)

� .......

sf � ' J I

·f r ·f r 0

ll 40

t [}ls]

'�

80

120

I

Figure 1 7. 10. Waveforms of the electron beam current (a), current of a discharge in methane at a gap voltage of 38 kV and a discharge circuit resistance of 8.3 n (b), and current of a discharge with the same parameters, but with the electron beam turned off in 1 }lS (c)

Another example shows a rather high efficiency of iT's when operated in systems with inductive energy storage. In the experiment described by Schoenbach and Schaefer (1 987), a capacitor charged to a voltage of 26 kV delivered energy to a 1 .5-J..!.H inductor through an IT filled with a mixture of CH4 and C 2F 6 at a pressure of 5 atm. The pumping of the inductor occurred within 0.7 J..l.S . As the current in the IT was cut off due to the termination of the electron flow, a voltage pulse of amplitude 280 kV, current 1 0 kA, and duration 60 ns was generated. Vitkovitsky ( 1987) proposed a hybrid pulse-forming circuit in which the terminal stage (consisting of an energy storage line, a closing IT, and a load) was the same as that shown in Fig. 1 7 .6. However, instead of the primary energy storage in a capacitor, the inductor L0 was charged by current /0 through an explosion-triggered switch (designated by the symbol S in the circuit diagram). Note that some current generators, such as unipolar generators, may call for additional stages for primary compression of the pulse. For an individual module (20 kA, 200 kV, and 40 ns), the energy in a single pulse is small: 1 60 J. For generating a burst of ten pulses, it is required that the inductor be capable of storing at least -2 kJ. Since the efficiency of conversion of the stored energy to the energy of a pulse is 30%, the energy storage system must be capable of storing -6 kJ for charging one module of the pulse-forming line. For an accelerator consisting of many modules (ATA) (Vitkovitsky, 1 987), this results in hundreds of kilojoules. When designing a switching system, it is necessary to know the number of modules

ELECTRON-TRIGGERED GAS-DISCHARGE SWITCHES

321

to be powered with the help of one switch. The majority of design problems would be solved with a switch for a ten-module pulse train generator producing no more than five pulses in a burst. Now we dwell shortly on three types of electron accelerators used for triggering IT's. The first type of device is an accelerator with explosive electron emission capable of producing pulses of voltage 0. 1 5-1 MeV and duration 1 o-9-1 o-s s with the pulse repetition rate ranging from a few hertz to 1 03 Hz and more. Accelerators (such as SINUS) with an average energy of up to 1 00 kW have already been developed. First experiments on studying IT's were carried out with BEE-based accelerators (Koval' chuk et al. , 1 97 1 a, 1 976; Koval' chuk and Mesyats, 1 976). Accelerators of the second type are systems with plasma cathodes, which have an important advantage: they can operate at electron currents of long duration: from 1 0-6 s to continuous. Like accelerators of the first type, they are capable of producing electron beams with a cross-sectional area of several square meters. The third type systems are hot-cathode accelerators. Some of them are described by Vitkovitsky ( 1 987); in particular, an accelerator for an IT built in a coaxial line. As suggested, to realize repetitive switching at a theoretically attainable frequency of 2 MHz, it will be necessary to use thermionic emission cathodes to produce the electron beam. Other types of opening IT's, generators operating with IT's, and comprehensive investigations of the physical processes occurring in these devices are described in reviews by Koval'chuk et al. ( 1 979), Mesyats ( 1 982), Vitkovitsky ( 1 987), and Schoenbach and Schaefer ( 1 987).

REFERENCES Efremov, A. M. and Koval'chuk, B. M., 1 982, Study of an Electron-Beam-Controlled Non­ Self-Sustained Discharge in Methane, Izv. Vyssh. Uchebn. Zaved. , Fiz. 4:65-68. Efremov, A. M., Kovaltchuk, B. M., and Mesyats, G. A., 1 99 1 , A Coaxial Injection Thyratron. In Proc. XVIII IEEE Intern. Pulsed Power Conf, San Diego, CA, pp. 356-358. Femsler, R. F., Conte, D., and Vitkovitsky, I. M., 1 979, Repetitive Electron Beam Controlled Switching. In Proc. II IEEE Pulsed Power Conf, Lubbock, TX, pp. 368-37 1 . Guenther, A., Kristiansen, M., and Martin, T., eds., 1 987, Opening Switches. Plenum Press, New York. Hunter, R. 0., 1 976, Electron Beam Controlled Switching. In Proc. I IEEE Pulse Power Conf, Lubbock, TX, pp. (IC-8) 1 -6. Koval'chuk, B. M. and Mesyats, G. A., 1 976, On the Possibility of Rapid Interruption of a Large Current in a Volume Discharge Initiated by an Electron Beam, Pis 'ma Zh. Tekh. Fiz. 2:644-648. Koval'chuk, B. M., Korolev, Yu. D., Kremnev, V. V., and Mesyats, G. A., 1 976, The Injection Thyratron as a Fully Controlled Ion Device, Radiotekh. Elektron. 2 1 : 1 5 1 3- 1 5 1 6.

322

Chapter 1 7

Koval'chuk, B. M., Kremnev, V. V., and Potalitsyn, Yu. F., 1 979, High-Current Nanosecond Switches (in Russian, G. A. Mesyats, ed.), Nauka, Novosibirsk. Koval'chuk, B. M., Kremnev, V. V., Mesyats, G. A., and Potalitsyn, Yu. F., 1971a, Discharge in High Pressure Gas Initiated by Fast Electron Beam. In Proc. Xth Conf. on Phenomena in Ionized Gases, Oxford, England, p. 1 75. Koval'chuk, B. M., Kremnev, V. V., Mesyats, G. A., and Potalitsyn, Yu. F., 197 1 b, The High-Pressure Gas Discharge Initiated by a Fast Electron Beam, Zh. Prikl. Mekh. Tekh. Fiz. 6:2 1 -29. Koval'chuk, B. M., Kremnev, V. V., Mesyats, G. A., and Potalitsyn, Yu. F., 1 972, The High­ Pressure Gas Discharge Initiated by a Fast Electron Beam. In Proc. II All-Union Conf. on Charged Particle Accelerators, Moscow, USSR. Vol. 1 , pp. 1 04- 1 06. Levinshtein, M. E., Pozhela, Yu. K., and Shur, M. S., 1 975, The Gunn Effect (in Russian). Sov. Radio, Moscow. Lopantseva, G. B., Pal, A. F., Persiantsev, I. G., Polushkin, V. M., Starostin, A. N., Timofeev, M. A., and Treneva, E. G., 1979, The Instability of Non-Self-Sustained Discharges in Mixtures of Argon with Molecular Gases, Fiz. Plazmy. 5 : 1 3 70- 1379. Mesyats, G. A., 1 982, High Power Injection Switches. In Injection Gas Electronics (in Russian, 0. B. Evdokimov, ed.), Nauka, Novosibirsk. Mesyats, G. A., Koval'chuk, B. M., and Potalitsyn, Yu. F., 1972, USSR Patent No. 356 824 (November 23, 1 972). Schoenbach, K. H., and Schaefer, G., 1 987, Diffuse Discharge Opening Switches. In Opening Switches (A. Guenther, M. Kristiansen, and T. Martin, eds.), Plenum Press, New York, pp. 49-91 . Vitkovitsky, 1., 1 987, High Power Switching. Van Nostrand Reinhold Company, New York.

PART 7. PULSE POWER GENERATORS WITH SOLID-STATE SWITCHES

Chapter 1 8 SEMICONDUCTOR CLOSING SWITCHES

1.

MICROSECOND THYRISTORS

The switching process in any high-power semiconductor device consists in that a region that previously contained free charge carriers in insignificant amounts and therefore blocked the voltage applied to the device is filled with well-conducting electron-hole plasma. This is, as a rule, the space charge region (SCR) of a reverse-biased p-n junction, and the filling of this region with plasma is accomplished by various methods depending on the requirements placed on the switching parameters. Generally speaking, there are only two practical ways of producing electron-hole plasma in a semiconductor: injection of carriers through the barriers of p-n junctions and ionization produced either by carriers accelerated in an electric field or by ionizing radiation. Injection of carriers is more energetically profitable since to introduce charge carriers in the base region of a device through a p-n junction, it suffices to reduce the barrier of the junction by some fractions of an electron-volt, while ionization demands an energy greater than the width of the forbidden gap of the semiconductor ( 1 . 1 2 eV for silicon). However, charge carriers are injected at the edges of the base region, while in ionization, plasma is produced in the bulk of the region, and this is an essentially faster process. Therefore, high-power semiconductor switches operating on the microsecond and nanosecond scales are injection­ type devices, while the plasma production in faster devices calls for ionization of a kind (Grekhov, 1 987). The thyristor is a triggered semiconductor switch based on a four-layer structure of the p-n-p-n junction type (Fig. 1 8. 1 ). The development of thyristors with operating voltages of several kilovolts and microsecond

Chapter I8

326

switching times goes back to the 1 960s (Grekhov, 1 987). An important parameter of a thyristor, along with the voltage and the current rise time, is its operating current. As reported by Page ( 1 976), for thyristors developed by Westinghouse company, currents of up to 2 kA were achieved at a voltage of 2 kV and dlldt = 1 0 1 0 A/s. Driscoll ( 1 976) reported on improvements of thyristors aimed at increasing dlldt to 1 0 1 1 A/s at a current density of 1 03 A/cm2 • Anode

(a)

Gate

(b) Anode

p

n

p

n

Cathode

Gate Cathode

Figure 18.1. Thyristor schematic symbol (a) and structure (b)

A high-current thyristor is shown schematically in Fig. 1 8.2 (Grekhov, 1 987). This is a semiconductor structure consisting of four layers of alternating conductivity type ( p+ -N-p-n structure) that form three p-n junctions located one over the other. When a voltage of polarity indicated in Fig. 1 8.2 is applied to terminals AB, junctions I and 3 are forward-biased (emitters), while junction 2 is reverse-biased (collector). The external voltage is almost completely applied to the SCR of the collector, and the most part of this region lies within a broad weakly doped N layer. To turn the device on, a trigger pulsed current is passed through the A C circuit. The current passage is accompanied by injection of electrons from the (highly doped) n+ layer through the barrier of the n+ -p junction I into the p layer ( p base). Because of the rather high resistance of this layer, the longitudinal injection is appreciable only in the region 80 of width 0. 1-0.2 mm adjacent to the interface between the n+ layer and the gate. The injected electrons diffuse through the p base, arrive at the SCR, and then are ejected by the field, already as major carriers, into the N base. This lowers the barrier of the p + junction 3 and causes injection ofholes into the N base. As these holes come in the p base, they cause injection of electrons, and so on. When the losses of charge carriers due to recombination and going away through the barriers of the p-n junctions become lower than their income, the thyristor goes into the on state, and the turn-on region ( 80 , see Fig. 1 8.2) is filled with electron-hole plasma. The on state extends, rather slowly ( v :::::: 0 . 1 -0.0 1 mm/J.ls), from this region [referred to as the initial turn-on region (ITR)] throughout the device area. If the external circuit restricts the rate of current rise insufficiently, the devise is destroyed in the

SEMICONDUCTOR CLOSING SWITCHES

327

region Do because of intense heat release. A natural way of increasing the power switched by a thyristor and the admissible switching rate is to increase the area of the SCR. Investigations (Grekhov, 1 987; Grekhov et a/. , 1970) have shown that the Do width cannot be increased substantially and the only way of increasing the area is to increase the length L of the interface between the emitter n+ layer and the gate. Moreover, it turned out that for the switching along this boundary to be uniform, the linear density of the trigger current should be rather high, over 3 A/em (Belov et. a/. , 1 970). A

-

Figure 18.2. Schematic diagram of the semiconductor structure of the thyristor: 1, 3 - emitter junctions; 2 collector junction; 4 space charge region (SCR), and 5 - initial turn-on region (ITR) -

-

Therefore, to provide a required linear density of this current and, at the same time, a not very large amplitude of the trigger pulse in modem microsecond pulse thyristors with L = 5-50 em, so-called regenerative triggering is used (Grekhov, 1 987). A thyristor with regenerative triggering is shown schematically in Fig. 1 8.3. The trigger pulsed current flowing in the circuit A C turns on an auxiliary thyristor 1 in region 2. The anode current of this thyristor, which is limited by the tangential resistance of the p base, is the trigger current for the main thyristor 3. Thus, the needed linear density of the trigger current for the main thyristor is provided even at very large L and comparatively low trigger currents. The pulsed thyristor with double regenerative triggering described by Brylevsky et a/. ( 1 982a) has L = 40 em and a linear trigger current density of about 8 A/em, although the trigger pulse amplitude is as low as 1 .5 A. The thyristor is capable of switching a current of 5 kA with di/dt = 1 kA/Jls at an operating voltage of 2 kV and a frequency of 250 Hz. Devices of this type are very good switches when operated with pulses whose duration is much longer than the time it takes for the on state to extend throughout the device area. For a microsecond thyristor, this time is 80-100 JlS.

328

Chapter 18

Figure 18.3. Thyristor with regenerative triggering: 1 - auxiliary thyristor; 2 - initial tum-on region; 3 - main thyristor

When the device is operated with shorter pulses, a considerable part of the area of the p-n-p-n structure has no time to be turned on, and the efficiency of the device operation decreases. It seems to be natural to further increase the interface length L and to decrease the linear size of the emitter regions. In this case, however, the working area is partially lost for the gate, uniform turn-on throughout the interface length becomes problematic, and the production technology becomes more complicated. A radical solution of this problem is a simultaneous and uniform turn-on throughout the device area, which calls for a simultaneous and uniform introduction of extra carriers into the base layers to activate them. The concentration of carriers to be introduced should be considerably greater than the minimum concentration necessary for activation, since, as this is done, the current filamentation due to the nonuniform distribution of the device properties over its area becomes less probable. This principle of activation is realized rather simply in a reversely switched dynistor (RSD) (Grekhov, 1 987). This device (Fig. 1 8.4) is based on a power integrated circuit consisting of several tens of thousands of alternating thyristor and transistor sections of characteristic size about 1 00 f..Lm . The sections have a common high-voltage p+ -n junction, which serves as a collector for the thyristor sections and blocks the external voltage. To trigger an RSD being under forward bias voltage (relative to the thyristor sections), a pulsed voltage whose polarity is inverse to the voltage to be blocked is applied to the device. As this takes place, the low-voltage n+ -p junction is broken down and a pulsed accumulation current lac starts flowing through the transistor sections; that is, there occurs injection of electron-hole plasma into the transistor and neighboring thyristor sections. The density distribution of the excessive charge carriers is shown in the right part of Fig. 1 8.4. The total

SEMICONDUCTOR CLOSING SWITCHES

329

introduced charge is controlled by varying the accumulation current pulse amplitude and duration. As the pulse is over, the current in the main circuit starts rising. This current is uniformly distributed over the area since the trigger charge density at any point of the device is far above the critical one.

1 Figure 18.4. Schematic diagram of a reversely switched dynistor: 1 transistor sections Table 18.1. Th�ristor-!}:re devices for Eulsed rower technology Diameter Pulsed Producer Type of silicon current, structure, kA* mm

-

thyristor sections; 2

dlldt,

kA/J.j,S

••

Operating voltage, kV

Pulsed version of 6RT-500 thyristor

Silicon Power Corp., USA

125

220 (450)

5STH20H4501 thyristor

ABB Semiconductors AG, Switzerland

56

80 (250)

18

4.5

55PY36L4502 thyristor

ABB Semiconductors AG, Switzerland

76

140 (50)

10

4.5

Reversely switched dynistor (RSD)

Elektrovypryarnitel Co., Saransk, Russia

76

250 ( 1 00)

60

2.5

2.0

-

2.5

*Bracketed is the current pulse duration in microseconds. ..In pulsed operation with a high on-off ratio.

Table 1 8. 1 lists some parameters of devices specially developed for use in pulsed power technology. The data are taken from advertising pamphlets of the companies.

2.

NANOSECOND THYRISTORS

To switch high powers on the nanosecond scale, pulsed thyristors with increased operation speed are used. The operation speed is increased due to some design features and a special triggering mode. The process of

330

Chapter 18

triggering of a thyristor from a trigger circuit consists of three clearly distinguished phases. The first phase - a delay in triggering - is combined from the "physical delay", which is determined by the diffusion-drift transfer of the carriers injected from the n+ layer through the p base, and the delay associated with the accumulation of minority carriers in the base layers in numbers sufficient for the process of avalanchelike increase in their concentration to be initiated. The second phase, during which the device current rapidly increases, while its voltage decreases, is determined by the diffusion-drift transfer of carriers through the p and N base regions. Finally, the third phase, where the voltage across the device slowly decreases at an almost constant current, is determined by the buildup of electron-hole plasma in the tum-on region with the on state slowly extending throughout the device area. The first phase can be shortened by making the thickness of the p base as small as possible, thus reducing the physical delay, and by increasing the trigger current amplitude and dl/dt, thus reducing the duration of the carrier accumulation process. For now available fast thyristors with a 20-25-J..lm thick p base, the duration of the first phase lies in the range 20-50 ns. Evidently, the smaller the thickness of the base regions, the shorter the duration of the second phase; however, decreasing the thickness of the N base decreases the operating voltage. Therefore, to speed up the transfer of carriers through the (thick) N base in a fast high-power, high-voltage thyristor, the triggering should be performed so that the field in the N base be high enough throughout the second phase to provide fast transfer of carriers. For this to take place, the voltage applied to the thyristor before triggering should be as high as possible and the current density in the course of triggering should be high enough. With this character of the process in modem thyristors with an operating voltage of 1 .7-2 kV, the second phase lasts 20-50 ns; however, the residual voltage across the device at the end of this phase is rather high: 1 00-200 V. The third phase of the process in a fast thyristor has, as a rule, no time to be completed, since its duration is generally much longer than the duration of the operating current pulse, and the switching process occurs in fact in the initial tum-on region. When thyristor structures are triggered in a fast mode with high block voltages and high current densities, the process at the second stage can be spontaneously localized due to the dependence of the rate of current rise on voltage and current density (Brylevsky et al. , 1 982a). When the thyristor voltage is still high enough and the current density in some region reaches a critical value }cr characteristic of the given type of device earlier than in the neighboring regions, there occurs an abrupt speedup of the transient current rise in the region under consideration, which is related to the transition from

SEMICONDUCTOR CLOSING SWITCHES

331

the diffusion to the field mechanism of carrier transfer. This phenomenon is essentially nonstationary in character. As time goes on, the current distribution in the structure levels off, the duration of the leveling-off process being substantially longer than the rise time of the current pulse. Experiments with low-power triggered thyristors have shown that only 20% of the ITR or 0.02 of the power electrode area are involved in the fast phase. Thus, in fast thyristors, highly pronounced localization of current takes place, resulting in local heat release and giving rise to mechanical stresses, which limit the switched power and are mainly responsible for the degradation of these devices. To suppress this effect, it is necessary, using some external trigger, to increase, within a short time, the current density in the structure to a value greater than jcr and to eliminate the initial (slow) phase of the transient process. As this is done, the current density will increase rapidly and uniformly throughout the area of the structure. When a thyristor is triggered from a triggering circuit, this can be realized by increasing the amplitude of the trigger current pulse, provided that its rise time is much shorter than the rise time of the anode current. In experiments with low-power thyristors (Grekhov, 1987), where the trigger current pulse had an amplitude of 20 A and duration of 1 0 ns and the pulse repetition rate was 50 Hz, the switched current was increased to 1 03 A, which was 20 times greater than its rated value. As this took place, the current was almost uniformly distributed over the ITR. The voltage that can be blocked by the now available fast thyristors is comparatively low, 1 -2 kV, and it cannot be increased without a decrease in operation speed of the thyristors. At the same time, the amplitude of a pulsed current flowing through a load is restricted by the wave resistance of the load and the current rise rate is limited by the time constant of the discharge circuit. Therefore, to increase the power of thyristor switches, it has sense to increase not only the operating current, but the operating voltage as well. The latter can be attained by using several thyristors connected in series, as this was done in a fast switch capable of blocking a voltage of 1 0 kV (Brylevsky et al. , 1 982b). To trigger a switch with a triggering circuit containing five slave thyristors (Fig. 1 8.5), a trigger pulse sufficient to suppress spontaneous localization of charge carriers was supplied only to one master thyristor T 1 • As the latter was turned on, a short-rise-time, large­ amplitude pulsed current passed through the triggering circuits of the other thyristors. The switch provided an increase in current through a resistive load of 1 0 Q to 1 03 A within about 50 ns over a wide range of blocked voltages: from 2 to 9 kV.

332

Chapter 18

Figure 18.5. Switch with subordinate triggering with the help of slave thyristors

A considerable increase in the power switched by thyristor-type devices on the nanosecond scale can be achieved only by the methods that provide uniform and simultaneous turn-on of large areas of p-n-p-n structures. A radical solution this problem would be the creation of a reversely switched dynistor operating on the nanosecond scale. However, for the rise time of the current in the main circuit of a dynistor to be -1 0-7 s, the duration of the carrier accumulation current pulse should be -1 0-8 s. To inject an activating charge of required density within such a short time is conjectural. Turning on a thyristor by a capacitive current at a rapidly increasing anode voltage (dV/dt effect), notwithstanding that this current is uniformly distributed over the area, cannot be uniform since the charge introduced by this current is too low to exclude spontaneous localization of charge carriers. A possible solution could be to tum on a thyristor by a short overvoltage pulse, such that carriers would be generated due to impact ionization immediately in the SCR of the collector junction (Grekhov, 1 987). For this type of device, the overvoltage pulse duration should be of the order of the main current rise time. Numerous experiments have shown that the breakdown over the surface of a p-n junction has no time to develop. It should be noted that to exclude spontaneous current localization during the second phase of the tum-on process, the overvoltage should be high enough to produce a current of density j > }cr· For instance, for a thyristor of area about 0.5 cm2 with }cr :: 20 Ncm2, the current produced by an overvoltage should be no less than 1 00 A, which corresponds to a voltage twice as large as the quasi­ steady switching voltage.

SEMICONDUCTOR CLOSING SWITCHES 3.

333

PICOSECOND THYRISTORS

In studying the dynamics of the avalanche breakdown of a p-n junction in silicon, Grekhov ( 1 987) observed that if a quasi-steady bias was applied to the diode in the blocking direction (Fig. 1 8.6) and then, within a few nanoseconds, an increasing pulsed voltage was applied in the same direction, there were no impact ionization for several nanoseconds notwithstanding that the net applied voltage was a factor of 1 .5-2 greater than the steady avalanche breakdown voltage. Thereafter, the voltage across the diode abruptly decreased and the current increased within a time shorter by 1 .5-2 orders of magnitude than the time it took for an electron to fly with the highest possible (saturated) velocity through the base region. Physically, this phenomenon can be interpreted as follows:

�

4

80

....... 60

2 mm

3

2:. 3

:1.

a

.....

� 40 20 0

0

:::..

2

1

0 N N

n+ Diode D

2 0

2

4

6

8 t [ns]

10

14

12

16

Figure 18.6. Picosecond switching in a semiconductor diode: 1 - diode current; 2 - diode voltage; 3 - total diode and load voltage. Schematic of the diode is shown on the right

The field distribution in a diode under steady-state conditions is shown by curve 1 in Fig. 1 8.7, a. Curves 2 and 3 represent the field distribution for an increasing overvoltage. Simple estimates show that if the base region is not substantially contaminated with deep-level impurities, the number of heat-generated carriers that enter the overvolted region � during the rise time of the overvoltage pulse is only a few carriers per square centimeter. These carriers initiate individual breakdown channels, which develop along the field lines rather slowly (with saturated velocity Vs 1 07 cm/s). In this case, the induced current is low and, at actual values of the load resistance (Rroad = 50 0) matched to that of the high-frequency duct, it does not hinder the increase in the overvoltage across the diode. Therefore, it appears possible to apply to the diode, for several nanoseconds, a voltage two or three times greater than the steady avalanche breakdown voltage and to create near the p +-n junction a region � where the field strength would be substantially greater than its critical value. -

Chapter 18

334

X

0

n

0---j p+l

(b)

'

0

,_

I n+r--o +

_ _ _ _ _ _ _ _ _

X

Figure 18. 7. Electric field distribution in the diode base: (a) before switching: 1 - at a steady bias, 2 - at de breakdown voltage, and 3 - immediately before switching; (b) propagation of the impact ionization wave: hatched region - electron-hole plasma, L\ - overvolted region, w ­ velocity of motion of the wave front

As the voltage is increased, the space charge region rapidly extends into the neutral region 80 that carries the conduction and capacitive currents. The conduction current induces a rather strong field, which is sufficient for impact ionization of the superconductor material by majority carriers to occur. The holes appearing in this case drift toward the overvolted region and enter the latter in a delay time equal to the time it takes for them to pass through the section wscR-� of the space charge region. Estimates show that the rate of voltage rise of the order of 2 · 1 0 1 2 V·s- 1 , which was typical of this experiment, provided a hole flux density such that the impact ionization caused by the holes in the overvolted region occurred almost simultaneously throughout the device area. For the overvoltage achievable in experiments, the characteristic time of the development of an avalanche is about 1 0- 1 1 s. Therefore, the overvolted region is filled with electron-hole plasma within a short time, and the field in this region decreases (Fig. 1 8.7, b). This leads to an increase in the field in the neighborhood region where breakdown is initiated by the flow of holes. Thus, an ionization wave is generated and propagates toward the flow of holes, leaving behind electron-hole plasma.

SEMICONDUCTOR CLOSING SWITCHES

335

Once the wave has traveled, the whole of the base region of the diode appears to be filled with high-density electron-hole plasma, the voltage across the diode abruptly decreases, and the current in the circuit increases. The wave propagation velocity is determined by the rate of breakdown development in the overvolted region and by the hole flux density, i.e., by the overvoltage magnitude and rise rate. This velocity may be higher than the saturated velocity of the carriers by one or two orders of magnitude, and therefore the experimentally observed switching time is shorter than that characteristic of all known switches of the same power by two orders of magnitude. As can be seen from the previous figures, the device switched a current of 30 A produced by a voltage of 3 kV within a time shorter than 0 . 1 ns. Noteworthy is high stability of the switching process: an instrument capable of fixing a jitter of 3 0 ps fixed no jitter. Thus, the phenomenon of a delayed breakdown followed by the generation of an impact-ionization wave in a diode makes it possible to switch hundreds of kilowatts of pulsed power on the subnanosecond scale. The frequency limit of such a diode is determined by the process of plasma decay, and it should range to some tens of megahertz.

4.

LASER-ACTIVATED THYRISTORS

It was proposed (Zucker et a/. , 1 976a, 1 976b; Pittman and Page, 1 976) to activate a thyristor by a laser beam (Fig. 1 8. 8). As appeared, silicon and a neodymium laser form an optoelectronic pair appropriate for switching high powers. The matter is that the radiation of a neodymium laser with a wavelength of 1 .06 J..Lm has a characteristic length of absorption in silicon of about 1 mm, and the best types of silicon and a rather clear technology for the production of p-n junctions in silicon make it possible to produce thyristors with a base region of thickness - 1 mm. This allows one to utilize the laser light pulse for the production of electron-hole plasma almost simultaneously throughout the device thickness. If the pulse power is high enough, the leading edge of the rising current will merely follow the leading edge of the light pulse. When silicon is illuminated with light, the absorbed photons produce electron-hole pairs. This extremely fast process may occur in a carrier-depleted region, and the plasma generation occurs with no diffusion of charge from the near-electrode regions. In practice, the 1 .06 J..Lm infrared radiation is produced by a YAG laser with a neodymium additive. This radiation closely corresponds to the forbidden gap of silicon and provides efficient optical generation of electron­ hole pairs. To ensure an optical contact with silicon, polarized radiation is introduced into the latter at the Brewster angle.

336

Chapter 18

Figure 18.8. Cross-sectional view of a light-activated semiconductor switch: 1 - current path, 2 cathode, 3 polarized infrared radiation from YAG laser, 4 anode, and 5 plasma of electron-hole pairs -

-

-

-

With this method, it is possible to promptly obtain plasma of electrons and holes similar to that generally existing in the base regions of a thyristor in the on state. The turn-on area can be large and the limitations on the time of flight, which take place when plasma is created by injection of carriers from the cathode and anode emitters, can be substantially lowered. Moreover, the series connection of several devices becomes much simpler since the triggering system is isolated. In this case, one laser beam is split into several beams, each activating a semiconductor device. This scheme ensures simultaneous switching. Since turning on is a fast process, to provide a uniform voltage distribution over the devices, a small number of simple equalizing circuits are necessary. Optothyristors were created (Page, 1 976) with a current of up to 3 kA, a reverse voltage of each thyristor of 1 .2 kV, and a rate of current rise of 0.4· 1 0 1 0 A/s, which operate on the microsecond scale at a pulse repetition rate of up to 60 Hz. Experiments with laser-triggered semiconductor devices (Zucker et a/. , 1 976a, 1 976b; Pittman and Page, 1 976) were performed to elucidate whether nanosecond switching times are feasible and which is the highest achievable rate of current rise. To illuminate the switch surface, a doped Nd YAG laser (1 .06 ).lm) with a pulse energy of 3-5 mJ was used. Cable or strip pulse­ forming lines with the wave impedance ranged from 0.04 to 50 0 and a charge voltage of up to 1 700 V served as energy stores. The pulse rise time was 5 - 1 0 ns for the peak current varied between 1 5 and 25000 A. Note that for laser-activated semiconductor optothyristors, the jitter is some fractions of a nanosecond. For the device used in the experiment performed by Volle et al. ( 1981), the laser-illuminated area was 0. 1 cm2 of the total area equal to 2.5 cm2 . Thus, even at 50% efficiency, this device was capable of switching a current higher than 1 00 kA if the whole of its working area was irradiated. Devices of this type can be made having a diameter of 5-7.5 em, and a forward extrapolation suggests that megaampere switches are feasible. The inductance of the diode is very low (0. 1 nH/kV and less); some types of

SEMICONDUCTOR CLOSING SWITCHES

337

switches can be started highly synchronously; therefore, the delay and charging times of the Marx generator can be substantially decreased, especially when compact liquid-insulated energy stores with a high specific energy capacity are used. Further improvements in the operation of optothyristors are described by Grekhov ( 1 987), Grekhov et al. ( 1 970), and Volle et a/. (198 1 ). On the top plane of the thyristor structure, there are several thousands of photodetector windows whose total area is about half the working area. The rest of the area is taken by an emitter with a metal terminal. The light pulse illuminates the whole of the device area and plasma columns are formed simultaneously in all photodetector windows. Figure 1 8.9 presents typical current waveforms for two limiting cases: for a resistive load whose resistance much greater than the characteristic resistance of the circuit and for the short-circuit mode. In the first case, the current leading edge follows the leading edge of the laser pulse (10 ns), while in the second case the current rise time is determined by the system inductance (20 nH) and equals 60 ns. The switch is capable of switching a power of about 300 MW in 60 ns at a frequency of up to 1 00 Hz. This calls for a laser pulse energy (with due regard for all losses) of 1 0-3 J. Thus, the above method makes it possible to switch gigawatt powers within some tens of nanoseconds in a rather simple way, and a highly synchronous operation of a great number of switches can be provided. However, the reliability, lifetime, and frequency limits of this type of switch depend on the characteristics of neodymium lasers, and this is now the limiting factor for the practical implementation of this method. 1 80

(a)

135

� .......

90 45 0 40

(b)

10

20 t [ns]

30

40

30 ...--. 20

� .......

10 0 -10

400

-20

Figure 18.9. Current waveforms recorded in switching with a high-resistance load (R1oad 21 0) (a) and in the short-circuit mode (b). L - laser light pulse waveform =

338

Chapter 18

REFERENCES Andreev, D. V., Dumanevich, A. N., and Evseev, Yu. A., 1 983, Preobrazovate/ 'naya Tekh. 9:5. Belov, A. F., Voronkov, V. B., Grekhov, I . V., et a/., 1 970, Ibid. 5 : 1 5 . Brylevsky, V. 1 . , Grekhov, I. V., Kardo-Sysoev, A . F . , and Chashnikov, I. G., 1 982b, A High­ Power, High-Voltage Fast Switch, Prib. Tekh. Eksp. 3:96-98. Brylevsky, V. I., Kardo-Sysoev, A. F., Levinshtein, M. E., and Chashnikov, I. G., 1 982a. Mechanism of the Localization of Current in Turning on Submicrosecond Modular Thyristors, Pis 'rna Zh. Tekh. Fiz. 8: 1 288- 1 292. Driscoll, J. C., 1 976, High Current, Fast Turn-on Pulse Generation Using Thyristors. In Energy Storage, Compression, and Switching: Proc 1st Intern. Conference on Energy Storage, Compression and Switching (Nov. 5-7, 1974) (W. H. Bostick, ed.), Plenum Press, New York-London, pp. 433-440. Grekhov, I. V. Levinshtein, M. E., and Sergeev, V. G., 1 970, Investigateon of the Extension of the On State along ap-n-p-n Structure, Fiz. Tekh. Poluprovodn. 4:2 1 49-2 1 56. Grekhov, I. V., 1 987, Pulsed Power Switching by Semiconductor Devices. In Physics and Technology of Pulsed Power Systems (in Russian, E. P. Velikhov, ed.), Energoatomizdat, Moscow, pp. 237-253. Page, D. J., 1 976, Some Advances in High Power, High dildt, Semiconductor Switches. In Energy Storage, Compression, and Switching: Proc. 1st Intern. Conference on Energy Storage, Compression and Switching (Nov. 5-7, 1974) (W. H. Bostick, ed.), Plenum Press, New York-London, pp. 4 1 5-42 1 . Pittman, P . F . and Page, D . J., 1 976, Solid State High Power Pulse Switching. I n Proc. I IEEE Intern. Pulsed Power Conf., Lubbock, TX, pp. (IA3 ) 1 - 1 2. Volle, V. M., Voronkov, V. B., Grekhov, I. V., Levinshtein, M. E., Sergeev, V. G., and Chashnikov, I . G., 1 98 1 , A Nanosecond High-Power Thyristor Switch Triggered by a Light Pulse, Zh. Tekh. Fiz. 51:373-379. Zucker, 0. S. F., Long, J. R., Smith, V. L., Page, D. J., and Hower, P. L., 1 976a, Experimental Demonstration of High-Power Fast-Rise-Time Switching in Silicon Junction Semiconductors, Appl. Phys. Lett. 29:26 1 -263. Zucker, 0. S., Long, J. R., Smith, V. L., Page, D. J., Roberts, J. S., 1 976b, Nanosecond Switching of High Power Laser Activated Silicon Switches. In Energy Storage, Compression, and Switching: Proc. of the 1st Intern. Conference on Energy Storage, Compression and Switching (Nov. 5- 7, 1974) (W. H. Bostick, ed.), Plenum Press, New York-London, pp. 538-552.

Chapter 1 9 SEMICONDUCTOR OPENING SWITCHES

1.

GENERAL CONSIDERATIONS

There are two principal approaches used in the production of nanosecond high-power pulses that differ from one another by the method of energy storage. The first method is based on the accumulation of the energy of an electric field in fast capacitive stores, such as low-inductance capacitors and pulse-forming lines, followed by energy delivery to a load through switching devices - nanosecond high-current closing switches. By the second method, energy is accumulated in the magnetic field of an inductive current-carrying circuit and delivered to a load with the help of opening switches. The latter method holds promise for pulsed power technology since the energy density stored in inductive stores is about two orders of magnitude greater than that stored in capacitive ones. On the other hand, fast interruption of high pulsed currents is a much more technically complicated problem than the problem of closing. This problem is most critical in the production of nanosecond high-power pulses where the switch must hold off megavolt voltages and be capable of interrupting currents of tens or even hundreds of kiloamperes within a few or tens of nanoseconds. These requirements are satisfied by three main types of nanosecond opening switch: plasma opening switches with nanosecond and microsecond triggering, opening switches based on electrically exploded wires, and injection thyratrons. However, these switches either are essentially incapable of operating repetitively (exploded wires) or have low pulse repetition rates and limited lifetimes because of electrode erosion (see Chapters 1 6 through 1 8). The creation of essentially new pulsed power systems that would be technologically applicable calls for new principles of switching. In this

340

Chapter 19

respect, the schemes with inductive energy stores and solid-state semiconductor opening switches hold the greatest promise for pulsed power devices with high specific characteristics and long lifetimes. The main problem is to develop repetitive high-power solid-state opening switches which could interrupt kiloampere currents within nanosecond times and hold off voltages ofthe order of 1 06 V. The well-known principles of nanosecond current interruption in solids are based either on injection of charge carriers into the base of a p+-n-n+ structure followed by extraction of the built-up charge by the reverse current (Tuchkevich and Grekhov, 1 988) or on electron-beam initiation of high conduction in the inherent semiconductor (Schoenbach et al. , 1 989) with the ionization source quickly turned off. The obvious engineering difficulties involved in the second method that are associated with the need of using charged particle accelerators to control the operation of the opening switch, along with the low parameters of switched currents (hundreds of amperes) and hold-off voltages (a few kilovolts), make this method impracticable in pulsed power technology. The method of injection of charge carriers was proposed to cut off the reverse current in semiconductor diodes in the 1 950s when much work was done on the creation of fast pulsed diodes. Diodes with the effect of abrupt current cutoff were named charge storage diodes (CSD's) (Eremin et al. , 1 966). A CSD depends for its operation on the built-in braking electric field that exists in the base of a diffuse diode due to the donor concentration gradient. At the stage of charge buildup by the forward current, the built-in electric field directed from the n base into the p region hinders the propagation of the injected holes into the base bulk and holds the charge near the p - n junction. Owing to this, during the passage of the reverse current, almost the whole of the accumulated charge has time to go away from the diode base at the stage of high reverse conduction. The small charge remaining in the base by the moment a space charge has formed at the p - n junction has the result that the reverse current is cut off within I Q-9- 10- 1 0 s. The operation of a diode in the charge storage mode is possible only at a low level of injection of charge carriers and a high level of doping of the base with a donor impurity. When going to a high-current mode of operation (high and superhigh level of injection) or reducing the level of doping of the n base with the aim to increase the reverse voltage of the diode, the built-in electric field disappears and current cutoff fails to occur. In view of this, the operating currents and reverse voltages characteristic of CSD's with a built­ in field lie in the ranges 1 0- 1 00 rnA and 1 0-50 V, respectively. Grekhov et al. ( 1 983) proposed and realized a high-current operation mode for a p+-n-n+ structure with a cutoff current density of up to 200 A/cm2, a current cutoff time of about 2 ns, and an operating voltage of

SEMICONDUCTOR OPENING SWITCHES

341

1 kV. These diodes received the name fast-recovery drift diodes (FRDD's). The principle of operation of an FRDD is as follows: Owing to the short duration of the forward current pulse (hundreds of nanoseconds), a thin layer of injected plasma is formed in the base near the p - n junction in which most of the accumulated charge is localized. During the passage of the reverse trigger current, the plasma layer near the p - n junction resolves and, simultaneously, holes go out from the rest part of the base. The structure parameters (base length and doping level) and the triggering mode (current density and duration) must be chosen such that the drift current density reaches a maximum for a given level of doping of the base as the nonequilibrium charge carriers are completely removed from the structure. If this condition is fulfilled, the process of reverse current cutoff involves the removal of equilibrium carriers from the base with the highest possible saturation rate (�1 07 cm/s). In view of this, an FRDD has a limitation on the current density that can be carried by the structure. To obtain an about 1-2-kV reverse voltage across the structure, the donor impurity concentration in the base should be not over 1014 cm-3, which corresponds to a maximum current density of 1 60-200 A/cm2 in the opening phase. However, the operating current and voltage of the switch can be increased by increasing the structure area and by making a set of series-connected structures. Of fundamental importance to the progress in nanosecond pulsed power technology has been the discovery of the so-called SOS (semiconductor opening switch) effect at IEP (Kotov et al. , 1 993a). It turned out that harnessing this effect makes it possible to interrupt currents of density up to 1 04 A/cm2 within nanosecond and subnanosecond times at voltages of up to 1 06 v. The principle of operation of a semiconductor opening switch is as follows: The triggering circuit, whose diagram is given in Fig. 1 9. 1 , includes a semiconductor diode. Generally, such a diode is a set of series-connected p - n junctions produced by diffusion of donors and acceptors into n-type low-doped silicon (Fig. 1 9.2). The triggering circuit is designed so that the current passing through the diode is oscillatory in character: during the positive and the negative trigger half-wave, the diode conducts in the forward and in the reverse direction, respectively (Fig. 1 9.3). The mechanism of current interruption in SOS 's is essentially different from that in switches with lower current densities, such as FRDD's. First, in an SOS, the low-conductivity region where a strong field is localized appears not in the diode base, as this is the case of an FRDD, but in the highly doped (with the dopant concentration of the order of 1 0 1 5 cm-3 or higher) p region where the saturation current density is several kiloamperes per square centimeter. Therefore, SOS' s are essentially high-current devices,

Chapter 19

342

which operate at reverse current densities of the order of 1 03-104 A/cm2 • Second, in the phase of current decay, plasma remains in the diode in appreciable amounts; therefore, the onset of current decay has no relation to the principle of equality of the charge introduced into the structure during the positive trigger half-wave to the charge removed from the structure during the negative half-wave, which is of fundamental importance, for instance, for fast-recovery drift diodes. Detailed information on the mechanism of operation of semiconductor opening switches is given elsewhere (Bonch-Bruevich and Kalashnikov, 1 977; Madelung, 1 982; Darznek et a/. , 1 996, 1 997, 2000; Rukin, 1 999). s

L D v

Figure 19. 1. Experimental arrangement: C and V - capacitance and output voltage of the primary generator; L - its circuit inductance; D - semiconductor opening switch; R1oad - load 1 020 ....... ,.., I

E .£.

�

�

1 0 19

\ \

B

\�

1 01 8

I ' \

1 0 17

'

'

1 016

'

'

',� ' AI

\ \ \ \ \

1 01 5 1 0 14 1 013

'

p+ 0

p

n+

n 200 1 00 Coordinate [!-lm]

3 00

Figure 19.2. Schematic of doping of a semiconductor diode. Solid curve - distribution of donors; dashed curve - distribution of acceptors. The arrow at the abscissa axis points to the position of the p - n junction

SEMICONDUCTOR OPENING SWITCHES

343

/so

Vso Figure 19. 3. Conventionalized oscillograms of the current flowing through the opening switch and of the voltage across the load. /so and Vso - current and voltage of the semiconductor diode; tp - pulse duration

The best performance of FRDD's was achieved in the experiment performed by Efanov et al. ( 1 997) where pulses of peak voltage 80 kV, current 800 A, and pulse repetition rate 1 kHz were produced with the help of series-connected FRDD's. Grekhov ( 1 997) describes a generator with a semiconductor opening switch whose operation is based on the inverse recovery of the diode. The diode depends for its operation on the removal of the excessive plasma from the base in the phase ofhigh reverse conductance. Based on this diode, a generator with a voltage of 30 kV, a current of 600 A, and a pulse repetition rate of 1 kHz has been developed.

2.

OPERATION OF SOS DIODES

Thus, FRDD-based pulse generators are capable of producing pulsed voltages of tens of kilovolts and currents of up to 1 03 A. To produce pulses with higher parameters, SOS diodes are used. The SOS effect was discovered by Rukin and co-workers (Kotov et al. , 1 993a) in semiconductor diodes intended for rectification of alternating current at a certain combination of current density and triggering time. On the other hand, there are various classes of rectifying diodes that are different in recovery rates and in the character of voltage recovery upon diode reversal. By the reversal characteristics, diodes with conventional, "hard" recovery and modern, improved, diodes with "soft" recovery are distinguished.

344

Chapter 19

Technologically, soft and hard diodes are different in original dopant profile in the structure, in p n junction depth Xp, in base length, and in resistivity of the original base-forming n-silicon. Figure 1 9.4 presents a typical p+- p - n - n+ structure of a diode. A conventional (hard) diode has a p region formed by diffusion of aluminum for a depth xP 1 00 Jlm. To produce a soft diode, one of the following technological means (or their combination) is used: decreasing Xp with a simultaneous increase in the abruptness of the p - n junction by forming an epitaxial p+ region with a high gradient of acceptor concentration near the p - n junction (Duane and Ron, 1 988; Potapchuk and Meshkov, 1 996) and increasing the base length and conductivity of the original silicon (Assalit et al., 1 979; Chu et al. , 1 980). The above means have the result that as the current reverses its direction, on the one hand, the p - n junction very quickly becomes free of excessive plasma and, on the other hand, the plasma remaining in the diode in large amounts makes the decay of the reverse current longer, thus providing soft recovery of voltage. -

�

1 020 .------, I

n

10 1 3 '-----f----,f--' xp = 80-120 [J.tm] xp = 160-200

Figure 19. 4. The typical p+-p - n - n+ structure of a rectifier diode: I epitaxy (soft diode); 2 - conventional diffusion (hard diode); 3 - deep diffusion (superhard SOS diode) -

To investigate the effect of the structure parameters on the process of current interruption in the SOS effect mode, experimental opening switches were developed that differed from one another by the original resistance of the silicon, base length, structure area, and p - n junction depth. Each of the opening switches contained twenty series-connected diodes tightened with dielectric dowels. Each diode was a copper cooler on which four series­ connected structures were soldered. An increase in hardness of an opening switch was achieved when the p - n junction depth Xp was increased from 1 00 to 200 Jlm. The dependence

SEMICONDUCTOR OPENING SWITCHES

345

of the overvoltage across an opening switch in idle run on Xp was investigated by Darznek et a/. ( 1 999). For Xp over 1 60 J..lm, the overvoltage factor reached six. According to the existing classification, these diodes can be referred to as diodes with "superhard" recovery. Figure 1 9.4 shows the structure of a SOS diode in comparison with the structures of soft and hard diodes. An SOS diode, due to a small base length, is capable of passing, at the stage of triggering, and then interrupting high currents (as Xp was increased, the thickness of the silicon plate remained unchanged and equal to 3 1 0-320 J..lm). Shorter times of current interruption provide a higher overvoltage factor with a higher efficiency of energy switching, and the design of a SOS diode, with its developed surface of the coolers, offers the possibility to increase the dissipated power. For series-connected semiconductor devices, a practically important problem is to provide a uniform voltage distribution over the structures, which is necessary for the device to operate reliably and without emergencies. For this purpose, either resistive voltage dividers are used to compensate the technological spread in structure characteristics that appears in their production or the structures are selected before assembling by their capacitance-voltage and current-voltage characteristics. A very important feature of the SOS effect is that in the phase of current interruption the voltage is in uniformly distributed in an unattended manner over a great number of series-connected structures (diodes). This makes it possible to create megavolt opening switches by connecting in series a number of diodes without use of external voltage dividers. Thus, each branch of the opening switch of the Sibir system (Kotov et al. , 1 995) contained 1056 series­ connected structures (eight diodes each containing 1 32 structures) and operated at a voltage ofup to 1 . 1 MV. This property of the SOS effect, along with the high density of the interrupted current, has made it possible to attain gigawatt powers in nanosecond pulses produced by semiconductor devices. Investigations of the voltage distribution over the series structures of an opening switch operating in the SOS-effect mode were performed by Ponomarev et al. (200 1 ) The test diode contained ten series-connected structures. To simulate the technological spread in parameters, the value of Xp was varied from structure to structure with a step of 2 J..lm in the range from 1 70 to 1 88 J..lm. It was found that the formation of the strong field region (SFR) in structures with smaller Xp began earlier than in those with larger Xp. The largest time difference, 2.5 ns, was observed for the structures with most different Xp ( 1 70 and 1 88 J..lm) (Fig. 1 9.5). For the same structures, the difference in w, and, hence, in structure voltage, was a maximum. The mechanism of the earlier operation of the smaller-xp structures is as follows: .

346

Chapter 1 9

At the forward triggering stage, when there occurs charge buildup in the the excessive plasma density is higher in the smaller-xp structures the same charge is distributed over a thinner p layer. Accordingly, in the smaller-xp structures, the recombination processes are more intense and the built-up charge, which can later be removed from the structure by the reverse current, is smaller. During the reverse triggering phase, with the same law of variation of the current density in time (series-connected structures), the smaller built-up charge in the smaller-xp structures has the result that the saturation of the charge carrier velocities in the p region and the SFR formation come into play earlier than in the larger-xp structures.

p region,

(a)

1

30

e 20 �

5 · 1 05

3 · 1 05

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10

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1 · 1 05 0 490

0 - 1 · 1 05

12

(b)

e �
60

8

40

�

tO

�

4

0 490

20

495

500 t [ns]

505

5 1 0°

Figure 1 9. 5. Time dependences of the SFR width w ( 1, 2), rate of width variation v (3, 4), difference dw (5), and deviation B (6) in the phase of current interruption for structures with Xp 1 70 J.lm (curves 1, 3) and 1 8 8 Jlffi (curves 2, 4) =

By the onset of the SFR formation in the structure with Xp = 1 88 J.!m (curve 2 in Fig. 1 9 .5) the width of the SFR in the structure with Xp = 1 70 J.!m (curve 1 in Fig. 1 9.5) reached 1 1 .5 J.!m. At this point in time, the voltage distribution over the structures was most nonuniform and its largest deviation o from the average value was observed for the structure with Xp = 1 70 J.!m, reaching 56% for o estimated as o = I Vi Vav 1 · 1 00% /Vav , -

SEMICONDUCTOR OPENING SWITCHES

347

where Vav is the arithmetic average of the voltage per structure (curve 6 in Fig. 1 9.5). Darznek et al. (2000) have demonstrated that the velocities of expansion of the SFR are higher in the larger-xp structures due to the lower excessive plasma density in the p region. As can be seen in Fig. 19.5 (curves 3 and 4), in all cases the SFR expansion velocity in the structure with xp = 1 88 J..lm was greater than that in the structure with Xp = 1 70 J..lm. As a result, both the difference between the SFR widths, �w, and the voltage deviation from its average value, o , decrease during the process of current interruption. When the voltage across the structures reached a maximum (maximum value of w), the difference in SFR widths was not over 5 J..tm (curve 5 in Fig. 1 9.5) and o decreased to 4% (curve 6 in Fig. 1 9.5). Thus, it has been shown that in the SOS effect mode, in the phase of current interruption and voltage rise across series-connected structures a mechanism operates by which the voltage distribution over the structures in which the depth of the p - n junction is different levels off. This mechanism is associated with the fact that the SFR in 1arge-xp structures starts forming later in the phase of current interruption, but it expands with a higher velocity than in smaller-xp structures. Investigations of the influence of the dopant profile of a structure on the process of current interruption under the SOS effect for both long and short triggering times have formed the basis for the creation of a new class of semiconductor devices - SOS diodes, whose distinguishing design feature is the large depth of diffusion of aluminum into the structure (Darznek et a/. , 1 999). For nanosecond devices, Xp is 1 60-1 80 J..tm , while for devices with short-term triggering and subnanosecond current interruption times it reaches 200-220 J..tm . The typical design of a SOS diode is shown in Fig. 1 9.6. The switch involves a series of elementary diodes tightened with dielectric dowels between two output electrode plates. Each elementary diode consists of a cooler with four series structures soldered on it. A protective coating resistant to transformer oil is applied on the side surface of the structures. Before assembling the diodes, the contact surfaces were flattened and grinded. The assembly has a thermal expansion compensator consisting of two metal bushes with a rubber washer between them. On one of the electrodes, there is a screw to control the force in tightening the diodes. The assembled SOS diodes were tested on specially developed stands. An experiment has shown that the switched current through a SOS diode of area 1 cm2 was 5.5 kA and the time measured between 1 0% and 90% of the peak current was 4.5 ns. The switching rate was 1 200 kA/J..ts, which is about three orders of magnitude greater than the current rise rate in conventional fast thyristors.

348

Chapter 1 9 1

2

3

Figure 19. 6. Typical design of a SOS diode consisting of series-connected structures with coolers: 1 - insulator rod, 2 - cathode plate, 3 - tightening screw, 4 coolers with soldered­ on semiconductor structures, 5 anode plate -

-

Table 1 9. 1 lists the characteristics of the SOS diodes developed at IEP. The most powerful device whose structure area is 4 cm2 operates at a voltage of 200 kV and interrupts a current of 32 kA, which corresponds to an interruption power of 6 GW. A device has been created which is capable of operating in a continuous mode at a high pulse repetition rate. This device has a developed system of coolers and, with an interrupted current of 1-2 kA and a voltage of 1 00- 1 20 kV, operates at a pulse repetition rate of 2 kHz. There also exist devices that harness the effect of subnanosecond current interruption; they are intended to produce pulses of duration a few nanoseconds. With a short triggering time, they interrupt currents of up to 2 kA within 500-800 ps. Table 19. 1. Parameters of the SOS diodes developed at IEP Parameter Value Operating voltage Number of series structures Structure area

60-400 kV 80-320

0.25-4 cm2

Interrupted current density

0.4-2 kA/cm2 2-10 kA/cm2

Forward triggering time

40-600 ns

Forward current density

Reverse triggering time

1 5- 1 50 ns

Current interruption time

0.5- 1 0 ns

Power dissipated in transformer oil (continuous operation)

50-500 w

Length/mass

50-220 mm/0.05-0.6 kg

SEMICONDUCTOR OPENING SWITCHES

349

Investigations and use of the SOS diodes as units of various pulse generators have demonstrated their exceptionally high reliability and ability to withstand many-valued overloads in current and voltage. Since 1 995, when first pilot SOS diodes were made, up to 2002 there was no one failure of these devices. Stand tests carried out to specially disable such a device have shown that an increase in trigger current density (and in di/dt) by an order of magnitude (from 5 to 50 kA/cm2) increases the energy losses in the triggering phase and reduces the efficiency of operation of the opening switch. In this case, the structures operate as a resistor that limits the trigger current, since at these high current densities the modulation of the base is accompanied by the appearance of high forward voltages. Attempts to disable a SOS diode by applying a high operating voltage (a device with an operating voltage of 1 20 kV was incorporated in a generator with an output voltage of 450 kV) have shown that in the phase of current interruption the SOS diode operated as a voltage limiter (the pulse amplitude was not over 1 50 kV), consuming energy from the trigger capacitor. Simulations performed for this operating mode have demonstrated an abrupt intensification of the processes of avalanche multiplication of carriers in the electric field region and a corresponding decrease in structure resistance in the current interruption phase. Obviously, this ability of SOS diodes to withstand overloads is due to the specific operation of a semiconductor structure that is filled with plasma in the SOS mode. Investigations have also revealed another feature of SOS diodes: the current interruption characteristics are improved when the semiconductor structure is heated. In contrast to conventional power devices (diodes and thyristors) whose structure under reverse voltage is free of excessive plasma and an increase in temperature results in breakdown of the structure due to an increase in reverse current and its localization at irregularities, the base of a SOS diode remains filled with excessive plasma during the current interruption and generation of a reverse voltage pulse. In an experiment with an overheated SOS diode, it has been established that as the structure temperature increases in the course of operation until the onset of melting of the high-temperature solder, the charge extracted at the stage of reverse triggering increases by about 1 0-1 5%. The increase in extracted charge increases the interrupted current amplitude and decreases the interruption time. This effect is related to the increase in lifetime of minority carriers with temperature and with the corresponding decrease in charge losses due to recombination. The operating parameters of SOS diodes, such as current density, peak voltage, and pulse repetition rate, should be matched to the required efficiency of energy switching into a load and to the temperature regime of the device operation. The main energy losses (80-90%) in a SOS diode take

350

Chapter 19

place in the phase of current interruption. Therefore, for the same triggering mode, variations in load parameters vary the current interruption characteristic, the peak voltage across the switch, and the amount of energy released in the switch. This leads to problems with the determination of the admissible pulse repetition rate. For the above reasons, we give recommended values of the current density and trigger pulse duration in Table 1 9. 1 where, instead of the pulse repetition rate, the admissible power losses are given which correspond to the temperature difference between the cooler and the surrounding transformer oil lying in the range 50-80°C (0.25-0.4 W/cm2 ). The typical pulse repetition rates for the switch operation under invariable heat removal conditions range between 200 and 2000 Hz. When a device operates in the burst mode for which the thermal regime is nearly adiabatic, the pulse repetition rate is, as a rule, limited by the repetitive operation capabilities of the power supply generator, since the intrinsic limiting pulse repetition rate of a SOS diode, which is determined by the duration of the triggering process, is over 1 MHz. The operating voltage of the devices, given in Table 1 9. 1 , makes up 80% of the voltage at which a SOS diode starts operating in the voltage limitation mode. When SOS diodes are incorporated in a generator, their parallel-series connection is admissible to attain required parameters of the opening switch.

3.

SOS-DIODE-BASED NANOSECOND PULSE DEVICES

The method of increasing the power of capacitive generators with the help of an intermediate energy store and an opening switch has been known long ago. This method is based on the fact that the inductance of the discharge circuit, which is a passive element of a capacitive generator and prevents rapid energy extraction from the capacitors into the load, becomes an active element when an opening switch is used and operates as an inductive energy store. In this case, an increase in pulse power is achieved since the energy delivery from such a system to a load takes a short time. In pioneering experiments on harnessing the SOS effect for the production of pulse power (Kotov et a/., 1 993a), the power enhancement mode was realized for a Marx generator with an opening switch based on high-voltage rectifier diodes. The Marx generator had a capacitance of 0. 1 3 �F and an idle-run voltage of 1 50 kV. The SOS opening switch was assembled from 64 rectifier diodes ( 1 6 parallel branches each containing four series-connected diodes). The forward and reverse trigger currents of the switch were 25 and 20 kA, respectively. The reverse current triggering time was 300-400 ns. Under these conditions, as the current was cut off,

SEMICONDUCTOR OPENING SWITCHES

351

voltage pulses of amplitude up to 400 kV and FWHM 40-60 ns were produced across a 1 00-Q load. In another version, the opening switch had 20 parallel branches consisting of diodes of the same type. With the Marx idle run voltage equal to 1 50 kV, pulses of amplitude 420 kV were produced across a 1 50-Q load. For a load of resistance 5.5 n, the pulse amplitude was 1 60 kV with the current rise time equal to 32 ns. In this experiment, record values of the switched power and di/dt in a load have been achieved with semiconductor opening switches, which were, respectively 5 GW and 1 012 A/s. For a minimum inductance of the discharge circuit (without an additional inductor) and with the Marx generator operated into the same load (5.5 Q) without an opening switch, the load current rise time was 1 80 ns with the peak current equal to 25 kA. Thus, the use of a rectifYing-diode­ based semiconductor opening switch has made it possible to increase di/dt in a load about seven times. Nanosecond pulse generators and accelerators with semiconductor opening switches based on commercial rectifYing semiconductor diodes operating in the SOS-effect mode are described in (Kotov et al. , 1 993a; Kotov et al. , 1 993b). Marx-based capacitive generators and single- and double-circuit triggering schemes were used as power supplies. The generators had an output voltage ranged from 1 50 to 450 kV and differed from one another in stored energy by three orders of magnitude. One of them is a compact generator designed as a portable unit of mass 1 0 kg and length 600 mm. The Marx generator contains four modules with inductive decoupling, which are pulse-charged from a thyristor charging device to a voltage of 1 8 kV in 20 J.!S. The output parameters of the generator are as follows: capacitance 0.85 nF, voltage 70 kV, and stored energy 2 J. The inductance of the intermediate energy store in the one-circuit triggering scheme of the opening switch is 2.5 J.tH. As the Marx generator is turned on, the pulsed forward triggering of the SOS lasts 1 50 ns; the duration of the reverse trigger pulse is 80 ns. The current interruption occurs within 1 0 ns, resulting in the formation of a voltage pulse of amplitude 1 60 kV and FWHM 1 0- 1 2 ns across a 1 80-Q load. The interrupted current is about 1 kA. The SOS opening switch is assembled of 88 rectifier diodes: four parallel branches each containing 22 series-connected diodes. The maximum current density in the structure during forward triggering and prior to current interruption is, respectively, 1 5 and 1 2.5 kA/cm2 • The generator is designed in an oil-free version; the elements of the input unit are insulated from the case with a removable screen consisting of several layers of Dacron film. The device operates with a pulse repetition rate of 50 Hz.

352

Chapter � + Triggering (+ )

(a)

vt

+

(b)

>

"'

0

.,.. ....

6

--- --fct

I

I

I I I I I I I I I I I I \ \

0.4 t [!lm]

0

r-�--��

Marx generator (-)

� 0.2 ;:::' 0.4

c+

A

to

,, � I \1 \

: rV\.

0

- 30

0.8

19

60

�

=0

...:f;


0.7

0.8 t [!lm]

0.9

Figure 19. 7. Schematic diagram of an electron accelerator with double-cycle triggering of the opening switch (a) and the switch voltage (solid line) and current waveforms (dashed line) (b)

Subsequently, a more powerful nanosecond electron accelerator with an output voltage of up to 450 kV has been developed (Mesyats 1 995) (Fig. 1 9.7). It is based on a three-stage Marx generator capable of storing 1 .5 kJ of energy at an output voltage of 1 50 kV. Its essential difference from the above generator is the use of two-circuit triggering of the switch in the mode of reverse current amplification. The accelerator is placed in a metal case of dimensions 1 800 x 1 000 x 800 mm3 and has a mass of 300 kg. The Marx and case inductances are responsible for inductive energy storage. The absence of lumped inductances results in insignificant voltages across the structural components relative to the case during forward and reverse triggering of the SOS, allowing one to operate the accelerator in air not using oil or compressed gas. Initially, the forward triggering capacitor c+ is turned on, resulting in the forward current passage through the switch. In a delay time td , the Marx generator is started, giving rise to the reverse current (whose magnitude is four or five times greater than that of the forward current) through the switch. The subsequent current interruption in a time results in the formation of a high voltage pulse across the accelerator diode and in the generation of an electron beam. The main parameters that determine the output pulse power and the overvoltage factor in this scheme are the capacitance c+ and the delay time The maximum overvoltage was 0.75 t + , where achieved at c + 0.05 JlF and is the half-period of the current oscillation in the forward triggering circuit. The overvoltage factor

et al. ,

t0

=

t11 :::;

tct. t+

SEMICONDUCTOR OPENING SWITCHES

353

reached 3 .3-3.5 . The current interruption time was in the range 30-70 ns; the interrupted current reached 45 kA for the reverse triggering time ranged between 200 and 400 ns. The maximum di/dt in the load was 2 · 1 01 2 A/s. The voltage pulse of amplitude up to 450 kV had an FWHM of 25-50 ns with a rise time of 1 0- 1 5 ns. The accelerator produced an electron beam of maximum energy 400 keV, current 6 kA, and FWHM 30 ns. The SOS opening switch contained 90 rectifier diodes with a reverse voltage of 1 60 kV. Structurally, the SOS consisted of two parallel panels each containing 1 5 parallel branches of three series-connected diodes. The forward and reverse trigger current densities were, respectively, 1 .8 and 7.5 kA/cm2• Once experimental and theoretical investigations of the SOS effect had been performed and first pulsed power generators and accelerators had been developed that used spark-gap generators to pump a semiconductor opening switch, it became obvious that essentially new nanosecond pulsed power devices could be built which would differ from the conventional devices by a all-solid-state energy switching system using magnetic switches. This will be discussed in detail in the following chapter.

REFERENCES Assalit, H. B., Erikson, L. 0., and Wu, S. J., 1979, High Power Controlled Soft Recovery Diode Design and Application. In IEEE Industry Application Society: Annual Meeting, pp. 1 056- 1 06 1 . Bonch-Bruevich, V . L., and Kalashnikov, S. G., 1977, Physics of Semiconductors [in Russian]. Moscow, Nauka. Chu, C. K., Johnson, J. E., Spisak, P. B., and Kao, Y. C., 1 980, Design Consideration on High Power Soft Recovery Rectifiers. In IEEE Industry Application Society: Annual Meeting, pp. 720-722. Darznek, S. A., Lyubutin, S. K., Rukin, S. N., Slovikovskii, B. G., and Tsiranov, S. N., 1 999, SOS Diodes as Nanosecond Interrupters of Super-High-Density Currents, Elektrotekhnika. 4:20-28. Darznek, S. A., Mesyats, G. A., and Rukin, S. N., 1 997, The Dynamics of an Electron-Hole Plasma in Semiconductor Interrupters of Super-High-Density Currents, Zh. Tekh. Fiz. 67:64-70. Darznek, S. A., Mesyats, G. A., Rukin, S. N., and Tsiranov, S. N., 1 996, Theoretical Model of the SOS Effect. In Proc. XI Intern. Conf. on High Power Particle Beams, Prague, Czechia, Vol. 2, pp. 1 24 1 - 1 244. Darznek, S. A., Rukin, S. N., and Tsiranov, S. N., 2000, The Effect of the Structure Dopant Profile on the Current Interruption in High-Power Semiconductor Opening Switches, Zh. Tekh. Fiz. 70:59-62. Duane, W. E. and Ron, D. W., 1 988, Fast Recovery Epitaxial Diodes. In Proc. IEEE Industry Application Society: Annual Meeting, Pittsburg, PA, Pt 1 :2-7.

354

Chapter 19

Efanov, V. N., Kardo-Sysoev, A. F., Larionov, M. A., et a!., 1 997, Powerful Semiconductor 80 kV Nanosecond Pulser. In Proc. Xlth Intern. IEEE Pulsed Power Conf., Baltimore, MD, Vol. 2, pp. 985-987. Eremin, S. A., Mokeev, 0. K., and Nosov, Yu. R., 1966, Charge-Storage Semiconductor Diodes and Their Application [in Russian]. Sov. Radio, Moscow. Grekhov, I. V., 1 997, Mega- and Gigawatts-Ranges, Repetitive Mode Semiconductor Closing and Opening Switches, Proc. Xlth Intern. IEEE Pulsed Power Conf., Baltimore, Md, Vol. 1, pp. 425-429. Grekhov, I. V., Efanov, V. M., Kardo-Sysoev, A. F., and Shenderei, S. V., 1983, Formation of Nanosecond Fall Voltages across Semiconductor Diodes with the Drift Mechanism of Voltage Recovery, Pis 'rna Zh. Tekh. Fiz. 9:435-439. Kotov, Yu. A., Mesyats, G. A., Rukin, S. N., and Filatov, A. L., 1 993a, A Solid-State Opening Switch for the Production of Nanosecond High-Power Pulses, Dokl. RAS. 330: 3 1 5-3 1 7. Kotov, Yu. A., Mesyats, G. A., Rukin, S. N., Filatov, A. L., Lyubutin, S. K., 1993b, A Novel Nanosecond Semiconductor Opening Switch for Megavolt Repetitive Pulsed Power . Technology: Experiment and Applications. In Proc. IXth IEEE Pulsed Power Conf , Albuquerque, NM, Vol. 1, pp. 1 34-1 39. Kotov, Yu. A., Mesyats, G. A., Rukin, S. N., Telnov, V. A., Slovikovskii, B. G., Timoskenkov, S. P., and Bushlyakov, A. 1., 1 995, Megavolt Nanosecond 50 kW Average Power All-Solid-State Driver for Commercial Applications. In Proc. X IEEE Intern. Pulsed Power Conf., Albuquerque, NM, Vol. 2, pp. 1 227-1230. Madelung 0., ed., 1982, Landolt-Boernstein Numerical Data and Functional Relationships in Science and Technology (Vol. 1 7 A: Physics of Group IV Elements and III-V Compounds). Springer, Berlin. Mesyats, G. A., Rukin, S. N., Lyubutin, S. K., Darznek, S. A., Litvinov, Ye. A., Telnov, V. A., Tsiranov, S. N., and Turov, A. M., 1 995, Semiconductor Opening Switch Research at IEP. In Proc. Xth IEEE Pulsed Power Conf, Albuquerque, NM, Vol. 1, pp. 298-305. Ponomarev, A. V., Rukin, S. N., and Tsyranov, S. N., 200 1 , Study of the Process of Voltage Distribution over the Structures in a High-Power Semiconductor Opening Switch, Pis 'rna Zh. Tekh. Fiz. 27:29-34. Potapchuk, V. A. and Meshkov, 0. M., 1 996, Power Superfast Epitaxial-Diffusion Diodes, Elektrotekhnika. 12: 14- 1 6. Rukin, S. N., 1 999, High-Power Nanosecond Pulse Generators with Semiconductor Opening Switches, Prib. Tekh. Eksp. 4:5-36. Schoenbach, K. H., Lakdawala, V. K., Stoudt, D. C., Smith, T. F., and Brinkmann, R. P., 1 989, Electron-Beam-Controlled High-Power Semiconductor Switches, IEEE Trans. Electron Devices. 36 (Pt I): 1 793- 1 802. Tuchkevich, V. M. and Grekhov, I. V., 1988, New Principles of High Power Switching by Semiconductor Devices [in Russian]. Nauka, Leningrad.

Chapter 20 PULSE POWER GENERATORS IN CIRCUITS WITH MAGNETIC ELEMENTS

1.

PROPERTIES O F MAGNETIC ELEMENTS IN PULSED FIELDS

The use of active contactless magnetic elements in pulse circuits is highly promising due to their high reliability and relative simplicity of the design. The methods of production and transformation of pulses with the help of nonlinear magnetic elements were originally proposed and developed for circuits operating on the microsecond scale (Meerovich et al. , 1 968). Some of these methods can be used with almost no change to produce pulses of nanosecond duration (Mesyats, 1 974). A body placed in a magnetic field acquires a magnetic moment whose value depends on the dimensions of the body and on the properties of its material. If the magnetic flux inside the body is uniform, the magnetic moment of the body, Mb, is defined as (20. 1 ) where M i s the magnetization (magnetic moment per unit volume) (Nm) and V is the volume of the body (m3 ). An important quantity that defines the magnetic state of a body is magnetic density B, which is measured in teslas ( 1 T = 1 04 Gs) and, for a ring core, is given by

B = J.Lo(M + H),

(20.2)

where J.!o = 4x· 1 o-7 Him is the permeability of empty space and H is the magnetic field strength (Nm) ( 1 Nm = 1 .25· 1 0-2 Oe). A distinctive feature of ferromagnetics is magnetic hysteresis, i.e., the dependence of the

356

Chapter 20

magnetic moment density and flux density on the formerly operating fields. From the hysteresis curve of magnetic density (Fig. 20. 1 ) the residual magnetic density Br. the saturation magnetic density B•• the coercive force He. and the saturation field strength H. can be found. The saturation magnetic density Ms and the residual magnetic density Mr are related to B. and Br by relation (20.2). However. as a rule. H5 « Ms. and. according to relation (20.2). we have B. ::::: 11oM.. B I I I I I I

-H

Hs

H

Figure 20. 1. Hysteresis loop of a ferromagnetic material

To design pulse circuits using ferromagnetic materials. it is necessary to know the relationships that describe the processes of pulsed magnetic reversal of ferrites. i.e.. so-called dynamic characteristics of ferrites. An important parameter which characterizes the dynamic properties of ferromagnetics is the time of magnetic reversal of the core by which is meant the time it takes for a magnetic state to change from -Br to +Br and which is determined by the rate of magnetic reversal of the core. The simplest experiment on studying the rate of magnetic reversal involves the application of two magnetic field pulses to a ferromagnetic. One of these pulses should be intense enough to obtain the initial state of residual saturation. while the second one should admit variations in amplitude. During the action of the second pulse. magnetic reversal is observed. and it is supposed that the time corresponding to the rise time of the pulse executing magnetic reversal is much less than the magnetic reversal time of 'trev · Under these conditions. if the core is switched from one stable state to another and if the reverting field Hrev > He. the time 'trev is inversely proportional to the field: (20.3) where Srev is the magnetic reversal coefficient. For low fields and magnetic reversal times of about 1 0-6 s. the relation (20.3) is accounted for by the displacement of domain boundaries (Pavlov and Sirota. 1 964). However. this model is valid only for magnetic reversal times shorter than -1 o-6 s. As the acting field is increased. the rate of magnetic reversal increases and the

GENERA TORS IN CIRCUITS WITH MAGNETIC ELEMENTS

357

theory of displacement of domain boundaries does not explain any more the available experimental data. In this connection, Gyorgy ( 1957) developed the theory of flux reversal by incoherent rotation of the magnetization vector. According to his model, the magnetization vector rotates simultaneously throughout the body. For the equation of motion of the magnetization vector, the Landau-Lifshits equation (Landau and Lifshits, 1 959) is used with the dissipative term written in Hilbert form. If we assume that a toroidal core is equivalent to an infinite cylinder arranged along the z-axis and that a magnetic field Hrev is applied along the -z-axis, we then have

[

dMz = yaMsHrev 1 + a2 dt

](

1-

)

M} , Mi

(20.4)

where y = 2.2· 1 05 m/(A·s) is the gyromagnetic ratio for an electron and a is the dissipation coefficient depending on the physical properties of the ferromagnetic element. Whether or not the magnetic reversal rate calculated from Eq. (20.4) will corresponds to that obtained experimentally depends on the choice of the coefficient a. Equation (20.4) includes the quantity a' = a(l + a 2 t 1 that weakly depends on a. For instance, as a is varied from 0.5 to 1 , a' varies from 0.4 to 0.5. Thus, when solving practical problems, an approximate value of a can be taken. As a rule, for the calculations in the range of moderate magnetic reversal fields ( 1 02-1 06 Aim), it is generally assumed that a = 0.4- 1 . The magnetic reversal time decreases with increasing magnetic reversal field. However, due to the finite dimensions of some crystals of the magnet and the demagnetizing fields appearing around them (Steinbei� and Vogler, 1 968), it is impossible to obtain a magnetic reversal time shorter than 1 ns. According to this, the dissipation coefficient in Eq. (20.4) decreases. The determination of a for strong magnetic reversal fields (Hrev > 1 06 Aim) was carried out by using a conventional testing technique for ferromagnetic elements and by measuring the parameters of electromagnetic waves initiated in the test element. It was obtained that a varied from 0.05 for 2BT ferrite to 0. 1 1 2 for NZ-1 000 ferrite. For Hrev < 1 06 Aim, the proper choice is a = 0.5. It should be pointed out that in strong fields, the ferrites with rectangular and flat hysteresis curves lose their substantial differences in hysteresis curve shape and in magnetic reversal rate. Thus, both mentioned types of ferrite can be successfully used on the nanosecond scale. The operation of microsecond magnetic pulse generators is described by Melville ( 1 95 1 ) and Meerovich et al. ( 1 968). The principal requirements to the material of the core of a magnetic switch are determined its specific operation: the switch should have high inductance in the unsaturated state (open state) and the least possible

358

Chapter 20

inductance in the mode of profound saturation (closed state). The most usable materials for magnetic switch cores in high-power magnetic generators are ferrites, iron-nickel alloys (permalloys), and amorphous alloys. The main advantage of ferrite cores over cores made of ferromagnetic (permalloy and amorphous alloy) strip is their high resistivity that practically eliminates energy losses due to eddy currents (Meshkov, 1 990). In this connection, ferrites are usable at supershort magnetic reversal times (tens of nanoseconds) and enable a magnetic switch to operate with pulse repetition rates of a few and even tens of kilohertz. However, ferrites rank far below metal ferromagnetic alloys in magnetic properties. They have lower saturation flux densities (less than 0.5 T) and Curie temperatures ( 1 00-200°C) and higher permeabilities in the saturated state. Besides, the diameter of ferrite cores is limited to 200-300 mm, and this, other things being equal, increases the inductance of a magnetic switch in the saturated state and reduces the switched pulse power and the operating voltage. In this connection, the ferrite switches are most usable in magnetic generators operating with high pulse repetition rates and moderate output voltages (50-200 kV) and pulse powers (tens and hundreds of megawatts) at pulse durations of tens and hundreds of nanoseconds. The highest pulse power achieved is 7 GW (Meshkov, 1 990). The characteristics of some ferrite materials commercially produced in Russia are given in Table 20. 1 (Mesyats, 1 974). Table 20. 1.

a

(for H > 1 06 Aim)

Ferrite type

He, Aim

B,, T

1 000NN

30

0.08

0.3

0.1

2

600NN

35

0. 1 5

0.35

0. 1 1

1 00

12.5

I 07

15

B5, T

1 00NN

50

0.2

0.46

0.08

1 000NM

28

0. 1 1

0.37

0.1

p, O·m

H5, kA/m 7.5

In contrast to ferrites, ferromagnetic alloys show high saturation flux densities ( 1 .3-1 .55 T for permalloys and 1 .6-1 .8 T for amorphous alloys), low coercive forces (a few amperes per meter), high Curie temperatures (400-700°C), high coefficients of rectangularity of the hysteresis loop (0.95-0.98), and low saturation permeabilities (approaching unity in high fields). The main disadvantage of ferromagnetic alloys is their low resistivities: 0.45-0.55 J.!O-m for permalloys and 1 .2-1 .4 J.!O-m for amorphous alloys. On the one hand, this necessitates that the cores be manufactured from a thin strip (a few or some tens of micrometer thick) and insulation be provided between the turns, which makes the product more complicated and expensive and reduces the fill factor of the core. On the other hand, the low resistivity restricts the shortest possible time of magnetic

GENERA TORS IN CIRCUITS WITH MAGNETIC ELEMENTS

359

reversal, which is several hundreds of nanoseconds. For a magnetic reversal time shorter than 1 00 ns, the energy losses due to eddy currents, even if amorphous alloys are used, increase to values unacceptable in practice. In this connection, cores made of ferromagnetic alloys find use in high­ power magnetic generators with a high stored energy (from tens of joules to hundreds of kilojoules), a voltage ranging from several hundreds of kilovolts to a few megavolts, and a moderate pulse repetition rate ( 1 0-1 000 Hz). In contrast to ferrite cores, the use of ferromagnetic alloys enables one to make cores of large diameter to reduce the inductance of the switch in the saturated state. In superpower single-tum switches built in a pulse-forming line, the diameter of the core can reach 2 m. As an example of the performance of one of the most powerful magnetic switches, we give the results obtained on the Comet system (Neau et al., 1 984). The magnetic switch of this machine switches 1 3 5 kJ of energy at a voltage of 2.7 MV. The pulse power developed in a load of resistance 1 .9 Q is 3 .7 TW at a voltage pulse rise time of 25 ns. Table 20.2 lists characteristics of the most frequently used modern magnetic materials (Fish and Avery, 1 990). Table 20.2.

P

Material (25-mm strip)

Bs (T)

B, (T)

metglas 2605CO

1 .8

1 .7

3 .2

415

1 .23

3.5

metglas 2605SC

1 .6

1 .5

2.4

370

1 .35

3.1 1 .4

H0 (Nm)

Tc CC)

(!!0-m)

MJ (T)

metglas 2705M

0.7

0.7

0.8

365

1 .36

metglas 2714A

0.55

0.5

0.2

205

1 .30

1 .05

3.2% Si-Fe

1 .97

1 .4

730

0.50

3.4

50

50% Ni-Fe

1 .6

1 .5

8

480

0.45

3.1

80% Ni-Fe

0.8

0.7

2.2

460

0.55

1 .5

Ni-Zn ferrite

0.33

0.25

80

>280

1 012

0.58

Ni-Zn ferrite

0.5 1

0.12

12

>230

1 07

0.63

The main difference of amorphous alloys from permalloys is that the resistivity of the former is approximately three times higher, while the coercive force is about three times smaller. This difference affects in the main the specific energy lost for magnetic reversal. Amorphous alloys show smaller specific losses for hysteresis due to the narrow static hysteresis loop for magnetic reversal times over 3 0 J.I.S and due to the elevated resistance to eddy currents for magnetic reversal times less than 300 ns. For magnetic reversal times ranging from 0.3 to 30 J.I.S, the specific losses in permalloys and amorphous alloys are almost the same.

Chapter 20

360

2.

GENERATION OF NANOSECOND HIGH-POWER PULSES

A first generator of nanosecond high-power pulses using ferromagnetic elements with fast magnetic reversal is described by Mesyats (1 960). In this generator, sharp pulses of duration w-s s and amplitude up to 30 kV were obtained with the use of a fast nonlinear inductance coil (Fig. 20.2, a). The capacitor c� . charged through the resistor R1 and thyratron T, was discharged into the coil L. The coil inductance was proportional to the permeability of the ferromagnetic material, f.l · The typical dependence of f.l on the magnetization current I is given in Fig. 20.2, b. The permeability and, hence, the inductance peaked at a current Imax · This behavior of the inductance provided conditions for the production of a short pulse. (b)

(c) I

Figure 20.2. Production of nanosecond pulses with the help of a thyratron and a ferromagnetic coil: a circuit diagram of the generator (a), the current dependence of permeability 1.1 (b), and the production of a nanosecond pulse by discharging a capacitor (c)

If the capacitor discharge through the thyratron was periodic, two pulses were generated: negative and positive. With an aperiodic discharge (R2 � 2.JLIC) , the thyratron passed a unipolar current pulse; therefore, a short voltage pulse (Fig. 20.2, c) appeared across the inductance coil. To increase of the steepness of the pulse trailing edge, the inductance coil L was shunted by the spark gap P with the damping resistor R3• This made possible a sharp pulse of voltage up to 1 0 kV and duration 5 ns. Further development of this technique gave rise to a considerable increase in power. The output pulse power of generators now reaches several terawatts. Owing to these high powers and nanosecond pulse durations attained with magnetic generators, new applications of these systems have been brought into practice. While earlier magnetic pulse generators were used in the main in radiolocation and in automated and computer facilities, the new types of generator are mainly intended for use in physical experiments. One new field of application has arisen in connection with improved electron accelerators as an alternative to generators based on spark gaps and

GENERA TORS IN CIRCUITS WITH MAGNETIC ELEMENTS

361

thyratrons. Magnetic generators offer the possibility to produce charged­ particle beams of nanosecond duration with pulse repetition rates as high as several kilohertz (Meshkov, 1 990). Structurally, all nanosecond magnetic pulse generators are practically identical irrespective of the output power and purposes. Let us consider a magnetothyristor generator (Meshkov et a/., 1 984) as an example. Figure 20.3 presents a simplified circuit diagram of one of the four parallel­ connected and synchronously operated modules of the generator. The circuit consists of three main parts: a primary pulse generator, magnetic compression sections, and a pulse-forming device. Besides, the generator may contain additional units such as load-matching devices and pulse peakers and transformers. Among other units necessary for the operation of this type of generator are power supplies with filters, start-up systems, power supplies and decoupling elements of the bias circuits, cooling systems, etc. (a) I

I I I I I + �------------+;----�-----+--��--+---+---�

0.38 kB

l

l

______

L

______

�-------------�-------------J

R 1 .6

(b) Input I

Output

- - - - - - - - - - - - - - - - - - - - - - - - -

Figure 20. 3. Circuit diagram of a nanosecond high-power pulse generator (one of the four parallel-connected modules): 1 - primary pulse generator, 2 - energy compression sections with a transformer, 3 - pulse-forming device (a); one of the 22 parallel-connected circuits of the pulse-forming device: L 1 - 1-m long rf cable, L2 - 25-ns, 37-0 line, L3 - two parallel­ connected sections of the output rf cable (b)

The transmission line L 1 only connects the units. The capacitor C7 serves as a capacitive energy store and, together with choke Ch8 and line L2, produces a quasirectangular pulse in the load line L3 • The saturation mode for the core of Ch8 is chosen such that the current of the discharge of C7 into L2 and L3 has the waveform of the first period of the squared-sine function (so-called squared-sine waveform) of duration 1 00 ns. In the line L3 , this discharge pulse is summed up with an identical one reflected from the open end of the line L2 • If the length of L2 is chosen properly, a pulse with a flat top is generated across the load. The output pulse has a duration of 1 00 ns

362

Chapter 20

and an energy of 0.5 J, which makes 0.65 of the energy received from the power supply. At a frequency of 5 kHz, the net average output power of four modules is 1 0 kW. Energy losses take place in the sections and in the transformer. For stabilization of the temperature regime, the generator is immersed in circulating transformer oil, and the thyristors give up heat to water-cooled radiators. Other types of magnetic generator are described in the review by Meshkov ( 1 990). A breakthrough on the way of increasing of pulsed power was the use of magnetic switches with metglas (strip of amorphous magnetic material) coils. We now consider the operation of the Comet system designed at SNL (Neau et a/. , 1 984) as an example. This was a generator with two stages of magnetic compression. For the primary store, a Marx generator capable of storing 370 kJ of energy at a charge voltage of 95 kV was used. The Marx generator charged, through a gas gap switch, a coaxial water line that charged, through the first magnetic switch, the second energy storage line. This storage line was then discharged, through the second magnetic switch, into a transmission line terminated in a 1 .9-0 (copper sulfate solution) load. In the final version, 42% of the stored energy was delivered to a load, 80% were transferred through magnetic switches, and the remaining losses took place in the Marx generator and in the gas gap. Eventually, a pulse of power 3.7 TW, voltage 2.7 MV, and FWHM 3 5 ns was produced across the load. Magnetic elements can efficiently operate in pulse peaking and chopping circuits. On the nanosecond scale, it is necessary to take into account the dissipation processes involved in magnetic reversal of the magnetic element. Let us consider the transformation of a wave described by Vj (t) = V0 f(ct) , where c is a proportionality factor, with a monotonicly rising front and a flat top that propagates from an infinitely long line L 1 with wave impedance Z0 into an identical line L2, the lines being connected through a nonlinear inductance coil (Fig. 20.4) (Mesyats and Baksht, 1 965). The wave incident on the nonlinear inductance coil, V1(t), and the wave passed through the coil, V2 (t), are related as (20.5) The flux linkage 'I' is determined by the parameters of the nonlinear inductance coil: \jl = L/ + J..lo wsM(t) ,

(20.6)

where L is the inductance of the choke as t � oo , the so-called "self'­ inductance of the choke; w and s are, respectively, the number of turns and the cross-sectional area of the choke core; the magnetization of the core, M(t), is related to the magnetic field strength H =pi by Eq. (20.4).

GENERA TORS IN CIRCUITS WITH MAGNETIC ELEMENTS

363

Figure 20.4. Circuit for wave transformation in a long line with a series-connected nonlinear inductor

0

20

40

0

20

40

Figure 20.5. Refracted wave amplitude as a function of normalized time for m0 = 0.5 and various values of b (a) and for b = 1 0 and various values ofm0 (b)

The shape of the refracted wave (Fig. 20.5), constructed with (20.5) and (20.6), indicates that the time of appearance of the wave in the line L2 depends on b = j.t o M5swA.p I 2 Z0 , where A. = a'yj.t0 , and can be controlled by varying m0 = MnlMs ( Mn being the initial magnetization of ferrite). Alongside with in-series connection of a nonlinear choke, its

connection in parallel with a long line can also be used. Such a circuit can serve to differentiate a pulse (Baksht and Mesyats, 1 964) and allows one to vary the pulse duration. Hence, the most important characteristic of the circuit is the time during which the impedance of the choke will be far in excess of the wave impedance of the line.

A nonlinear inductance coil is most effective in circuits in which a prepulse with a rather tapered leading edge is generated by some additional device, such as, most frequently, a gas-discharge switch. Most widespread is the circuit, first described by Il'in and Shenderovich ( 1 965), where a nonlinear inductance coil and a uniform line are connected in series. In this circuit, the pulse produced by the primary pulse generator comes in the first line and then passes, through a ferrite element, into the second line. With a voltage of 20 kV and a primary pulse rise time of 20 ns, a proper choice of the dimensions of the ferrite ring and magnetization make it possible to produce a secondary pulse rise time of about 1 ns. Other circuits that are

364

Chapter 20

used to produce nanosecond high-power pulses with the help of nonlinear inductance coils are described elsewhere (Kerns, 1950; Wilhelm and Zwicker, 1 965; Kunze et al. , 1 966; Mesyats, 1 965; Nasibov et al. , 1 965). In the nanosecond pulse power technology, chokes with saturated cores are used not only for the correction of the pulse shape, but also in cases where, within a certain time upon application of voltage, an abrupt change in circuit impedance is required. A typical device using a nonlinear inductor is a spark gap overvolted with the help of so-called "ferrite-based decoupling". This type of device was first proposed by Kerns (Kerns, 1 950). Several versions of this type of spark gap were developed later (Wilhelm and Zwicker, 1 965; Kunze et al. , 1 966). For nanosecond circuits, the need often arises to pass pulses of only one polarity through some device. This problem can be solved with the help of a nonlinear inductor connected in series with a uniform line (Mesyats, 1965).

3.

MAGNETIC GENERATORS USING SOS DIODES

Once experimental and theoretical investigations of the SOS effect had been performed and powerful generators and accelerators using semiconductor opening switches pumped by generators with spark gaps had been developed, it became obvious that qualitatively new nanosecond pulse power devices must use an all-solid-state power switching system with magnetic switches. The circuit ideology of this approach is illustrated by the block diagram shown in Fig. 20.6. The thyristor charging device (TCD) executes dosed energy takeoff from the supply line. From the TCD, the energy comes in a magnetic compressor (MC) at a voltage of 1-2 kV within 1 0- 1 00 J!S. The MC compresses the energy within about 300-600 ns and increases the voltage to hundreds of kilovolts. The SOS appears as a final power amplifier, shortening the pulse duration to 1 0- 1 00 ns and increasing the voltage 2-3 times. The TCD contains a primary capacitive energy store, a thyristor switch, and charging and energy recuperation circuits and operates in the single­ pulse mode, such that a unit portion of energy is taken from the supply line which is necessary to produce a single pulse at the output of the entire system. The criterion for choosing the pulse duration for the energy transfer from TCD to MC is self-contradictory. On the one hand, to simplify the MC, in particular, to reduce the volume of the cores and the number of energy compression stages, it is necessary to shorten the duration of the pulses formed in the TCD. On the other hand, to reduce the time of energy extraction from the TCD to several microseconds calls for a great number of simultaneously operating fast thyristors, complicating the system of primary

365

GENERATORS IN CIRCUITS WITH MAGNETIC ELEMENTS

energy switching and making it less reliable. In this connection, the optimum time of energy extraction from TCD ranges from 1 0 to 1 00 J.!S for the pulse energy ranging from a few joules to hundreds ofjoules. 1-2 kB 1 0-100 JlS

1 00-400 kB 300-600 ns

200-1 000 kB 1 0 - 1 00 ns

!-!.___ !-!._SO-__ S !-! --' .___

'--TC ----- 0 -'

M---C -'

Wad -----'

Figure 20. 6. Block diagram of a generator with an all-solid-state energy switching system

The pulse parameters at the output of the MC are determined by the operating conditions of the semiconductor opening switch and by the pulse parameters to be obtained at the load. The pulse amplitude at the MC output is determined as VMc = "VJoadiKov, where Kov is the overvoltage factor at the instant the current is interrupted by the opening switch and "VJoad is the desired amplitude of the pulse across the load. The time of energy extraction from the MC determines the duration of the forward triggering of the opening switch: fMc = t+ . The use of the magnetic energy compression section was dictated by the need to match the parameters of the TDC output pulse to the parameters of the pulse that pumps the opening switch. To obtain nanosecond pulses of amplitude about 1 MV at the output of the system as a whole, the magnetic compressor should form pulses of duration several hundreds of nanoseconds with a peak voltage of several hundreds of kilovolts. Thus, with an input pulse of amplitude 1-2 kV and duration 1 0- 1 00 J.!S, the MC should ensure about 1 00-fold energy compression in time and an increase in voltage by a factor of 1 00-400. Figure 20.7 presents a circuit diagram of the magnetic compressor proposed by Rukin ( 1 997) in which energy compression in time is realized with a simultaneous increase in output voltage. The principal difference of this compressor circuit from conventional ones is that the capacitive energy store of each energy compression section has a middle point or it is composed of two series-connected capacitors of the same capacitance. In this case, the output of each previous energy compression section is connected to the central point of the capacitor of the next section, and the bottom capacitors of each section are shunted by magnetic switches. Upon energy compression, the voltage across each section doubles. The output voltage of the MC, without regard of active energy losses, is 2n times greater than the input voltage (n being the number of capacitor sections).

366

Chapter 20 Voutput = 2n li'input

TCD

V= 2

'\ _

MC

Figure 20. 7. Circuit diagram of a magnetic compressor doubling the voltage across each section

Such an MC does not require additional circuits for magnetic reversal of the magnetic switch cores, since in this type of circuit this process occurs automatically because of different directions of the charging and discharge currents in each switch (in Fig. 20.7, the charging and discharge currents are shown by dotted and solid arrows, respectively). One more distinctive feature of the circuit is that in each capacitor section there occurs a double compression of energy due to the recharging of the bottom capacitors. Therefore, to compress an energy in time by two orders of magnitude, it suffices to have two sections with a compression factor Kc 3-4 provided by each magnetic switch. Another important problem concerned with the energy transfer from an MC to a semiconductor opening switch is associated with the circuit embodying double-loop triggering of the opening switch in the mode of amplification of the reverse current. This solution was proposed independently by Kotov et al. ( 1 993) and Grekhov et al. ( 1 994). The matching circuit is given in Fig. 20.8. Between the magnetic compressor output and the opening switch, a reverse triggering capacitor Crev and a reverse triggering magnetic switch (or a pulse transformer) are connected. After saturation of the forward triggering switch MS+, which is the output switch of the magnetic compressor, energy is transferred from the last section of the compressor to the capacitor. In this case, the current r charging the capacitor Crev is simultaneously the forward triggering current for the SOS (Fig. 20.9). The increasing voltage across Crev executes the magnetic reversal of the switch Ms-. After the operation of this switch, the reverse current 1- , which is several times greater than r , is passed into the opening switch, and the energy from Crev is switched into the inductance of the reverse triggering circuit (the inductance of the winding of the saturated switch Ms- or an additional inductance). As the current is interrupted by the opening switch, energy is transferred to the load in a nanosecond pulse. -

GENERATORS IN CIRCUITS WITH MAGNETIC ELEMENTS

367

sos

Figure 20.8. Circuit matching the MC and the SOS

Isos

k r ---...

" "·

Vc�lLi\T-'

•

t

Figure 20.9. Waveforms of the currents and voltages in the MC-to-SOS matching circuit

The above circuit concept was verified by developing and testing a series of setups with an all-solid-state switching system. Ruk:in et al. ( 1 995) describe a desktop small-sized generator intended for investigations of streamer coronas in air. The generator operates at an output voltage of 200 kV, a current of 1 kA, a pulse duration of 40-50 ns, and a pulse repetition rate of 30-50 Hz in continuous operation. In the mode of bursts of duration 1 min, the pulse repetition rate is 300 Hz. The housing dimensions are 650 x 600 x 320 mm and the generator mass is �80 kg. The Sibir system (Fig. 20. 1 0) was developed (Kotov et al. , 1 995) to elucidate the possibility of creating generators capable of producing megavolt voltages with an average power of several tens of kilowatts. Its output parameters are as follows: pulsed voltage 1 MV, current 8 kA, pulse duration 60- 1 00 ns, and pulse repetition rate 1 50 Hz. The input power is 1 07 kW, the power delivered to the opening switch is 75 kW, and the design

Chapter 20

368

value of the output power is -50 kW. The generator consists of three units: a thyristor charging device (TCD), an intermediate magnetic compressor (IMC), and a high-voltage unit (HVU) placed in a tank with transformer oil. The dimensions of the high-voltage unit are 3. 7 x 1 .4 x 1 .2 m and its mass is about 7 t. air

IMC

air

TCD

c,

oil

-��

Figure 20. 1 0. Circuit diagram of the Sibir generator

One of the main inferences from the results of experiments on the Sibir system was that the SOS effect in the phase of current interruption is characterized by automatic uniform distribution of voltage over series­ connected diodes (structures). This enables one to create megavolt opening switches by merely connecting in series a number of diodes without use of external voltage dividers. Based on SOS diodes, a series of small-sized generators repetitively operating on the nanosecond scale have been developed which are intended for experimentation in various fields of electrophysics. At the same time, these systems are used for testing SOS diodes, allowing one to obtain data on the characteristics and reliability of these devices under various operating conditions. The circuits of these generators embody the above principle according to which the energy necessary for the production of a pulse is initially stored in a TCD and then is compressed in time with the help of an MC. An opening switch based on SOS diodes executes the function of a final power amplifier, producing a nanosecond pulse at the output of the generator. Structurally, the generator elements inside the housing are separated into two main parts. In

GENERA TORS IN CIRCUITS WITH MA GNETIC ELEMENTS

369

the air part, the low-voltage elements of the TCD, the primary energy store, and the monitoring, alarm, diagnostics, and control circuits are placed. The high-voltage elements of the magnetic compressor and the SOS diodes are located in a tank with transformer oil, which is also disposed inside the housing. The front panel of the housing has a cut for a bushing insulator through which high voltage is led out. The TCD is cooled either with fans or with running water. The MC elements and the SOS diodes give up their heat to oil. To remove heat from the tank, running water is used. The absence of gas-discharge switches in these generators lifts the essential limitation on the pulse repetition rate. In continuous operation, the pulse repetition rate is limited by the heat loads on the elements of the generator, first of all, on the magnetic switch cores. When the generator operates in the burst mode, it is limited by the repetitive operation capabilities of the TCD, i.e., by the recovery time of the thyristors and by the charging time of the primary energy store. The burst mode, in which the generator operates during a time from some tens of seconds to about several minutes with the pulse repetition rate and output power being several times greater than their rated values, is important both for some technological applications and for the improvement and modeling of new technologies under laboratory conditions. Therefore, in developing these generators, in order that their repetitive operation capabilities be realized more completely, the TCD was designed proceeding from the requirement of the least time of energy storage, and the choice of the generator elements was based, among other things, on the results of the calculation of their adiabatic heating in the burst mode. These generators, when operated in the mode of a burst of duration from 30 to 60 s, allow a 5-1 0-fold increase in pulse repetition rate and output power against their rated values. Two megavolt SOS generators of the S-5N series have been developed and built at IEP (Mesyats et a/. , 2000). The generator circuit (Fig. 20. 1 1 ) includes an input thyristor charging device and a preliminary energy compression stage, which are located in the air part of the housing. The elements of the high-voltage pulse former are placed in a tank filled with transformer oil. After preliminary compression, the energy is transferred through the pulse transformer PT2 into the intermediate energy store C3 , which is charged to 1 34 kV within 1 8 �s. After inversion of the voltage across the bottom capacitor, the voltage at point 3 increases to 250 kV within 3 �s. As the core of the switch MS+ is saturated, energy is transferred to the triggering capacitor C through the transformer PT3 • As this takes place, the 4 semiconductor opening switch, SOS, is pumped by the forward current and the capacitor is charged to 400 kV within about 0.5 �s. The saturation of the core of the switch of the transformer PT3 initiates the process of reverse triggering of the opening switch during which energy is transferred from the

370

Chapter 20

triggering capacitor, as it discharges, to the intermediate inductive energy store L-. The reverse triggering current, depending on the inductance of the store L- increases to 3-6 kA within about 1 00 ns. As this occurs, the current is interrupted by the opening switch within about 1 0 ns and the inductive energy store is connected to the external load where an output pulse of amplitude up to 1 MV and duration about 50 ns is generated. Table 20.3 gives the parameters of the process of energy compression in the elements of the generator. Table 20.3. Voltage

Time

I I kV

1 30 flS

2

1 34 kV

1 8 flS

3

252 kV

3 flS

4

405 kV

0.47 flS

5

0.5- 1 MV*

40-60 ns*

Point number

* depending on the load parameters.

Rtoad CD

Figure 20. 1 1. Circuit diagram of the S-5N generator

(b)

t

Figure 20. 12. Waveforms of the reverse current (a) and voltage (b) of the semiconductor opening switch of the S-5N generator (time base scale: 20 ns/div)

GENERATORS IN CIRCUITS WITH MAGNETIC ELEMENTS

37 1

Figure 20. 1 2 presents the pulse waveforms that demonstrate the capabilities of the semiconductor opening switch. The peak reverse current through the opening switch was obtained in the mode with the store L- short­ circuited. The current amplitude prior to interruption was 7 kA and the interruption time was 8 ns. The peak voltage across the opening switch, obtained for L- = 6 !-!H and external load resistance R1oad = 1 . 1 kn was 1 . 1 MV with the pulse FWHM equal to about 50 ns. The situation in this field drastically changed once the phenomenon of subnanosecond interruption of current in high-power SOS diodes had been detected (Lyubutin et a/. , 1 998). The experimental and theoretical investigations of this phenomenon have shown that a SOS diode, being in essence a plasma-filled diode, has the property, inherent in other plasma opening switches, that the current interruption characteristic improves as the di/dt of the trigger current for the opening switch is increased. As the triggering time was decreased from 300-600 ns to 35-50 ns for the forward current and from 80-1 00 ns to 1 0-1 5 ns for the reverse current, the current interruption time decreased from 5-1 0 ns to 500-700 ps.

REFERENCES Baksht, R. B. and Mesyats, G. A., 1 964, Ferrite-Containing Circuit for the Production of Nanosecond High-Voltage Pulses, Prib. Tekh. Eksp. 3 : 1 08-1 1 0. Fish, G. and Avery, K., 1 990, Magnetic Materials Group; Working Group Report. In Proc. of Int. Magnetic Pulse Compression Workshop, California, Vol. 2, pp. 1 58-1 70. Grekhov, I. V., Efimov, V. M., Kardo-Sysoev, A. F., and Korotkov, S. V., 1 994, RF Patent No. 2 009 6 1 1 . Gyorgy, E . M., 1957, Rotational Model of Flux Reversal in Square Loop Ferrites, J. Appl. Phys. 28: 1 0 1 1 - 1 0 1 5 . Il'in, 0 . G . and Shenderovich, A. M., 1 965, Shortening o f the Rise Time o f High-Voltage Pulses with the Help of a Nonlinear Inductor, Prib. Tekh. Eksp. 1 : 1 1 2- 1 1 7. Kerns, 0. A., 1 950, U.S. Patent No. I 035 843. Kotov, Yu. A., Mesyats, G. A., Rukin, S. N., Filatov, A. L., and Lyubutin, S. K., 1 993, A Novel Nanosecond Semiconductor Opening Switch for Megavolt Repetitive Pulsed Power Technology: Experiment and Applications. In Proc. IXth IEEE Intern. Pulsed Power Conj, Albuquerque, NM, Vol. I, pp. 134-1 39. Kotov, Yu. A., Mesyats, G. A., Rukin, S. N., Tel'nov, V. A., Slovikovsky, B. G., Timoshenkov, S. P., and Bushlyakov, A. I., 1 995, Megavolt Nanosecond 50 kW Average Power All-Solid-State Driver for Commercial Applications. In Ibid., Vol. 2, pp. 1227- 1 230. Kunze, R. C., Mark, E., and Wilder, H., 1 966, Ferrit Decoupled Crowbar Spark Gap. In Proc. IVth Symp. on Eng. Problems in Thermonuclear Research, Institut fiir Plasmaphysik, Miinchen. Landau, L. D. and Lifshits, E. M., 1 959, Electrodynamics of Continuous Media (in Russian). Fizmatgiz, Moscow.

372

Chapter 20

Lyubutin, S. K., Mesyats, G. A., Rukin, S. N., and Slovikovsky, B. G., 1 998, Subnanosecond Current Interruption in High-Power SOS Diodes, Dokl. AN RAS. 360:477-479. Meerovich, L. A., Vagin, I. M., Zaitsev, E. F., and Kandykin, V. M., 1 968, Magnetic Pulse Generators (in Russian). Sov. Radio, Moscow. Melville, W. S., 1 95 1 , The Use of Saturable Reactors as Discharge Devices for Pulse Generators, Proc. lEE. 98, No. 53. Meshkov, A. N., 1 990, Nanosecond High-Power Pulse Magnetic Generators, Prib. Tekh. Eksp. 1 :24-36. Meshkov, A. N., Shishko, V. I., and Eremin, S. N., 1984, Nanosecond High-Power Pulse Generator, Ibid. 2 : 1 03-105. Mesyats, G. A., 1 960, Production of Short-Rise-Time High-Voltage Pulses. In High- Voltage Test Equipment and Measurements (in Russian, A. A. Vorob'ev, ed.), Gosenergoizdat, Moscow-Leningrad, pp. 379-393. Mesyats, G. A., 1 965, Ferrite Choke for Short High-Power Videopulses, Zh. Tekh. Fiz. 35: 1 685-1 689. Mesyats, G. A., 1 974, Generation of High-Power Nanosecond Pulses (in Russian). Sov. Radio, Moscow. Mesyats, G. A. and Baksht, R. B., 1 965, Deformation of Strong Waves Passing through a Ferrite Irregularity in a Line, Zh. Tekh. Fiz. 25:889-895. Mesyats, G. A., Ponomarev, A. V., Rukin, S. N., Slovikovsky, B. G., Timoshenkov, S. P., and Bushlyakov, A. I., 2000, MV, 500 Hz All-Solid-State Nanosecond Driver for Streamer Corona Discharge Technologies. In Proc. Xll/th Intern. IEEE Conf on High Power Particle Beams, Nagaona, Japan, pp. 1 92-195. Nasibov, A. S., Lomakin, V. P., and Bagramov, B. G., 1965, Generator of Short High-Voltage Pulses, Prib. Tekh. Eksp. 5:1 33-1 36. Neau, E. L., Woolston, T. L., and Penn, K. J., 1 984, "Comet-H", A Two-Stage, Magnetically Switched Pulsed-Power Module. In Proc. XV/th Power Modulator Symposium, New York, pp. 292-294. Pavlov, V. I. and Sirota, N. N., 1964, Evolution of the Process of Pulsed Magnetic Reversal of a Ferrite with a Rectangular Hysteresis Loop, Fiz. Tverdogo Tela. 6 : 1 267-1270. Rukin, S. N., 1 997, Device for Magnetic Compression of Pulses (in Russian). RF Patent No. 2 089 042. Rukin, S. N., Lyubutin, S. K., Kostirev, V. V., and Telnov, V. A., 1 995, Repetitive 200 kV Nanosecond All-Solid-State Pulser with a SOS. In Proc. Xth Intern. IEEE Pulsed Power Conf, Albuquerque, NM, Vol. 2, pp. 1 2 1 1 - 1 2 1 4. Steinbei�, E. and Vogler, G., 1 968, Uber eine Abschatzung der minimalen Schaltzeit der Rechterckferrite, Ann. Phys. 20:370-385. Wilhelm, R. and Zwicker, H., 1 965, Uber eine einfache Kurzschlu� - Funkenstrecke fiir sto�stromanordnungen, Z. fiir angew. Physik. 19:428-43 1 .

I

Chapter 2 1 LONG LINES WITH NONLINEAR PARAMETERS

1.

INTRODUCTION

In studying electromagnetic waves propagating in lines, the telegraph equations are known to be used. These equations are derived by simplifying Maxwell's equations. In the general form, they are linear with respect to the physical quantities involved, namely, the fields, the inductions, and the conduction current, and the space in which the wave propagates is of no concern. When seeking solutions to Maxwell's equations, it is necessary to define concretely the properties of this space. From the variety of the space properties, its geometry and the relation of the inductions and conduction current to the fields, which characterizes the medium occupying the space, are usually specified. If the space is boundless, the source generating the wave is pinpointed. In a limited space not containing wave sources, the type of "incident" waves that arrive from the outside at the space boundary and the properties of the neighboring space are specified. In both cases, it is necessary to know the medium state and the fields in the medium prior to the action of the wave. It is well known that a medium occupying a space can be characterized by permeability and conductivity. These parameters are factors of proportionality in the linear equations relating the inductions and the conduction current to the fields. The coupling equations can be written in functional form for the case of not too quickly varying fields. If the fields are rapidly varying, the conduction current and the inductions vary with some delay. This delay can be characterized by the time interval during which the medium comes to equilibrium after a stepwise change of the fields.

374

Chapter 21

Propagation of waves was usually considered in media whose parameters could be considered constants. As a result, a theory of electromagnetism was created which is based on linear equations. Obviously, if any of the above quantities is a function of the strength of even one field of the wave, the system of Maxwell's equations becomes nonlinear. Many interesting phenomena can be considered only within the framework of the theory based on the nonlinear equations. Electromagnetic shock waves are among these phenomena. Interest in these electrodynamic phenomena aroused in connection with the wide use of ferrites and ferroelectrics. The relation between inductions and fields in these media is nonlinear even if the fields vary only slightly. In some cases, the conduction current varies nonlinearly with electric field. These circumstances called for more general assumptions concerning the medium in which an electromagnetic wave propagates, such as the dependence of the permeability and conductivity of the medium on the fields of the wave. The profile of an electromagnetic wave propagating in a transmission line filled with a nonlinear medium has discontinuities, testifying that there occur electromagnetic shock waves (Kataev, 1 963) similar to gas-dynamical and hydrodynamic shock waves. Mathematically, this implies that even if the solutions of Maxwell's equations for a nonlinear medium are smooth functions in some range of independent variables, they cannot be extended without breaks to other ranges where the equations remain regular. Obviously, for these conditions, the wave superposition principle will not work. These two circumstances make an analysis in nonlinear electrodynamics specific and difficult. Kataev ( 1 963) considered a plane electromagnetic wave propagating in a medium with nonlinear permeability and permittivity. He obtained solitary waves and proved theoretically and experimentally the existence of electromagnetic shock waves (ESW's) in lines containing ferrites and ferroelectrics. In the experimental study, the problem was to find a more perfect, technically acceptable means for the production of large dlldt and short current pulses. The very first tests demonstrated that electromagnetic shock waves are promising for meeting this goal: leading edges of duration 1 o-9 s and shorter were obtained at pulsed currents of some tens and hundreds of amperes. The physics of this technical innovation (Kataev, 1 958) that involved a number of new electrodynamic effects was of considerable interest. Gaponov and Freidman (1 959) established the relation between the jumps of fields and inductions at a discontinuity or the boundary conditions at a discontinuity. Subsequently, solitary and electromagnetic shock waves in some particular types of transmission lines were investigated by Greenberg and Treve ( 1 960).

LONG LINES WITH NONLINEAR PARAMETERS

375

Two mechanisms of the occurrence of shock waves can be distinguished. The first one is based on the drag of the wave vertex caused by the fact that its velocity is greater than the base velocity, resulting from the nonlinear permeability or permittivity of the medium or from the nonlinear running parameters L and C of the line. The second mechanism is associated with the dissipation of the wave front energy due to the energy losses by the magnetic viscosity or nonlinear conductivity of the medium.

FORMATION OF ELECTROMAGNETIC SHOCK

2.

WAVES DUE TO INDUCTION DRAG

We first consider the formation of an ESW at a rather low rate of variation of the field. For an unbounded nonlinear nonconducting medium, the propagation of plane homogeneous linearly polarized electromagnetic waves, E = Ex (z, t) , H = Hy (z, t) , is described by Maxwell's equations which, in this case, are reduced to two first-order partial differential equations (Gaponov and Freidman, 1 959):

aH az

1

aD at

-=- - -, c

D = c.E ,

aE aB , B = B(H) . = - -1 az c at

(2 1 . 1 )

Here, we take the case of a space filled with ferrite where the relation between the D and E vectors of the electric field is assumed linear, while the relation between the B and H vectors of the magnetic field is considered nonlinear. For rather slow, quasistatic processes, the induction B at any point of space is uniquely determined by the field H at this point at the same point in time. For a bounded space, such as a transmission line of small cross section, the equations can be written as two first-order equations (telegraph equations) (Gaponov and Freidman, 1 959, 1 960):

av az

a at

-=- -

(2 1 .2)

Here, V(z, t) is the voltage between the wires of a two-wire line in the cross section z; I(z, t) is the current in one of the wires in the same cross section; Q is the charge per unit length of the line, and is the magnetic flux per unit length of the line. For rather slow processes, the flux is considered only a function of current:

376

Chapter 21

= (J ) .

(2 1 .3)

The charge Q is linearly related to the voltage:

Q = CV .

(2 1 .4)

Here, C is the capacitance per unit length of the line. Equations (2 1 .2) are applicable to nonuniform and artificial lines if the quantities involved are replaced by their average values on condition that the time and space scales of J(z, t) and V(z, t) are much greater than the respective scales of an individual unit of the line. The nonlinear equations (2 1 .2)-(2 1 .4) have not been solved for the general case. However, their particular solutions are known for the case of so-called solitary waves where one of the sought-for quantities is a one­ valued function of another. Assuming that V = V(I) , we find (2 1 .5) Then Eqs. (2 1 .2) have solutions that can be written as (Morugin and Glebovich, 1 964):

z = ±v(I)t + F(I) ,

(2 1 .6)

(2 1 .7) where F and F1 are functions to be determined from boundary and initial conditions, L(I) = d/dl is the inductance per unit length of the line, and v is the velocity of the wave propagating in the line. Solution (2 1 .6) describes a running (solitary) wave. For a solitary wave, the velocity of each point of its front depends on the current at this point. If the inductance L(I) of the line is a monotonicly decreasing function of the current magnitude, the points of the front where the current is higher will propagate with greater velocities. Hence, if a pulse is transferred, the steepness of its front increases as it propagates along the line, and the trailing edge of the pulse becomes more tilted (Fig. 2 1 . 1 ) Solution (2 1 . 7) admits that at some points in time some points at the wave front will "overtake" points with lower values of current. Solution (2 1 .7) thus becomes ambiguous (at t = t3 in Fig. 2 1 . 1 ), implying that the solution is discontinuous, and, in the case under consideration, the discontinuity has formed at the front of the wave. .

LONG LINES WITH NONLINEAR PARAMETERS

377

I

z

Figure 21. 1. Distortion of a pulse propagating through a line

Once a discontinuity has formed, the wave ceases to be solitary: an electromagnetic shock wave occurs. The position and time of the discontinuity are determined from solutions (2 1 .6) and (2 1 . 7). The time at which a discontinuity appears, t * , and the coordinates of the point of its appearance are determined by the equations

(az) ai

t*

_ -

(:;n, . z

0'

= 0.

(2 1 .8)

where (I , t) is given by (2 1 .6). If L(l) is a nonmonotonic function, i.e., if the permeability of the ferrite, J.t(H), is a nonmonotonic (one-valued or ambiguous) function, the velocity of propagation of various points of the pulse depends on the ferrite state at previous moments of time. In other words, the pulse waveform during its passage through the line will substantially depend on the choice of the initial working point on the magnetization curve (Fig. 2 1 .2) (Morugin and Glebovich, 1 964). In Fig. 2 1 .2, the hysteresis loop is displaced to the right since the origin of coordinates is displaced by the magnitude of the constant bias field. If the amplitude of the pulse is so significant that the field H becomes stronger than Ht . shock waves can arise at both the leading and the trailing edge of the original pulse. Actually, the steepness of the leading edge of the pulse, according to (2 1 .6) and (2 1 .7), increases for those its segments where dJ.!IdH < 0 for the ferrite, while the steepness of its trailing edge increases for dJ.!IdH > 0 . Hence, at the leading edge, the points at which the current is higher will move with a greater velocity, while at the trailing edge, on the contrary, the points with a smaller current will move more rapidly. Thus, if we choose for the ferrite, by biasing it continuously, such a mode in which the permeability has a maximum at some magnetic field strength, we shall obtain a wave with an abrupt front and an abrupt trailing edge (Fig. 2 1 .3).

378

Chapter 21

Figure 21.2. Dependences B(H) and �(H) for ferrite

z

Figure 21.3. Distortion of a pulse propagating through a line

However, it should be borne in mind that the phenomenon under consideration takes place until the dependence B(H) remains quasistatic, which is typical of the microsecond range of pulse rise and fall times, i.e., until the rate of variation of the magnetic field H at the front (tail) of the wave becomes over 1 07-1 08 Oe/s (Morugin and Glebovich, 1 964).

3.

THE DISSIPATIVE MECHANISM OF THE FORMATION OF ELECTROMAGNETIC SHOCK WAVES

If the magnetic field rise rate during the formation of a wave front is high (over 1 08-1 09 Oe/s ), the quasistatic dependence B(H) is broken and the necessity arises to take into account the dynamic process in the magnetic reversal of the ferrite. The magnetic viscosity of the ferrite resulting in energy losses at the wave front (Kataev, 1 963; Gaponov and Freidman, 1 960) becomes important. Therefore, if the magnetic field rapidly varies, one can speak of the dissipative mechanism of the formation of electromagnetic shock waves.

LONG LINES WITH NONLINEAR PARAMETERS

379

Some energy dissipation at the wave front also takes place during the formation of a shock wave by the drag mechanism when the front steepness appreciably increases. However, the energy dissipation is not a dominant phenomenon in this case, while it becomes essential at high rates of variation of the magnetic field. In this case, the fast magnetic reversal of the ferrite should be taken into account. For transmission lines with toroidal or cylindrical ferrite cores, the magnetic reversal of the ferrite at high rates of field variation is described by the model of nonuniform precession (Ostrovsky, 1 963 ). In this case, the relation between magnetization and magnetic field strength is described by formula (20.4). It should be noted that the initial magnetization of the ferrite is important in the formation of the front of a shock wave. By varying the magnitude and sign of the magnetization field, it is possible to influence the formation of a shock wave, in particular, to vary the width of its front. The physical pattern of the formation of waves is simple to explain graphically. As a wave with a plane front (Fig. 2 1 .4, a) is incident on a ferrite-containing line, there occurs energy dissipation at the wave front due to the energy losses by the magnetic reversal of the ferrite. As a result, early in the propagation of the wave through the line, a steep segment appears in the base of its front - a shock front. If the width of the front at which there occurs magnetic reversal is small compared to the width of the leading edge of the original pulse (Fig. 2 1 .4, b), this segment can be treated as a "discontinuity" in front of which the current is zero, and downstream of this segment the ferrite is completely saturated. The segment of the profile of the original wave upstream of the shock front is lost, and some part of its energy goes into magnetic reversal, while the rest is reflected from the region of the discontinuity. As the wave proceeds propagating, the amplitude of the shock front increases (Fig. 2 1 .4, c) until it reaches a maximum some distance from the beginning of the ferrite-containing line. As this takes place, the "discontinuity" stops developing, and the shape of the wave front further propagating through the nonlinear line remains unchanged. Such a wave is referred to as a stationary shock wave. After the formation of a stationary shock wave, the energy of the plane portion of the wave is spent for magnetic reversal of the ferrite ahead of the wave front. The current of the shock wave is the difference between the currents of the incident and reflected waves. When the front of the transformed wave passes from the ferrite-containing line into the linear line, the reflection from the front stops because of no magnetic reversal of the ferrite at the front. Under certain conditions, an incident wave with an abrupt front completely (except the lost forward segment) passes into the linear line, while the reflected wave is absorbed by the primary pulse generator.

Chapter 21

380 (a)

I I I I

I Io

: z=O

tn · Vo

I I

(b)

1I z = / z I I

i :b,�j ['{. � I I I

Vo (c) ;

Vo l

I

..

z

..

z

Figure 21.4. Formation of a short-rise-time pulse: v0 and /0 are the velocity and current of the incident wave; vsh is the velocity of the shock wave; In is the rise time of the original pulse, and I is the length of the shock-wave line

The theory of electromagnetic shock waves is presented in detail by Kataev ( 1 963). We shall dwell only on some inferences from this theory that are necessary for practical calculations. To describe the processes in transmission lines with nonlinear parameters, Belyantsev et al. ( 1 965) used the telegraph equations for a uniform line combined with Eq. (20.4) to take into account the dissipative properties of ferrites. They found the width of the front of a stationary shock wave in a ferrite-containing transmission line:

I

(2 1 .9)

where m0 = Min Ms with Un being the initial magnetization of ferrite. The quantities Hrev. y, and a are described in Section 1 of Chapter 20. The plot of the function f(m0 ) is given in Fig. 2 1 .5. When analyzing the propagation of a stationary wave through a line, one may introduce the notions of the effective magnetic permeability of a ferrite for a shock front: 110 + mo ) Ms f.lsh = 1 + --'-'--=-'---=pfsh -

(2 1 . 1 0)

and the resistance of a line to a stationary shock wave:

Vsh = Zo r.Zsh = v f.lsh , Ish

(2 1 . 1 1 )

LONG LINES WITH NONLINEAR PARAMETERS Z0 = (Lo!C0Y12 ; L0 C0

381

and are the line inductance and capacitance per where unit length, 11 is the filling factor dependent on the geometry of the line and ferrite cross section, and p is a factor dependent on the configuration of the transmission line. Expression (2 1 . 1 0) derived for a distributed-constant line is valid for a lumped-constant line only in the event that it is possible to neglect the dispersion associated with the step-type behavior of the line parameters,

T = .JLoCo

(2 1 . 1 2)

« fr z . 14 12 10 8

\

""'

......, 6

......

....1"--. .. ..

r--t---

........_

4 2 -1.0

-0.6

-0.2 0 0.2 mo

0.6

1 .0

Figure 21.5. Plot of the functionj{m0)

In actual nonlinear lines with lumped parameters, the width of the front of a stationary shock wave coincides with the time constant of a unit for a shock wave (Mesyats, 1 974): (2 1 . 1 3) Ostrovsky ( 1 963) found the distance within which the amplitude of a discontinuity reaches a maximum, i.e., that distance which should be covered by the wave in a nonlinear line up to the moment of the formation of a stationary shock wave. For a lumped-constant line, the optimum number of units in the line is given by

/0

pi no =-tTn TJMs O-m o)

(2 1 . 1 4)

Any nanosecond high-power pulse generator based on ferrite-containing lines is a wave system whose one part consists of uniform segments of ferrite-containing lines, while the other is composed of linear tran�inission

Chapter 21

382

lines. In this case, the matching of the system elements is necessary to provide the most efficient power delivery to the load and to produce pulses of desired shape. If the line has a matched load, the condition for the formation of pulses of regular shape and for complete delivery of power to the load is the equality of the output impedance of the ferrite-containing line, Z0 , with the ferrite completely saturated and the direction of the magnetization vector invariable, to the load impedance (Kataev et al. , 1 968):

Rtoad

=

Zo

=

� vc;;

·

(2 1 . 1 5)

If the original pulse comes into the ferrite-containing line through a linear line with wave impedance Z0 1 , in order that the power delivery be complete, it is necessary to match the impedance Z0 1 to the resistance of the nonlinear line to a shock wave:

(21 . 16) Obviously, the ferrite-containing line should be so long that the leading edge of the original pulse passed through this line would be eliminated and the width of the pulse top remained unchanged. In this case, to transfer a videopulse without distortions (except for the leading edge), it is necessary to satisfy the following condition for the width of the primary pulse top ftop (Kataev et al. , 1 968):

21

ftop = - '

Vo

(2 1 . 1 7)

where l is the length of the ferrite-containing line and v0 is the velocity of the wave propagating through the line with the ferrite saturated. An ESW can also be generated if a line has a nonlinear conductivity. Actually, if the conductivity decreases with increasing voltage, more energy will be absorbed at the wave front than near the top. Therefore, some portion of the wave front will be "corroded". A typical example of such a line is a line where the magnetron effect takes place. Let us consider a vacuum coaxial line in which the inner conductor (cathode) is heated up and thermionic emission from its surface takes place. Assume that an electromagnetic wave propagates through this line. The electric field of the wave accelerates electrons in the radial direction. The magnetic field of the current passing through the inner conductor "twists" the electron trajectories around the magnetic force lines. At some relation between current and voltage, electrons cease to get on the outer conductor

LONG LINES WITH NONLINEAR PARAMETERS

383

and return back to the inner conductor by the magnetic field. Hence, while the electric and magnetic fields of the wave are low in magnitude (at the beginning of the front), electrons come from one conductor to another, i.e., there is high conductivity between the conductors, resulting in a leakage current. As these fields of the wave increase (at the end of front), electrons start "twisting" and, finally, come back to the inner electrode. Kataev ( 1 963), who foretold this effect, termed it the "magnetron" effect. We already considered this effect when describing vacuum lines with magnetic self­ insulation, operating in the mode of explosive electron emission (see Chapter 8).

4.

DESIGNS OF LINES WITH ELECTROMAGNETIC SHOCK WAVES

The maximum rise rate of current or voltage pulses, if they are formed by the method of shock waves, is limited by the dispersive properties of the ferrite and by the dispersion in the ferrite-containing transmission line. Due to the dispersive properties of a ferrite-containing coaxial transmission line, this type of line is used as the basic element in the production of extremely short high-power pulses. In Fig. 2 1 .6, a schematic diagram of the coaxial line used in a nanosecond pulse generator (Meshkov, 1 965) is given. On the central conductor I, ferrite rings 2 are closely put. Atop of the rings, fluoroplastic tape is wound to form insulation 3, and the outer conductor 4 is put on the insulation. If the central conductor is at high potential, in order to prevent the air in the gaps from being ionized, all the system is placed in a tube filled with oil. The design procedure for lines with ESW's is proposed by Belyantsev and Bogatyrev ( 1 965).

Figure 21. 6. Coaxial line with ferrite

Chapter 21

384

An artificial ferrite-containing long line can be represented by a chain of units (Fig. 2 1 . 7). The use of artificial long lines is limited in the main by the spatial dispersion resulting from the step-type character of the line units because of which it is impossible to obtain a pulse rise time shorter than the time constant of a line unit. However, with the help of an artificial pulse-forming line, it is possible to substantially reduce the dimensions of the pulse generator in the event that the rise time of the original pulse calls for a too long coaxial line. In this case, it is expedient to shorten the leading edge of the pulse with the help of an artificial long line. Besides, the initial magnetization is much simpler to control in an artificial line, which is especially important for smooth control of the pulse duration in a generator with two pulse-forming lines (Meshkov, 1 965). In designing artificial long lines, special attention should be given to the oscillations at the wave top, resulting from the step-type character of the line. To suppress these oscillations, it is necessary to shunt the inductances of the last units of the line by resistors of resistance Ro = (2 -3)Z0 . Besides, the oscillations at the flat top of a wave propagating through an artificial line may be induced by the fluctuations developing in the line units in the case where the duration of the wave front formed by the line is close to the time constant of a unit, T. Practically, the duration of the wave front is limited to frz = (1 .5 - 2.5)T.

Figure 21. 7. Artificial line with ferrite: 1 capacitor of a unit, and 3 line base

-

inductance coil on a toroidal ferrite core; 2

-

-

Electromagnetic shock waves can be generated not only in ferrite­ containing lines, but also in lines with ferroelectrics and semiconductors. With ferrite-containing pulse-forming lines, it is possible to produce voltage pulses of short rise time and significant amplitude across a low-resistance load. It is possible to obtain voltage pulses with large dV/dt across a high­ resistance load with the help of electromagnetic shock waves generated in lines with ferroelectrics. In this case, an artificial delay line used as a pulse­ forming line consists of units each containing a coil of constant inductance L and capacitors with ferroelectrics with a nonlinear capacitance C( V). The

LONG LINES WITH NONLINEAR PARAMETERS

3 85

voltage dependence of the capacitance of these capacitors is because the permeability of a ferroelectric is a function of electric field, c = f(E) (capacitors of this type are called varicaps). Pulse-forming lines with semiconductors can also be used. A line of this type is made as an artificial delay line consisting of semiconductor diodes as units of constant inductance L and nonlinear capacitance C( V) (Belyantsev and Ostrovsky, 1 962). It is well known that the static differential capacitance in transition layers of semiconductors varies with applied voltage (Berman, 1 963). Therefore, each unit of the line includes a semiconductor diode with a highly nonlinear capacitance (diodes of this type are sometimes called varicaps). For example, according to Berman ( 1 963 ), the capacitance of the transition layer in a semiconductor varies as v- 1 1 2 • The now available semiconductor diodes with a nonlinear capacitance allow one to generate in a line electromagnetic shock waves with a front width of about a nanosecond. With semiconductor materials containing proper impurities, diodes can be created which would allow shock waves with a front of duration 1 0- 1 0 s to be generated in a line. Lines with semiconductors make it possible to transfer pulses with a repetition rate of up to 1 0 MHz (while in ferrite-containing lines, the pulse repetition rate is not above 1 00 kHz).

5.

GENERATION OF NANOSECOND HIGH-POWER PULSES WITH THE USE OF ELECTROMAGNETIC SHOCK WAVES

As follows from the above considerations, the property of lines to generate electromagnetic shock waves can be harnessed for shortening the rise time of current and voltage pulses. Besides, a line with ESW's can be used as an element of a pulse generator of complex design. In particular, a number of generators of this type were developed by Meshkov ( 1 990). Three types of circuit have found application in producing pulses of duration a few nanoseconds (Fig. 2 1 .8). In each of these circuits, between the energy storage capacitor and the load, a swinging choke and some combination of a linear transmission line, L, and a ferrite-containing transmission line, Lr, are connected. In the circuit shown in Fig. 2 1 .8, a (Meshkov, 1 990), as the choke is saturated, the line L is charged to a maximum voltage. As this takes place, the line Lr carries almost no current, except the low current of the magnetization shock wave flowing toward the load. As the shock wave propagates through the line, its front shortens to -1 ns and at the instant the wave front arrives at the right end of Lr, both

Chapter 21

386

lines, L and Lr, appear to be charged. At the second stage, the practically uniform line consisting of L and Lr discharges into the load R. The magnetization of the ferrite of Lr does not vary: it remains saturated; the line discharges as if it were a conventional linear line, and a rectangular pulse is formed across the load. In the second circuit (Fig. 2 1 .8, b) (Meshkov, 1 990), all processes proceed in a similar manner, but Lr is connected between the choke and the linear line segment to increase the efficiency. It was earlier supposed that the charging time of a pulse-forming line connected through a switch to a load (here, Lr serves as a switch) should be an order of magnitude longer than the discharge time; otherwise, wave processes would develop in the course of charging and the pulse shape would be distorted. Meshkov ( 1 990) has made a conceptual statement that the times of charging and discharging can be made comparable without any distortion of the shape of the output pulse. Such a mode is just typical of magnetic nanosecond pulse generators. To realize this mode, it suffices to provide a special (e.g., the square-sine) waveform of the capacitor discharge current by properly choosing the magnitude of the magnetic field in the choke core.

(a) · - - -

R

L (b) R

(c)

R

Figure 21.8. Circuits with a shock-wave line for the formation of rectangular pulses

LONG LINES WITH NONLINEAR PARAMETERS

387

The third circuit (Fig. 2 1 .8, c) is proposed by Dolbilov et a/. (1 984) . Here, a ferrite-containing line is a component of a double ferrite-containing pulse-forming line (L and Lf in Fig. 2 1 .8, c) with Lf short-circuited on one end and the load R connected in a break in the line envelopes. In contrast to the previous circuit, the current charging the lines flows in part through the load, and a small prepulse is formed across the load. As the ferrite of the line Lf is saturated, the double pulse-forming line is completely discharged into the load, and a rectangular pulse is formed. Compared to the previous circuit, the transfer of voltage from the capacitor to the load is more efficient (-0.85%), the compression factor is greater (k ::::: 8 ) , and the pulse rise time is shorter due to the increase in current at the short-circuited end (Meshkov, 1 965); however, the efficiency is comparatively low ( ::::: 0.55) . Nanosecond high-power pulse generators using nonlinear lines with ferrite elements have been developed by Dolbilov et a/. (1 987) and Meshkov ( 1 990). In these generators, the original pulse is produced by a thyratron generator. Reviews of the work on the generation of nanosecond high-power pulses using nonlinear lines with ESW's are given by Mesyats ( 1 974) and Meshkov ( 1 990).

REFERENCES Belyantsev, A. M. and Bogatyrev, Yu. K., 1 965, Design of Nonlinear Pulse-Forming Lines, Izv. Vyssh. Uchebn. Zaved. , Radiotekhnika. 8: 1 5-2 1 . Belyantsev, A . M . and Ostrovsky, L . A., 1 962, Propagation of Pulses in Transmission Lines with Semiconductor Diodes, lzv. Vyssh. Uchebn. Zaved. , Radiofiz. 5: 1 83. Belyantsev, A. M., Gaponov, A. V., and Freidman, G. I., 1965, On the Structure of the Electromagnetic Shock Wave Front in Transmission Lines with Nonlinear Parameters, Zh. Tekh. Fiz. 35:667. Berman, L. S., 1 963, The Nonlinear Semiconductor Capacitance (in Russian). Fizmatgiz, Moscow. Dolbilov, G. V., Kazacha, V. I., Sarantsev, V. P., and Sidorov, A. I., 1987, The Modulator of the LUEK-20 Linear Induction Accelerator of Electron-Ion Rings, Prib. Tekh. Eksp. 5:38-41 . Dolbilov, G. V., Krasnykh, A. K., and Razuvakin, V. N., 1 984, Use of Compression Sections and Nonlinear Pulse-Forming Circuits in the Modulator of a Linear Induction Accelerator, Ibid. 4:26-3 1 . Gaponov, A . V . and Freidman, G. I., 1 959, On the Electromagnetic Shock Waves in Ferrites, Zh. Eksp. Teor. Fiz. 36:957. Gaponov, A. V. and Freidman, G. 1., 1 960, On the Theory of Electromagnetic Shock Waves in Nonlinear Media, Izv. Vyssh. Uchebn. Zaved. , Radiofiz. 3:79. Greenberg, 0. W. and Treve, Y. M., 1 960, Shock Wave and Solitary Wave Structure in a Plasma, Phys. Fluids. 3:769-785. Kataev, I. G., 1 958, USSR Inventor's Certificate No. 1 1 8 859. Kataev, I. G., 1 963, Electromagnetic Shock Waves (in Russian). Sov. Radio, Moscow.

388

Chapter 21

Kataev, I. G., Meshkov, A. N., and Rozhkov, P. 1 . , 1 968, On the Transmission of Pulses through a Channel Containing a Line with Ferrite, lzv. Vyssh. Uchebn. Zaved. , Radioelektronika. 1 1 :570-577. Meshkov, A. N., 1 965, Nanosecond High-Voltage Pulse Generator, Prib. Tekh. Eksp. 5: 1 36- 1 39. Meshkov, A. N., 1 990, Magnetic Generators of Nanosecond High-Power Pulses, Ibid. 1:24-36. Mesyats, G. A., 1 974, Generation of Nanosecond High-Power Pulses (in Russian). Sov. Radio, Moscow. Morugin, L. A. and Glebovich, G. V., 1 964, Nanosecond Pulse Power Technology (in Russian). Sov. Radio, Moscow. Ostrovsky, L. A., 1 963, Generation and Development of Electromagnetic Shock Waves in Transmission Lines with Nonsaturated Ferrite, Zh. Tekh. Fiz. 33: 1 080.

PART 8 . ELECTRON DIODES AND ELECTRON-DIODE-BASED ACCELERATORS

Chapter 22 LARGE-CROSS-SECTION ELECTRON BEAMS

1.

INTRODUCTION

In this chapter, we consider the production of large-cross-section beams (LCSB's) by means of diodes with explosive electron emission (EEE). The random character of the occurrence of primary ectons at the cathode eventually results in a nonuniform electron beam. As a strong enough electric field is applied to a diode, primary ectons can appear within several nanoseconds due to the enhancement of the electric field at cathode microprotrusions, resulting in their explosion by the field emission current. It could be expected that for this time the expanding cathode plasmas of primary ectons will merge to form a uniform plasma surface, and this could provide the formation of a rather uniform electron beam. However, experiments show that the occurrence of an electron beam as a result of EEE abruptly reduces the electric field strength around the zone where EEE has arisen. This is due to the screening action of the space charge of electron microbeams originating from the ecton zone. Therefore, new ectons do not appear near the primary ecton zone, the covering of the cathode surface with plasma is complicated (emission centers are located far apart), and the problem of the production of a uniform beam demands special research. However, the "screening" effect is moderated to some extent by the so­ called "pickup" effect. In this case, the plasma of primary ectons interacts with the cathode and initiates new ectons. It has also appeared that the beams from closely located individual cathode flares (CF' s) interact with one another, making the electron beam more irregular at the anode (the "stroke" effect).

Chapter 22

392

Let us consider the large-scale structure of electron beams in high-current diodes designed for the production of LCSB 's. We shall mean by the diodes such devices in which the electrode separation is much less than the geometric dimensions of the electrodes (cathode and anode). Besides, we shall investigate the properties of diodes of this type, paying special attention to the cathode phenomena. A considerable body of the data presented in this chapter, including those on the above effects, was obtained in the main by the team headed by Mesyats at IHCE (Belomytsev et al., 1980; Koval et al. , 1 983 ; Mesyats, 1 998; Bazhenov et al. , 1 970; Belomytsev et al. , 1976; Bugaev et al. , 1 973a; Belomytsev et a/. , 1 987). Recall that the phenomenon of explosive emission of electrons was considered in detail in Chapter 3 .

2.

THE CATHODES O F LCSB DIODES

2.1

Multipoint cathodes

For the production of a great number of ectons per unit area, cathodes are used on which numerous points are specially made. Sometimes, a metal or other type conductor is used on the surface of which many ecton zones can naturally be formed at a high electric field. To obtain a uniform electron beam, it is important that the cathode surface be covered with plasma as uniformly as possible. If we assume that new ectons arise at a distance from each other not smaller than the radius of screening, rscr. the minimum time it takes for covering the cathode with plasma will be of the order t � rscrlvc , where Vc is the expansion velocity of the cathode plasma. Obviously, the longer the pulse duration, the more uniform is the coating of the cathode with plasma and, hence, the more uniform will be the electron beam. The second important parameter responsible for the production of a uniform beam is the rise rate of the electric field in the diode, dEldt The higher dEldt , the larger the number of ectons that appear within the pulse rise time and the more uniform the electron beam produced (Hinshelwood, 1984). For multipoint cathodes, the basic challenge is to provide their stable operation and long lifetimes. These both characteristics depend on cathode material, emitter geometry, current carried by each emitter, applied voltage, and cathode-anode separation. A usual reason for failures of such cathodes is that the emitters are blunted because of material removal. When choosing the geometry of emitters, it is necessary to take into account two requirements. The first requirement is that the electric field strength must be such that the time delay to the explosion of points would be much less than the pulse rise time. The second one is reduced to providing a necessary lifetime of the cathode. These requirements are conflicting since an increase .

LARGE-CROSS-SECTION ELECTRON BEAMS

393

in electric field is achieved by reducing the emitter radius, and the smaller the radius, the greater the mass of the material removed. Obviously, for the creation of reliable long-living explosive-emission cathodes, emitters with an invariable cross section (foils and wires) are most promising. Foil emitters are most popular (Proskurovsky and Yankelevich, 1 983; Belkin and Aleksandrovich, 1 972), and, when used in the nanosecond range of pulse durations, they show lifetimes of the order of 1 07 shots. However, emitters of this type have a number of disadvantages. One of them is that the number and positions of ectons on the working edge of a foil cannot be controlled, and this results in a considerable nonuniformity of the electron beam (Bradley et al. , 1 972). Meanwhile, the localization of the current in a limited number of ecton zones shortens the delay time to the electrical breakdown of the acceleration gap. To clear up this trouble, attempts are made to use very thin (7-20 J..lm) metal foils for increasing the electric field at the cathode. However, for large-area cathodes operating on the microsecond scale of pulse durations, the appearance of leading ectons is detrimental to the formation of a beam. Moreover, cathodes made of thin metal foils are mechanically unstable. A given and controllable number of ecton zones on a large-area cathode can be created by using cylindrical emitters made of thin wires. A considerable advantage of this type of cathode is that there is a possibility to maintain uniform current extraction from all emitters by connecting a ballast resistor in the circuit of each of them (Link and Olander, 1 969). The use of cylindrical emitters fabricated of thin wires makes it possible to create simple in design and convenient to service long-living explosive-emission cathodes of large area. Since the breakdown electric field, the erosion characteristics of the cathode, and the parameters of newly arising microprotrusions are determined by the emitter material, it is necessary to use materials preferable from the viewpoint of creation of long-living cathodes. To reveal such materials, Proskurovsky and Yankelevich ( 1 983) tested emitters made of various materials and having identical geometric parameters under the same conditions. The results obtained for cylindrical cathodes are presented in Fig. 22. 1 . It can be seen that copper emitters show the greatest resistance to erosion. Special attention should be given to graphite cathodes. The most uniform beams are obtained in tests with plane graphite cathodes. This is due to the fact that graphite shows short delay times to the explosion of microprotrusions, td, at rather low macroscopic electric fields at the surface and small values of the critical current (Mesyats, 1 998). In has been shown (Koval et a/., 1 983) that carbon-graphite materials have the best properties, and the lower the material density, the shorter the time td and the more

394

Chapter 22

uniform the electron beam (Fig. 22.2). For example, in the electron guns of the Aurora excimer laser (LANL) (Rosocha and Riepe, 1987), a graphite fabric of felt or velour type served as cathode material. This material is used because low voltages are necessary for microexplosions to occur at a cathode. This allows one to have uniform plasma as early as within the pulse rise time. The graphite fibers constituting the carbon-graphite fabric are about 20 J..tm in diameter. On the side surface, the fabric has knots about 1 J..tm in size. These fibers and knots promote explosive emission at low voltages (Erickson and Mace, 1 983). Widely spread are multipoint cathodes made from a copper foil by the method of cold punching (Bugaev et a/., 1 984). 18

1 .6

e .§. � 0.8

';;'

14

S IO �

6

2 0

2

6 4 N · 1 05 [pulse]

8

10

Figure 22. 1. Height decrement o f a cylindrical emitter, Mf, as a function of the number of current pulses passed through the gap, N: 1 - W, 2 - Au, 3 - Ag, and 4 - Cu

2.2

0

2.4

5.6 4.0 E · I 0-5 [V/cm]

7.2

Figure 22.2. Breakdown delay time fct as a function of macroscopic electric field E: 1 fine-grained graphite of density 2.2 g/cm3 ; 2 and 3 - carbon graphite of density 0.8 and 0.2 g/cm3, respectively

Liquid-metal cathodes

For a solid cathode, the emission centers are natural microirregularities or specially produced microprotrusions. In the presence of a liquid phase, the latter can be formed as a result of the disturbance of the surface of the liquid metal in a strong electric field (Frenkel, 1 935). As shown for a liquid cathode, the vacuum breakdown is preceded by the occurrence of hydrodynamic capillary waves. The suppression of these waves increases the electric strength of the vacuum gap. The use of a liquid metal for the production of stable explosive emission is proposed by Bartashyus et a/. ( 1 97 1 ). 1t is obvious that if EEE at the initial stage of a vacuum breakdown is determined by the explosion of microprotrusions, its stability should substantially depend on the conditions

LARGE-CROSS-SECTION ELECTRON BEAMS

395

of self-recovery of microprotrusions from breakdown to breakdown. It seems that for liquid metals the cathode operation should be much more stable because microirregularities are formed under invariable initial and boundary conditions. In addition, the formation of microirregularities on a liquid surface can be controlled by some artificial way. In particular, such they can be created by exciting the surface with a piezocrystal. If a liquid metal is placed over a vibrating piezoquartz or barium titanate plate, standing waves are generated on the liquid surface, which can serve as ordered and controllable microirregularities. For a square plate with a square side a, the relation between the number of vibrations n and their frequency f, is expressed by the formula (Pigulevsky, 1 958) /,

n -

_

�

n2nh Eip(1 - cr2 ) 2

J3a2

'

(22. 1 )

where h i s the height of the standing wave, p i s the density o f the plate material, and cr is the Poisson coefficient. The corresponding relation for a round piezocrystal of radius r has the form r = Jn

� J3r2

n2nh Elp(l - cr2 )

(22.2)

In the experiment described by Bartashyus et al. ( 1 97 1 ), the frequency of the exciting vibrations ranged from 2 to 1 2 MHz. Thus, according to formulas (22. 1 ) and (22.2), the density of the irregularities produced varied with frequency from 1 90 to 6· 1 03 cm-2 • The calculated dimensions of microprotrusions (radii of curvature of their tips) ranged, respectively, from 37.2 to 1 .34 J..lm . The height of a microprotrusion depended on the power supplied from a generator and could reach 1 0 J..lm. As the exciting vibration amplitude was increased, the breakdown voltage decreased. As this took place, the spread in breakdown voltages decreased as well. Simultaneously, a substantial increase in EEE stability was observed. Without excitation of the surface, the spread in values of the electron current made up 1 0-1 5%; when artificial excitation with the help of piezoquartz was used, the electron current was stable within 5%. It is of importance that with artificial excitation of the cathode surface the transferred electron charge increased. This can be explained by the development of an active surface and the increase in the number of simultaneously exploding emission centers. The electron current was 2 · 1 03 A and the voltage was 3 00 kV. The electron component was separated from the plasma with a thin foil transparent to the electrons accelerated by the anode

396

Chapter 22

voltage. A new type of liquid-metal cathodes capable of operating at high repetition rates is described by Baskin et a/. ( 1 994). A detailed study of the EEE process at the surface of a cathode of this type has been carried out by Batrakov (2002).

3.

METAL-DIELECTRIC CATHODES

3.1

Explosive electron emission from a triple junction

Attempts to produce uniform LCSB' s due to more uniform covering of the cathode surface with plasma resulted in the creation of metal-dielectric cathodes (MDC's). With this type of cathode, EEE can be excited much easier and, as the velocity of motion of a plasma over the surface of a dielectric can be made higher than the velocity of expansion of a CF in vacuum, the covering of the cathode surface with plasma will occur more rapidly. Besides, metal-dielectric cathodes are easier to be made controllable, thus giving them new useful properties (Bugaev et a/. , 1 973b; Mesyats, 1 974). The operation of a metal-dielectric cathode is based on the excitation of EEE at a metal-dielectric-vacuum triple junction. We explain the mechanism of the operation of an MDC by the example of a metal needle leaning against the surface of a dielectric plate whose opposite side is metallized (Fig. 22.3) (Bugaev and Mesyats, 1 97 1 ). In the sketch shown in Fig. 22.3, needle I is a cathode, plate 3 is an anode deposited on dielectric 2, and electrode 4 is a trigger electrode. Assume that the cathode I is grounded, and a pulsed voltage too low to initiate EEE from the cathode is applied to the anode 3. If now a pulsed voltage is applied to the electrode 4, a dielectric surface discharge in vacuum starts from the electrode I . The current of this discharge will be closed on a microprotrusion of the cathode I leaning against the dielectric surface. This current just results in the explosion of the microprotrusion and in the occurrence of EEE from the metal emitter I toward the plane anode 3. The current of the dielectric surface discharge is caused by an increase in the dynamic capacitance of the gap between the plasma moving over the dielectric surface and the metal layer deposited on the opposite side of the dielectric. This is a rather simple and efficient way of exciting EEE in a diode. Such a diode is a triggered device; that is, EEE is initiated only on application of a trigger pulse. This method is used with various types of cathode, for example, with one having uniformly distributed emission centers, which is made of a metal grid pulled over the surface of a dielectric �Bugaev et a!. , 1 973b). At the sites of contact of the grid with the dielectric, discharges

LARGE-CROSS-SECTION ELECTRON BEAMS

397

occur over the surface of the latter, resulting in the formation of EEE centers. For a higher efficiency of such a cathode, it is better to take a high-s dielectric. 10 8

s

� 6 ..::;

4

�

2

0

2

Vo [kV]

3

4

Figure 22.3. Sketch of the initiation of an emission center: 1 cathode, 2 dielectric, 3 anode, 4 trigger electrode, and the discharge current as a function of voltage for a BaTi03 plate of thickness 2 mm. Electrode 1 is a cathode with respect to electrode 4 (open circles); electrode 1 is an anode (solid circles) -

-

-

-

=

The vacuum discharge over the surface of barium titanate (BaTi03) with s 1 500 was studied by Bugaev and Mesyats ( 1 9 7 1 ). A barium titanate disk 1 (Fig. 22.4) of thickness 2 mm was placed in a vacuum chamber. A silver layer 2 was burnt in one side of the disk, and a tungsten needle 3 was kept against another side. Electrons were extracted from the plasma by extractor 4. Between the electrodes 2 and 3, voltage pulses of amplitude 0.4-4 kV, rise time - 1 ns, and fixed duration (2, 4, 8, 20, and 50 ns) were applied. The discharge current Id and the voltage across the dielectric Vd were recorded by a fast oscilloscope, and the luminosity of the discharge in the vicinity of the needle 3 was photographed by an electron-optical device equipped with a light amplifier. The discharge luminosity spectrum was recorded by a spectrograph with the recording channel containing a photomultiplier and a signal amplifier. A voltage of amplitude up to 30 kV, rise time 1 ns, and duration up to 500 ns was applied to the extractor 4. At a pulse duration of several nanoseconds, the discharge over the dielectric surface arises at a voltage exceeding some threshold value. As this takes place, the lines of neutral and singly ionized barium ( Ba I and Ba II ) are detected in the luminosity spectrum. As the voltage is further increased, the lines of Ti I , 0 I , 0 II , and tungsten ( W I and W II ) appear in the spectrum.

398

Chapter 22 1

To oscilloscope

Ro Figure 22.4. Schematic of an experiment on surface dielectric discharges: 1 - dielectric, 2 electrode, 3 - needle, 4 - extractor. Rf= 56 Q, Rc = R0 = 75 Q

(a) (b)

\f'�__,f_vd -..�( == _ _ _

(c)

4 ns

(d)

8 OS

20 OS

"';O ns�}J 1------l

�

fe

Figure 22.5. Discharge voltage (a) and current (b) waveforms; photographs of the discharge luminosity (c), and waveform of the emission current from the discharge plasma (d)

The discharge current is caused by the variation in the dynamic capacitance of the gap between the plasma moving with a velocity vd over the dielectric, and the silver layer 2 (Fig. 22.5). For 8 » vdtp (8 being the dielectric thickness and tp the duration of the trigger voltage pulse of amplitude Vd), we have (Bugaev and Mesyats, 1971) (22.3) where A is a factor depending on the polarity of the needle relative to the electrode and on the dielectric type and thickness. For BaTi03 with 8 = 2 mm and the positive polarity of the needle, we have A = 5 · 1 02 cm/(s·V), while for the negative polarity A = 2· 1 03 cm/(s·V). The amplitude of the discharge current pulse is determined from the relation (22.4) where Eo and E are, respectively, the dielectric constant of vacuum and the permeability of the dielectric. In Fig. 22.3, the dependence of Jd on Vd is

LARGE-CROSS-SECTION ELECTRON BEAMS

399

shown for the positive and negative polarities of the point. In this experiment (Bugaev and Mesyats, 1971 ), BaTi03 of thickness 2 mm was used. A discharge current of several amperes can be obtained at a trigger voltage as low as 1 -2 kV. This current is sufficient for a microprotrusion of radius -1 J..lm contacting to a dielectric to explode within -1 o-9 s. Thus, this is a very efficient method of EEE excitation at the surface of a dielectric. 3.2

Metal-dielectric cathode designs

Mesyats and co-workers (Bugaev et al. , 1 973b; Mesyats, 1 974; Bugaev and Mesyats, 1 97 1 ) designed a cathode on which emission centers were created in large numbers due to a discharge over the surface of a dielectric in vacuum and a discharge between a metal grid and the dielectric. Figure 22.6, a shows a grid located on a barium titanate dielectric substrate I ; the opposite side 2 of the substrate is metallized. We now consider an equivalent circuit of the electron source (Fig. 22.6, b). In this circuit, one can distinguish the capacitance of the dielectric surface elements relative to the bottom plate, Ch and the capacitance of these elements relative to each other, C2, and relative to the grid, C3 • Because of the high e of the dielectric, we have C2 and C3 « C1 • Therefore, the pulsed voltage applied between the substrate and the grid appears to be applied to C2 and C3 • Therefore, a discharge occurs over the surface of the dielectric at those sites where the dielectric is in contact with the grid, while at those sites where there is no contact breakdown of the grid-dielectric gap is possible. In the latter case, due to the high tangential field at the dielectric, after the breakdown, the discharge will inevitably develop over the dielectric surface. Because of the high surface resistance of the dielectric, individual discharges can occur independently and cover a significant part of the cathode surface with plasma within a short time. (a)

(b)

Figure 22. 6. Diagrams showing the connection of a triggered electron source (a) and the equivalent circuit of the cathode discharge circuit: 1 ceramic plate, 2 acceleration electrode, 3 - metal grid (b) -

-

400

Chapter 22

In contrast to nontriggered electron sources, triggered ones produce considerably higher currents at the same voltage due to the application of a trigger pulse to the grid. These currents are tens times in excess of the Child­ Langmuir current. The considerable increase in current in a triggered source is due to the reduction of the anode-cathode gap resulting from the propagation of plasma deep into the gap and due to the neutralization of the electronic space charge by ions. Using a triggered cathode with a discharge over BaTi03 , Bugaev et a/. ( 1 973b) and Mesyats ( 1 974) obtained an electron current of 2· 1 03 A at a voltage of 50 kV. In a 5 00-keV electron accelerator with a cathode of diameter 4 em and an anode-cathode distance of 1 em, the amplitude of the electron current in the diode was about 1 04 A and the pulse duration was 25 ns. Later cathodes of this type were given the name segnetoelectric cathodes (Gundel, 1 992; Schachter et a/., 1 993). In these cathodes, PbZr03 , La 03 , and PbTi03 compounds are used rather than barium titanate. 2 Depending on the structure, these ceramic materials have a permeability g ( 1 -5} 1 03 • The cathode design is similar to that given in Fig. 22.6. Gundel ( 1 992) and Schachter et a/. ( 1 993) explain the operation of these cathodes by special properties of the ceramics. However, there is no doubt that they operate, much like conventional metal-dielectric cathodes, due to the ectons occurring at triple junctions and plasma generated at the dielectric. Andrews et a/. ( 1 969) used a metal cathode with numerous conical pits inlaid with a plastic with g 3-10. Due to the high electric field at sharp edges of the pits, electrons are emitted from these sites and, getting on the dielectric surface, initiate a surface discharge and fast covering of the cathode surface with plasma. As shown below, the dense plasma formed due to explosive destruction of the dielectric and metal, much like that formed by the explosion of a metal protrusion, intensifies the emission of electrons from the cathode. With this type of cathode, at a voltage of 500 kV, single electron current pulses of duration 50 ns and amplitude up to 1 05 A were produced. The quest for a diode with controllable current density at a fixed gap stimulated attempts to create plasma cathodes with the production of plasma independent of the accelerating voltage. For large-area cathodes, a dielectric surface discharge initiated with the help of an ignition circuit with capacitive coupling can be used. A description of this type of cathode was first given by Bugaev et a/. ( 1 973b ). A plasma emitter of this type intended for discharge initiation in gas lasers was used by Loda ( 1 977) and Ramirez and Cook ( 1 980). A triggered cathode with breakdown over the surface of a dielectric in vacuum consists of a set of round elements etched on the surface of foiled Getinaks. A great number of metal islets, separated by annular insulating

=

=

LARGE-CROSS-SECTION ELECTRON BEAMS

40 1

gaps from the plate metal, are capacitively coupled through the dielectric with the metal layer applied on the other side of the dielectric. A serious problem with the use of metal-dielectric cathodes is that the dielectric surface is metallized due to the presence of liquid metal, plasma, and vapor generated due to Joule heating of a cathode microregion by the ecton current. Moreover, the dielectric is destroyed when operated for a long time. To moderate these detrimental effects, it was proposed (Kotov et a/. , 2000) to use a cathode made as a rotating ceramic cylinder against which two electrodes are pressed (Fig. 22. 7). On application of a voltage pulse to the diode, because of the capacitive couplings between electrodes 2 and 4 and between the electrode 4 and the diode walls, a potential difference arises at the surface of the dielectric and a discharge develops over the dielectric through many channels. This discharge creates numerous EEE centers on the cathode edge. Cathodes of this type have long lifetimes (I 08 and more shots) at a pulse repetition rate of 1 02- 1 03 Hz and an average power of 1 0-20 kW. A

Figure 22. 7. Metal-dielectric cathode with a rotating ceramic cylinder: 1 - cathode holder, 2 main electrode, 3 - ceramic cylinder, 4 - auxiliary electrode, and 5 - insulator

Miller ( 1 998) described the operation of fiber dielectric cathodes, which sometimes are referred to as velvet cathodes. They are designed as follows: many dielectric fibers are fixed on a plane cathode normal to its surface (Fig. 22.8, a). An electric field applied between the cathode and the anode initiates a discharge over the surface of a fiber (Fig. 22.8, b). The discharge plasma, when touching the cathode, causes explosive electron emission (see Section 2 of Chapter 3). If dielectric fibers are placed rather close to each other, it is possible to produce continuous plasma on the cathode and a uniform electron beam because of the horizontal expansion of the surface discharge plasma (Fig. 22.8, c).

402

Chapter 22 (a)

Anode

(b)

Anode

Anode

Cathode

Cathode

------

{

Dielectric fib"

Cathode

Figure 22.8. Sketch showing the operation of a fiber-dielectric (velvet) cathode: a - location of the dielectric fiber before the onset of emission, b emission from a single fiber, and c emission from a cathode containing many fibers -

Kotov et a/. (2000) have developed a metal-dielectric ceramic cathode containing dielectric nanopowders (Ah03 ) of particle size -20 nm and steel nanopowders of particle size 1 0-30 nm. The ceramics was produced by magnetically pressing these powders. At the sites of contact of dielectric particles with the metal, there are cavities owing to which many triple junctions (TJ's) are formed. On application of an electric field, TJ's initiate a discharge over the dielectric surface that covers with plasma the whole of the cathode surface. Therefore, an electron beam of highly uniform current density is generated. In this case, an important role is played by the redistribution of the potential over the dielectric surface as a result of flashovers of the dielectric nanopowders. This effect reminds the operation of sequence spark gaps described in Section 6 of Chapter 9.

4.

PHYSICAL PROCESSES IN LCSB DIODES

4.1

Nanosecond beams

Let us consider a cathode consisting of a great number of tiny points arranged in rows a distant from each other with the distance between the points in a row equal to b (Fig. 22.9). If the dimensions of the points are such that on application of a voltage pulse the time to the explosion of each point is much less than the pulse rise time, it can be assumed that the points explode simultaneously. If a » b, the time it takes for the plasma to cover the distance between two neighboring points in a row, which is equal to b/2v ( v being the velocity of motion of the cathode plasma), will be much less than the time it takes for the plasma to cover the distance between two rows, and the multipoint cathode can be considered a cathode with a-spaced emitting fibers. For the cathode area S » d 2 and the pulse duration fp « d!v,

LARGE-CROSS-SECTION ELECTRON BEAMS

403

the electron current in the diode can be determined by the relation (Mesyats, 1 974)

I = 9.33 · 1 0-6 N(l/d) V31 2 f(ald) ,

(22.5)

where N is the number of rows; I is the length of a row; d is the cathode­ anode separation, and V is the voltage. The functionj{ald) has the form

fold[(1 + x2 )112 + llx arc sh x -2 . J dx 0

f(ald) =

(22.6)

For aid « 1 , we have fiald) � 1 14(ald) and, taking into account that the cathode area is given by S = a/N, we obtain a conventional expression for the current-voltage characteristic of a diode with plane-parallel electrodes:

I=

{2; V3' z s v-;;; 9mJ2 '

(22.7)

where e and m are, respectively, the electron charge and mass. Assuming that the pulse duration fp is comparable to dlv, we get

I --

v3'zs 9n(d - vt)2

•

(22.8)

Formulas (22.7) and (22.8) are valid for eV « mc2 • Figure 22.9 presents the theoretical dependence I( V) (22. 7) corresponding to the "312-power" law and the experimental points taken from the work by Garber et a/. ( 1 969) (for a cathode 2 em in diameter, a = 0.8 mm, b = 0.3 mm, the number of needles 1 500, and a gap spacing of 1 em). In this experiment, the relation tp « dlv was observed. The good agreement between calculations and experiment suggests that the multipoint cathode operated not in the field-emission mode, as Rukhadze et a/. ( 1 980) believed, but in the explosive mode. In Fig. 22.9, experimental points taken from the work by Mesyats ( 1 974) are also given. No dependence of the current determined by formula (22. 7) on the dimensions of the emission centers or on the relative positioning of the latter allows the assumption that if the conditions ald « 1 ,

JS » d

(22.9)

are satisfied, the "312-power" law is valid. For p = v01c « 1 , the relativistic factor is given by y

= 1 + e VImc2 •

(22 . 1 0)

Then, from (22.8) and (22 . 1 0) for tp « dlv ,

(22. 1 1 )

404

Chapter 22

where

v

( )

is the velocity of the cathode plasma during EEE, we get

mc3 r;:; ( )3/ 2 S I = - "2 y - 1 --2 e 9nd and

mc3 yS I = -- --2 e 2nd

for

for

y«3

(22.12)

y»1.

(22. 1 3)

These two expressions for the limiting electron current density in a planar diode can be united, taking advantage of interpolation, as (Rukhadze et a/. ,

1 980)

(22.14) 0

320

s

..-. 240

....

Cl)

�

;:;- 1 60 80

0

40

80

120

160 V [kV]

200

240

280

Figure 22.9. Generalized current-voltage characteristic of an EEE diode with a multipoint cathode. The curve is the result of calculations by formula (22.7). Data points, taken from publications of different authors, were obtained for different values of I, d, and S

It was shown (Mesyats, 1 99 1 b) that the electron current from a point cathode could be increased eight times due to a prepulse. This effect was observed in a diode with a triggered cathode (Bugaev et al. , 1 973b). With pulsed charging of the energy stores in electron beam generators, prepulses can arise due to the passage of the displacement current through the self­ capacitance of the switch during its operation delay time. The prepulses result in an increase in current not only because of the change in gap geometry. If during the action of a prepulse plasma has time to be formed throughout the diode volume due to evaporation of the walls and anode, the current will increase, in addition, because of the neutralization the electron

LARGE-CROSS-SECTION ELECTRON BEAMS

405

space charge by the plasma ions (Mesyats and Proskurovsky, 1 97 1 ). An increase in current in a diode under the action of prepulses was observed by Levine and Vitkovitsky ( 1 97 1 ) and Smith et a/. ( 1 97 1 ), and some experimenters pointed to the fact that this effect promotes the increase in electron current. For example, in the experiment of Levine and Vitkovitsky ( 1971) the current increased 1 0 times, becoming as high as 1 06 A. Deviations from the "3/2-power" law for a multipoint cathode are also possible if conditions (22.9) are not satisfied. We did not take into account that anode plasma can be formed in a diode. In this case, the velocity at which the electrodes come closer together is equal to the total velocity of the cathode and anode plasmas. This was clearly illustrated by Parker et a/. ( 1 974). Measurements were carried out for a diode with graphite electrodes of diameter 5 em. The rate of reduction of the vacuum part of the gap was evaluated by the behavior of the perveance of the electron flow. The surface of the graphite cathode became completely covered with plasma 30 ns after the arrival of a voltage pulse at the gap. Thereafter, the variations in perveance were well described assuming that the cathode plasma propagates toward the anode with a velocity of 1 .8· 1 06 crnls. However, approximately in 70 ns, the perveance started increasing more rapidly than this follows from the assumption that the velocity of the cathode plasma is a constant. It became necessary to suppose that at that moment an anode plasma appeared and started moving with approximately the same velocity toward the cathode. The validity of this supposition was shown in Chapter 3 of this monograph. This is also confirmed by experiments (Mesyats, 1 971 ). 4.2

Large-cross-section beams of microsecond and longer duration

Originally, after the appearance of diodes depending for their operation on EEE, it was believed that electron beams could not have a duration of more than 1 o-7 s. The duration of an electron current pulse in such a diode is limited to the time of closure of the cathode-anode gap with the plasma formed at the electrodes. The anode plasma can be eliminated by reducing the current density or by using a foil or grid anode, while the cathode plasma is essentially irremovable. Bugaev et a/. ( 1 973a) were first to demonstrate the possibility of the production of microsecond electron beams with the use of long cathode-anode gaps. In this experiment, electron beams of energy over 1 MeV, current up to 5 kA, and duration up to 4 J..l S were produced. The electron accelerator used is shown schematically in Fig. 22. 10. On the U-2 system at the Institute of Nuclear Physics (Novosibirsk) (Voropaev et a/. , 1987), an electron beam of energy about 1 MeV, current of 1 05 A, and

406

Chapter 22

duration 5 J..lS was produced; the average current density was over 200 A/cm2• For the production of longer pulses and realization of a quasistationary mode, it was necessary to solve three problems: 1 . to find conditions under which an EEE plasma cathode would operate in the saturation mode and the emission boundary would stop moving; 2. to develop methods for limiting the increase in current, and, hence, the generation of plasma, since the main difference of a diode with EEE from a diode with stationary plasma is the absence of a special circuit for plasma generation, and 3. to elucidate the mechanism of breakdown in order to find a way of hindering its initiation.

10

� To oscilloscope

Figure 22. 1 0. Experimental setup for the production of microsecond electron beams: 1 Marx generator, 2 spark gap, 3 vacuum chamber, 4 cathode, 5 70-J..Lm thick aluminum foil extractor, 6 collector, 7 current-measurement shunt, 8 voltage divider, 9 window, and 10 - camera

-

-

-

-

-

-

-

-

-

Bazhenov et a/. ( 1 975) in their investigations of the emissivity of the CF plasma in various phases of its propagation toward the anode established that in the initial phase the plasma front moves with a velocity greater than the average velocity of the directed scattering of plasma particles from the cathode ( v � 2 · 1 06 cm/s ). This seems to be related to the presence of a virtual cathode ahead of the CF front. As the plasma further expands, the conductivity of the vacuum part of the diode increases and the emissivity of the plasma falls because of the decrease in its density at the emission boundary. As this takes place, the virtual cathode "disperses", the screening of the plasma by the space charge field ceases, and its velocity decreases. The plasma emitter goes from the mode of unlimited emissivity to the saturation mode; that is, the condition je > jb changes to je = jb , where je and jb are, respectively, the thermal

LARGE-CROSS-SECTION ELECTRON BEAMS

407

current density of plasma electrons at the emission boundary and the current density limited by the space charge of the electron beam. As the emission boundary goes over to saturation, the current rise rate at the initial stage of EEE drops. Since the emission boundary moves with a velocity lower than v and the internal layers of the plasma of secondary ectons, moving with a high velocity, can catch up with the boundary, the mechanism of the occurrence of plasma density fluctuations at the emission boundary is clear (Mesyats, 1 998). If plasma blobs appear at the cathode surface, for instance, due to the formation of new ectons, the saturation condition is broken and the boundary speed up again as these blobs arrive at the emission boundary, and this will inevitably result in an increase in current (Burtsev et al. , 1 978; Bazhenov and Chesnokov, 1 976).

5.

DESIGNS OF LCSB ACCELERATORS

In the literature, a great number of accelerators designed for the production of large-cross-section beams are described. They vary in type of diode, power supply, application, current and voltage magnitude, etc. It is impossible to describe them within the framework of one section; therefore, we have to restrict ourselves by considering only some issues of principle. Examining the circuits of electron sources used in high-power gas lasers, one can distinguish two types of source: diode and triode. A diode source is most suitable if high current densities and low impedances are required. In this case, the energy source is a low-resistance pulse-forming line or a Marx generator. Application of a triode circuit is justified if the equivalent resistance of the diode is high enough ( 1 02 Q) and the current density is low (about 1 0-3 A/cm2). The advantages of this circuit are the rather simple uniform ignition of the whole of the cathode surface and the possibility to control the impedance of the source. The disadvantages are the complexity of the synchronization circuits and the rather low electric strength of the acceleration gap. To moderate the role of the magnetic field of the electron beam, the concept of a segmented electron gun was proposed (Rosocha and Riepe, 1987). In such a gun, a large cathode is subdivided into several separate ones owing to which the self magnetic field decreases. Depending on the volume, a laser can be pumped on one, two, four, and six sides, as well as in a coaxial manner. The circuit of the diode of an accelerator intended for one-sided pumping of a pulsed C0 laser with a pulse energy of up to 7.5 kJ is 2 described by Koval'chuk et al. ( 1 976). The design of a laser system in which two EEE diodes are used is shown in Fig. 22. 1 1 . The beams are produced by a bilateral blade cathode fixed on an aluminum plate 25x200 em in size.

408

Chapter 22

Tantalum strips of thickness 7.6 f.tm are protruded for 2. 7 em above the surface of the cathode plate. The cathode is located in a rectangular vacuum chamber and suspended, with the help of the cathode holder, to a vacuum insulator. Electrons, through a window 35x200 em in size, get in the laser cells where a volume discharge is initiated between the electrode and the protective grid of the window. A four-stage MG with an output voltage of 320 kV, a pulse rise time of 50 ns, and a capacitance of 1 .25 f.lF serves as a source of pulsed voltage. The voltage produced by the generator is supplied to the diode through a high-voltage cable.

1

6

Figure 22. 1 1. Schematic diagram of a gas laser with a double-beam electron source: 1 vacuum insulator, 2 - cathode holder, 3 foil emitter, 4 - extraction window, 5 - cell electrode, 6 - voltage lead-in, and 7 - laser cell -

A description of a KrF laser pumped on four sides is given by Edwards Pumping was performed by four accelerators, each having a two-cathode diode. Hence, it can be spoken in fact of an eight-sided pumping. The voltage across the diodes was produced by water lines charged from a 1 -MV, 40-kJ MG. The diode voltage was 550 kV and the total energy of the electron beam produced by the four diodes was 28 kJ. A XeCl excimer laser having the shape of a cylinder of volume 600 1 was pumped on six sides from twelve accelerators arranged in two floors on each side (Mesyats et a/. , 1 992) (Fig. 22. 1 2). The accelerators were powered directly from Marx generators whose distinguishing feature was that they operated under conditions of vacuum insulation. Therefore, the laser had no

et a/. (1980).

LARGE-CROSS-SECTION ELECTRON BEAMS

409

intermediate energy storage lines. The output voltage of the Marx generators was 600 kV, and the total electron current was 700 kA. This laser, because of the use of low-inductance vacuum MG's, was the most compact and reliable system at the time.

Figure 22. 12. Sketch showing six-sided pumping of a laser: 1 - pulse generator, 2 - diodes of the electron accelerator, 3 - beam inlet window, and 4 - laser chamber pumped with electron beams

The six-sided and the eight-sided pumping are in fact close to that realized with a coaxial pumping system. In this case, intense and uniform pumping of gas lasers is achieved and the optical characteristics of the light beam are improved. A coaxial diode source was shown to be the best choice for excitation of excimer lasers (Eden and Epp, 1980). The source was a cylindrical coaxial diode with an electrode gap of 2.5 em, powered from a low-inductance five-stage MG capable of producing 250-kV, 0.8 J..l.S pulses. Used as cathodes were strips of titanium foil, coal fibers, or graphite felt fixed on the inner surface of an aluminum cylinder of length 55 em and internal diameter 8.9 em. The cathodes made of titanium foil of thickness 25 J..l.m had were 6 mm high and 50 em long. The anode shaped as a hollow cylinder of length 1 00 em was welded from a titanium foil of thickness 25 J..l.m . Coaxial diodes are efficient in pumping lasers that demand high beam current densities. Ramirez et a/. ( 1 977) used for these purposes a diode with E = 1 MeV, I = 200 kA, j ::::: 1 30 - 260 A/cm2, and tp = 20 ns. Under these conditions, a coaxial diode has an advantage over a planar one: in strong electric fields necessary for the production of high currents, the beam is essentially nonuniform because of the discreteness of emission centers on the cathode surface; with radial injection, this nonuniformity is compensated.

410

Chapter 22

In creating diodes of high average power which would be capable of operating at pulse repetition rates of 50- 1 00 Hz, the tasks to be solved are: to increase the lifetime of the cathode, to reduce the beam electron losses in the foil and support grid, and to provide operating vacuum conditions in the diode. Besides, it is necessary to have complete information on the characteristic time of deionization, i.e., on the recovery capabilities of the acceleration gap. Tests of blade cathodes made of tantalum foil of thickness 7.6 !J.m (Loda and Meskan, 1 977) have shown that a cathode of length 25 em from which a current of 1 2 A with a duration of 1 0 !J.S was extracted at a voltage of 255 kV, was capable of operating with a frequency of up to 1 000 Hz. The height of the blade decreased by 1 mm after application of 2· 1 07 pulses. To power repetitively pulsed diodes, high-voltage pulse generators with step-up transformers are often used. These devices, with the pulse-forming element connected in the primary circuit, have been developed for certain ranges of impedances, pulse durations, and output voltages, since they are used in radiolocation to modulate the pulses of high-power klystrons. A disadvantage of this type of circuit is the high leakage inductance of the high-voltage pulse transformer. An accelerator with a high-voltage pulse generator whose Tesla pulse transformer is combined with an intermediate energy store (coaxial pulse-forming line) connected to the secondary winding is described by Mesyats ( 1 99 1 a). At an accelerating voltage of 400 kV, a current of 8 kA, and a pulse duration of 25 ns, the average power of the beam is 5.5 kW. The pulse repetition rate is 1 00 Hz; the beam size at the exit is 1 Ox 1 00 em.

REFERENCES Andrews, M., Bruza, J., Fleishman, H., and Rostoker, N., 1969, Effect of a Magnetic Guide Field on the Propagation of Intense Relativistic Electron Beams, Laboratory of Plasma Studies, Cornell Univ., Ithaca, New York, p. 1 8. Bartashyus, Yu. 1., Pranevichus, L. 1., and Fursei, G. N., 1 97 1 , Study of the Explosive Electron Emission from a Liquid Gallium Cathode, Zh. Tekh. Fiz. 41: 1943. Baskin, L. M., Batrakov, A. V., Popov, S. A., and Proskurovsky, D. I., 1994, Electrodynamic Phenomena on the Explosive-Emission Liquid Metal Cathode. In Proc. XVI ISDEIV, Moscow, Russia. pp. 2-5. Batrakov, A. V., 2002, Plasma Properties of Arc Cathode Spot at Liquid-Metal Cathode. In Proc. XX ISDEIV, Tours, France, pp. 1 23- 130. Bazhenov, G. P. and Chesnokov, S. M., 1 976, On the Maximum Current of Explosive Electron Emission, Izv. Vyssh. Uchebn. Zaved. , Fiz. 1 1 : 1 33 - 1 34. Bazhenov, G. P., Mesyats, G. A., and Chesnokov, S. M., 1 975, On the Deceleration of the Emission Boundary of a Cathode Flare in a Diode Operating in the Mode of Explosive Electron Emission, Radiotekh. Elektron. 20:24 1 3-24 1 5 .

LARGE-CROSS-SECTION ELECTRON BEAMS

41 1

Bazhenov, G. P., Mesyats, G. A., and Proskurovsky, D. I., 1 970, Investigation of the Structure of Electron Flows Emitted from Cathode Flares, Izv. Vyssh. Uchebn. Zaved. , Fiz. 8:87-90. Belkin, N. V. and Aleksandrovich, E. G., 1 972, A Two-Electrode Tube for the Production of Nanosecond X-Ray Flashes, Prib. Tekh. Eksp. 2 : 1 96- 1 97. Belomytsev, S. Ya. and Mesyats, G. A., 1 987, Structure of Electron Beams in High-Current Diodes, Radiotekh. Elektron. 32: 1 569- 1 583. Belomytsev, S. Ya., Il'in, V. P., Litvinov, E. A., and Mesyats, G. A., 1 976, On the "Stroke" Effect in Explosive Electron Emission. In Development and Use ofIntense Electron Beam Sources (in Russian, G. A. Mesyats ed.), Nauka, Novosibirsk, pp. 93-95. Belomytsev, S. Ya., Korovin, S. D., and Mesyats, G. A., 1 980, The Screening Effect in High­ Current Diodes, Pis 'rna Zh. Tekh. Fiz. 6 : 1 089-1 092. Bradley, L. P., Parker, R. K., and Martin, T. H., 1 972, Characteristics of Relativistic Field Emission High Current Diodes. In Proc. V ISDEIV, Poznan, Poland, pp. l 59-1 64. Bugaev, S. P. and Mesyats, G. A., 1971, Electron Emission from the Plasma of an Incomplete Discharge over a Dielectric in Vacuum, Dokl. AN SSSR. 196:324-326. Bugaev, S. P., Kassirov, G. S., Koval'chuk, B. M., and Mesyats, G. A., 1 973a, Production of Intense Microsecond Relativistic Electron Beams, Pis 'rna Zh. Eksper. Teor. Fiz. 18:82-85. Bugaev, S. P., Koval'chuk, B. M., and Mesyats, G. A., 1973b, Pulsed Plasma Source of Charged Particles, USSR Inventor's Certificate No. 248 09 1 . Bugaev, S . P., Kreindel, Yu. E., and Schanin, P . M., 1 984, Large-Cross-Section Electron Beams (in Russian). Energoatomizdat, Moscow. Burtsev, V. A., Vasilievsky, M. A., and Gusev, 0. A., 1 978, Investigations of a Diode with an Explosive-Emission Cathode at Long Pulse Durations, Zh. Tekh. Fiz. 48: 1494- 1 503. Eden, J. G. and Epp, D., 1 980, Compact Coaxial Diode Electron Beam System: Carbon Cathodes and Anode Fabrication Techniques, Rev. Sci. Instrum. 51 (6):78 1 -785. Edwards, C. B., O'Neill, F., and Shaw, M. J., 1 980, 60-ns e-Beam Excitation of Rare-Gas Halide Lasers, Appl. Phys. Lett. 36:617-620. Erickson, G. F. and Mace, P. N., 1 983, Use of Carbon Felt as a Cold Cathode for a Pulsed Line X-Ray Source Operated at High Repetition Rates, Rev. Sci. Instrum. 54:586. Frenkel, J., 1 93 5, On Tonks's Theory of Liquid Surface Rupture by a Uniform Electric Field, Phys. Zw. Sowjet. 8:675-679. Garber, R. I., Granova, Zh. I., Mansurov, N. A., and Mikhailovsky, I. M., 1 969, A Field­ Emission High-Current Pulse Cathode, Prib. Tekh. Eksp. 1 : 1 96- 1 98. Gundel, H., 1 992, Electron Emission by Nanosecond Switching in PLZT, Integrated Fe"oelectr. 2:202. Hinshelwood, D. D., 1 984, Explosive Emission Cathode Plasmas in Intense Relativistic Electron Beam Diodes. Massachusetts Institute of Technology. Kotov, Yu. A., Litvinov, E. A., Sokovnin, S. Yu., Balezin, M. E., and Khrustov, V. R., 2000, Metal-Dielectric Cathodes for Electron Accelerators, Dokl. RAS. 370:332-335. Koval, B. A., Mesyats, G. A., Ozur, G. E., Proskurovsky, D. I., and Yankelevich E. B., 1 983, Explosive-Emission Nanosecond Low-Energy Electron Sources for Surface Material Treatment. In Pulsed High-Current Electron Beams in Technology (in Russian, G. A. Mesyats, ed.), Nauka, Novosibirsk, pp. 26-39. Koval'chuk, B. M., Lavrinovitch, V. A., Manylov, V. I., Mesyats, G. A., and Rybalov, A. M., 1 976, Pulsed Electron Accelerator for Excitation of Gas in Large Volumes, Prib. Tekh. Exper. 6 : 1 25 - 1 27. Levine, L. S. and Vitkovitsky, I. M., 1971, Pulsed Power Technology for Controlled Thermonuclear Fusion, IEEE Trans. Nucl. Sci. 18 (Pt 2): 1 05-1 12. Link, W. T. and Olander, W. C., 1 969, U.S. Patent No. 3 484 643.

412

Chapter 22

Loda, G. K. and Meskan, D. A., 1 977, Repetitively Pulsed Electron Beam Generator. In Proc. II Intern. Topical Conf on High Power Electron and Ion Beam Research and Technology, Cornell, NY, Vol. I , pp. 252-273. Loda, G. K., 1 977, Recent advances in cold cathode technology as applied to high power lasers. Ibid. , Vol. 2, pp. 897-890. Mesyats, G. A., 1 97 1 , The Role of Fast Processes in Vacuum Breakdown. In Proc. X ICPIG, Oxford, England (Pt II), pp. 333-363. Mesyats, G. A., 1 974, Generation of High-Power Nanosecond Pulses (in Russian). Sov. Radio: Moscow. Mesyats, G. A., 1 99 l a, High-Power Particle Beams for Gas Lasers. In Pulse Powerfor Lasers III: Proc. SPIE, SPIE Press, Los Angeles, Vol. 141 1 , pp. 2-14. Mesyats, G. A., 199lb, Vacuum Discharge Effects in the Diodes of High-Current Electron Accelerators, IEEE Trans. Plasma Sci. 19:683-689. Mesyats, G. A., 1 998, Explosive Electron Emission. URO-Press, Ekaterinburg. Mesyats, G. A. and Proskurovsky, D. 1., 1971, Explosive Electron Emission from Metal Points, Pis 'rna Zh. Eksp. Teor. Fiz. 13:7-1 0. Mesyats, G. A., Bychkov, Yu. 1., and Koval'chuk, B. M., 1 992, High-Power XeCl Excimer Lasers. In Intense Laser Beams: Proc. SPIE, SPIE Press, Los Angeles, Vol. 1628, pp. 70-80. Miller, R. B., 1 998, Mechanism of Explosive Electron Emission for Dielectric Fiber (Velvet) Cathodes, J. App/. Phys. 84:739. Parker, R. K., Anderson, R. E., and Duncan, C. V., 1 974, Plastmainduced Field Emission and the Characteristics of High Current Relativistic Electron Flow, J. App/. Phys. 45:2463-2478. Pigulevsky, E. D., 1 958, The Structure of the Piezoradiation Field in an Ultrasonic Microscope, Izv. Leningrad Electrotechnica/ Inst. 34:2 1 3 . Proskurovsky, D. I. and Yankelevich, E. B . , 1 983, A Large-Area Explosive-Emission Cathode. In High-Current Pulsed Electron Beams in Technology (in Russian, G. A. Mesyats, ed.), Nauka, Novosibirsk, pp. 2 1 -26. Ramirez, J. J, and Cook, D. L., 1 980, A Study of Low Current Density Microsecond Electron Beam Diodes, J. App/. Phys. 51:4602-46 1 1 . Ramirez, J., Prestwich, K., Clark, R., et a/., 1977, E-Beam for Laser Excitation. In Proc. II Intern. Topical Conf. on High Power Electron and Ion Beam Research and Technology, Cornell, NY, Vol. 2, pp. 89 1 -902. Rosocha, L. A. and Riepe, K. B., 1987, Electron-Beam Sources for Pumping Large Aperture KrF Lasers, Fusion Techno/. 1 1:577-6 1 1 . Rukhadze, A . A., Bogdankevich, L. S., Rosinsky, S . E., and Rukhlin, V. G., 1 980, Physics of High-Current Relativistic Electron Beams (in Russian). Atomizdat, Moscow. Schachter, L., Ivers, J. D., Nation, J. A., and Kerslick, G. S., 1 993, Analysis of a Diode with a Ferroelectric Cathode, J. Appl. Phys. 73 (12):8097-8 1 1 0. Smith, I., Champney, P., Hatch, L., Nielsen, K., and Shope, S., 1971, High Current Pulsed Electron Beam Generator, IEEE Trans. Nucl. Sci. 18:491 -493. Voropaev, S. G., Knyazev, B. A., Koidan, V. S., Konyukhov, V. V., Lebedev, S. V., Mekler, K. 1., Nikolaev, V. S., Smirnov, A. V., Chikunov, V. V., and Scheglov, M. A., 1 987, Production of a Microsecond High-Power REB of High Current Density, Pis 'rna Zh. Tekh. Fiz. 13:43 1 -435.

Chapter 23 ANNULAR ELECTRON BEAMS

1.

PRINCIPLE OF OPERATION OF DIODES

A problem with EEE electron sources is to decelerate the expanding cathode plasma. Investigations in this field have gone in two basic ways. The first way (discussed in the previous chapter) involves application of an electric field, while the second one is based on the use of a magnetic field. In the first case, it is necessary to make the plasma corresponding to the mode of saturated electron emission, i.e., to reduce its density. With this purpose, the current through the ecton zone is reduced to have an average current density of 0. 1 - 1 0 A/cm2 • For the production of kiloampere currents in diodes of this type, large-cross-section electron beams are formed. A magnetic field applied transverse to the discharge gap, as shown in first experiments performed by Baksht and Mesyats (1970), also reduces the velocity of expansion of the cathode plasma. This allows one to eliminate or substantially reduce the current toward the anode, thus moderating the anode processes, and to do away with the anode foil - the weakest element in an explosive-emission diode. The first foilless coaxial diodes with magnetic insulation (magnetically insulated coaxial diodes, MICD's) based on EEE cathodes were proposed by Friedman and Ury ( 1970). Diodes of this type generate annular electron beams that are used for the production of microwave radiation. The operation of MICD's is described in detail in the monograph by Bugaev et a/. ( 1 991). Relativistic microwave electronics became in fact the main consumer of the results of investigations of MICD's. We discuss this in detail in Chapter 27. Many design versions of magnetically insulated coaxial diodes are known. By the relative positioning of cathode and anode, MICD's can be

Chapter 23

414

subdivided into two types: normal and inverse (Fig. 23. 1 ). In a normal MICD (Fig. 23. 1 , a, b), the inner electrode is cathode, while in an inverse one (Fig. 23. 1 , .f) it is anode. An annular electron beam is formed from the plasma generated at the cathode in the process of EEE and extracted from the diode into a vacuum drift tube along the lines of magnetic force. If a positive voltage pulse is applied to the inner electrode (see Fig. 23. 1 , b), the diode becomes an inverse one. This type of diode is used to generate microwaves in inverted magnetrons (Close et al., 1 983) and to produce ion beams (Dreike et al. , 1 976; Luckhardt and Fleischmann, 1 977; Bakshaev et al. , 1 979). From a diode of this type the electron beam is not extracted. Below we mean by MICD's normal diodes. 1 2 3 4 5

(b)

1 2 3 4 5

(c)

1 2 3 4 5

d@f ;£5]C rr___J 1 2 3 4 5

Figure 23. 1. MICD configurations: conical (a), cylindrical (b), planar (c), with a conical anode (d), with a multipoint cathode (e), inverse-type (f) ; 1 - cathode, 2 - anode, 3 solenoid, 4 - drift tube, and 5 - magnetic lines

MICD's can also be classed by the configuration of lines of magnetic force. Diodes with a uniform (Fig. 23. 1 , c) and nonuniform (Fig. 23. 1 , a, d, e) magnetic field are distinguished. For MICD's of the first type, the induction of the magnetic field in the diode, Be, is equal to that in the region of beam transportation, B0• The average radius of a thin-walled magnetized electron beam is approximately equal to the radius of the cathode (rb ;::: rc ) . In a second-type MICD, the magnetic field at the cathode is lower than that in the drift tube. It increases from the cathode in the direction normal to the lines of magnetic force. The degree of nonuniformity of the magnetic field is characterized by the bottleneck ratio (ratio of the magnetic field components parallel to the diode axis in the drift tube and at the cathode) k = B01Bc . The radius of a thin-walled annular beam for this type of diode with a magnetic field of uniform cross section, according to the law of conservation of magnetic flux, is given by

ANNULAR ELECTRON BEAMS

415 (23 . 1 )

In inverse MICD's (see Fig. 23. 1 , f) both uniform and nonuniform magnetic fields are used. By the geometry of electrodes (Bugaev et a/., 1991), conical (Fig. 23. 1 , a), cylindrical (b), and planar diodes (c) are distinguished. In a conical diode, the beam radius and the electrode gap spacing can readily be controlled by moving the cathode along the axis. In a planar diode, it is possible to vary the transverse-to-longitudinal component ratio of the electric field at the cathode. However, in the region of the rectangular jump from the anode to the drift tube, the electric field is nonuniform, and this may result in an additional increase in transverse velocity of the beam electrons. The electric field can be made more uniform by using a conical anode (see Fig. 23. 1 , d). In MICD's, graphite and, more seldom, metal cathodes are used. Best investigated are plane (with a solid face surface) (see Fig. 23. 1 , b), tubular (sometimes referred to as annular or edge) (b), and multipoint cathodes (c) . For electric field enhancement, the surface of a plane cathode facing the anode is made rough or, for a tubular cathode, the thickness of the wall is reduced. A disadvantage of a plane cathode is the emission current from the end face that occurs at a high electric field, which is parasitic in microwave devices. The use of multipoint cathodes is also limited by the EEE excited at the electrodes between which the points are located (see Fig. 23. 1 , e). Therefore, tubular cathodes are most widely used in relativistic microwave electronics. The induction of the magnetic field in an MICD is chosen so that, at a given voltage across the diode, the electrons emitted by the cathode do not cross the electrode gap of width d = I ra - rc I (Fig. 23. 1 . b), where ra and rc are the anode and the cathode radius, respectively. The magnetic field induction at which the electron current at the anode is cut off is referred to as critical, Bcr . For relativistic electrons under the condition of conservation of the total magnetic flux in the electrode gap (Voronin and Lebedev, 1 973; Lovelace and Ott, 1 974), we have

(23.2) Here, deff is the effective electrode gap spacing, which, in a planar diode, is equal to the cathode-anode separation. For a diode of cylindrical geometry (Lovelace and Ott, 1 974), the effective gap spacing is given by

deff = d(l - dlra) .

416

Chapter 23

For a cylindrical diode, the measured Bcr (Bekefi et a!. , 1 975; Orzechovski and Bekefi, 1 976) coincides, within 5%, with that calculated by formula (23.2). However, both in normal diodes (Bekefi et a!. , 1 975; Gorev et a/., 1 985) and in inverse ones (Luckhardt and Fleischmann, 1977; Bakshaev et a/. , 1 979), an unappreciable electron current across a magnetic field B > Bcr (less than 10% of the extracted electron beam current) was detected. The passage of this supercritical current in a diode, which is associated with diocotron instability of the electron layer around the cathode, correlates with the excitation of microwave oscillations of widely varying frequency (Bekefi et a/. , 1 975; Orzechovski and Bekefi, 1 976). For B > Bcr , the anode current may result in the formation of anode plasma, which is frequently undesirable. The conduction current flowing through the inner electrode (cathode) in a coaxial cylindrical diode with an external magnetic field B induces an azimuthal magnetic field Be . In this case, the trajectories of electrons in the diode are determined by the combined influence of both magnetic fields (Voronin and Lebedev, 1 973; Bekefi et a/., 1 975; Orzechovski and Bekefi, 1 976). The insulation of an electrode gap created only by the field Be is termed magnetic self-insulation. It is widely used in high-current accelerators to transfer energy from energy stores to diodes through coaxial vacuum lines. The critical current at which the self-insulation mode is attained is given by

1cr =

2 1 ' ] 2 t ) [ I__ ( Zo

+

2 mc eV

'

where Z0 is the wave resistance of the line and the diode.

2.

(23.3) V is the voltage applied to

DEVICE OF ELECTRON GUNS FOR MICD'S

The electron guns of MICD's intended for the production of high-current relativistic electron beams (REB' s) have some design features. The main elements of such an electron gun (Fig. 23.2) are a vacuum insulator, a cathode-anode unit, and a magnetic system. The residual gas pressure in the acceleration tube is typically � 1 o-2 Pa. Vacuum insulators are made solid (Fig. 23.2, c) or section (Fig. 23.2, a, b, d). Such an insulator is placed in a metal case (a, b) or serves as a case for the electron gun (c, d). The voltage is distributed over the insulator with the help of a capacitive, inductive, or resistive divider. If the first type of voltage division is used, the insulator sections - alternating dielectric and metal

ANNULAR ELECTRON BEAMS

417

rings - serve as capacitors. For inductive voltage division, a spiral is wound, with a certain pitch, on a solid insulator. For pulses of microsecond duration, resistive voltage dividers are used. For section insulators, these usually are chains of resistors fixed sequentially on grading metal rings. In solid insulators, resistive division of voltage can be realized with the help of a conducting liquid (electrolyte). In this case (Burtsev et a/. , 1 979), the insulator (see Fig. 23 .2, c) consists of two coaxial cylinders the space between which is filled with a solution of copper sulfate. The general requirement to voltage dividers is that the consumed current must be lower than the beam current. For a section insulator at a voltage pulse duration tP � 1 fJS, the electric field strength averaged over the insulator length is chosen to lie within the limits 1 0-20 kV/cm (Martin and Clark, 1 976). At nanosecond voltage pulse durations, it is several times greater, being typically � 80 kV/cm (Mesyats, 1 974). 1 2

3 4567 8

(b)

(d)

1 2

4 56 7 8

3

3 2 5 4 1 6

7

8

Figure 23.2. Schematic diagrams of the electron guns of MICD's: 1 vacuum insulator, 2 cathode holder, 3 - reflector, 4 - anode, 5 - cathode, 6 - solenoid, 7 - magnetic lines, and 8 collector -

Another challenge in providing efficient operation of electron guns is associated with the suppression of the backward current and the leakage from the cathode holder. These parasitic currents carry away part of energy and reduce the accelerator efficiency, which is determined as the ratio of the energy of the extracted electron beam to the energy ofthe high-voltage store. Besides, they influence the operation of the diode and the dielectric strength ofthe insulator. The backward current in an MICD is caused by the presence of an accelerating electric field component at the rear side of the cathode or cathode plasma. In first MICD's, the cathode was usually fixed on a holder of smaller diameter (see Fig. 23 . 1 , a, b). At a high electric field, ectons arose at the rear side of the cathode, and the electron beam was accelerated along

418

Chapter 23

the lines of the falling magnetic field toward the vacuum insulator. In this electrode geometry, the backward current can exceed the current of the forward beam of electrons injected into the drift tube. As the electrons hit on the insulator, they initiate breakdown over its surface (Bugaev et al. , 1 99 1 ; Burtsev et al. , 1 979), while getting on the anode, they cause the formation of anode plasma and the breakdown of the diode. When the cathode and the cathode holder are of the same diameter, the backward current is formed at the rear side of the cathode plasma, which, at microsecond durations of the voltage pulse, expands for several centimeters transverse to a uniform magnetic field (see Fig. 23. 1 , c). In this case, the backward current is lower than the forward one and it increases as the cathode plasma expands. In a nonuniform magnetic field (see Fig. 23. 1 , d), this current arises simultaneously with the forward beam within the rise time of the voltage pulse upon excitation of EEE at the cathode edge. To suppress the backward current, it is necessary to realize conditions under which the lines of magnetic force that emerge at the surface of the anode unit and at the insulator do not cross the emitting surface of the cathode (Kovalev et al. , 1 977). With this purpose, a reflector of electrons of conical (Fig. 23.2. a), plane (b) or spherical shape is generally placed between the cathode and the cathode holder. Thus the lines of magnetic force that, in view of the transverse expansion of the cathode plasma, correspond to the cathode radius should pass below the top of the cathode holder (a, b). Other methods of suppression of the backward current are based on a proper choice of the magnetic field configuration. Thus, the backward current in a uniform coaxial line, making 25-35% of the beam current, was eliminated by applying a magnetic field of bottleneck configuration behind the cathode (Bugaev et al. , 1 980). When the acceleration tube was immersed in a magnetic field (Fig. 23.2. c), the leakage current from the cathode holder (Burtsev et al. , 1 979) was also eliminated. In an electron gun (Voronin et al. , 1 98 1 ) where the solenoid was mounted inside the insulator (d), were practically no losses of the electron current. The efficiency of the accelerator with the conventional gun (b) at a voltage of 700 kV across the diode was 20%, while that of the accelerator with the gun shown in Fig. 23.2, d at the same voltage was 75-80%. These efficient electron guns are used only for the production of annular beams of small diameter. In the guns designed as one presented in Fig. 23.2, a, the cathode holder has a large area, especially in megavolt devices. This decreases the average electric field at which EEE arises and there is leakage from the cathode holder. Thus, in experiments carried out on the Gamma accelerator, the explosive emission delay time was 0.2-0.4 J.!S at E = 80-120 kV/cm and a few microseconds at E = 60 kV/em (Bastrikov et al. , 1 988). The leakage currents were as large as 30-60 kA, and this substantially reduced the efficiency of the accelerator.

ANNULAR ELECTRON BEAMS

419

The advantage of the gun presented in Fig. 23.2, b i s the small length of the cathode holder. For the reduction of the leakage current, an additional solenoid is used which is wound on the vacuum chamber.

THE CATHODE PLASMA

3.

IN A MAGNETIC FIELD

As shown in Chapter 3, application of a magnetic field to an MICD does not change the time delay of EEE occurrence. However, this field strongly influences the process of plasma formation. Photographs of the plasma luminosity taken through the flange of the drift tube have shown that the number of EEE centers increases with magnetic field, improving the uniformity of the emission plasma layer. This also follows from the photograph of the plasma luminosity at the surface of a graphite cathode (Fig. 23.3). The processes of plasma generation were investigated in detail by Belomytsev et a/. (1 980) and El'chaninov et al. (1981). In an MICD, a voltage pulse of amplitude 200 kV and duration 5 ns was applied to a tubular graphite cathode whose wall thickness was 0.5 mm . The magnetic field in the diode was varied from zero to 1 0 kGs. The radius of the cathode flare (CF) was small (r = vtp = 0. 1 mm). The principal screening effect was from the charge of the electron current. Investigations have shown that the number of emission centers increased in the main in the region of low magnetic fields, where rL » vtp (rL being the Larmor radius of electrons). In this case, the linear density of flares over the perimeter can be approximated by the relation N oc Ba., where a � 0.5, and the distance between two flares is AB-0·5 , where A - 1 cm·kGs0·5• In a rather strong magnetic field, where rL vtp, the increase in number of ectons was slower. �

�

• . I

•

'

•

(a)

•

' -. �'

(b)

(

"'" .

'

. . ..

•

• ,

... .

•

(c)

""

•

"

- �

�

.,

""

..

�

�

(d)

Figure 23. 3. Photographs illustrating the effect of the magnetic field on the density of cathode flares in a coaxial diode with a cylindrical cathode. B = 0 (a), I (b), 3 (c), and 1 0 kGs (d)

The formation of a plasma emission surface critically depends on the dynamics of formation of EEE centers, which was investigated for two

Chapter 23

420

essentially different experimental conditions (Mesyats and Proskurovsky, 1 989). In one case, the electric field strength in the diode was insufficient for the excitation of explosive emission at the cathode and the primary ecton plasma was created by an igniting electrode powered from a special voltage source. In the other case, EEE was initiated by an external electric field. In the first experiment (Fig. 23.4, a), the cathode was a copper disk of diameter 12 mm and thickness 0.5 mm. The electrode separation was 5 mm. For studying the dynamics of formation of primary ectons, probes made of a thin copper wire were placed some distance from the site of ignition. A rectangular voltage pulse of duration up to 1 .3 �s and amplitude up to 30 kV was applied to the diode. Simultaneously, a pulse of duration 5 ns was applied to the igniting electrode, and thus the site of formation of a primary ecton was fixed. It was found that new ectons appeared practically only during the high-voltage stage of the vacuum discharge and were multiplied along the direction of the Ampere force. With the probes, the time delay td to the appearance of explosive emission from a probe (Fig. 23.4, b) and the plasma potential at given points of the cathode were determined. The probe measurements and photographs of the plasma have shown that the velocity of motion of the boundary of formation of a primary ecton is (1-2} 106 cm/s and does not depend on the magnetic field in the range 2-10 kGs. 0.8 r-------,

�

0.6

0.4

0.2

0

2

4

x

6

[mm]

8

10

12

Figure 23. 4. Sketch of a coaxial diode (a) and the time delay to the appearance of a signal from a probe placed at a distance x from the site of ignition (b)

The characteristics of the cathode plasma formed during EEE in a magnetic field were investigated by Mesyats and Proskurovsky (1 989), Koshelev (1979), Gorbachev et al. (1 984), Stinnett et al. (1982; 1 984), and Baksht et a!. ( 1977). The ionic composition of the plasma was determined by its spectral luminescence in the region 200-700 nm. Both discharge-time­ integrated (Baksht et al. , 1977) and time-resolved measurements were performed (Stinnett et a!. , 1 982; 1 984 ). The plasma density was measured with the help of laser interferometry (Baksht et al. , 1 977; Gorbachev et al. , 1 984), schlieren photography (Stinnett et al. , 1 982), and holography (Stinnett et al. , 1 984) and by the Stark breadth of the lines of hydrogen

ANNULAR ELECTRON BEAMS

42 1

(Bekefi et al. , 1 975; Baksht et al. , 1 977). The minimum plasma density evaluated by the above methods was 1015-1016 cm3; the spatial resolution was :?: 0. 1 mm The plasma temperature was estimated (Stinnett et al. , 1 982) by the relative intensity of the luminescence of spectral lines under the assumption of local thermodynamic equilibrium. The experiments were carried out with voltage pulses of nanosecond (< 1 00 ns) and microsecond (� 5 J.LS) duration and amplitude 0.2-2 MV. When comparing the results obtained under various experimental conditions, the linear current density /1 = 1/2rrrc (current per unit length of the cathode perimeter) can be used as a parameter. Spectral investigations of the cathode plasma luminosity were carried out with graphite, aluminum, and copper cathodes (Baksht et al. , 1 973, 1 977; Bugaev et a/., 1 98 1 ). The spectrograms obtained testified that the plasma contained species of the cathode material ( AI I, AI II, AI III, Cu I, Cu II ), desorbed gas, and products of cracking of hydrocarbons (H, C I, C II, etc.), and the intensity of the luminescence of the last was much greater than that of the metal and was practically the same for all cathode materials (C, A 1 , Cu). Photometry in the axial direction showed a clear peak at the edge o f the cathode. In the radial direction, the intensity of the lines of the metal ( Cu I, Cu II ) dropped in going deeper in the gap more abruptly than that of the lines of C2 , H�, and C II. The latter might be due to the different mechanisms of plasma expansion across and along the magnetic field. Investigations carried out by different researchers allow the following principal conclusions: the cathode plasma consists of the cathode material coming during EEE, the desorbed gas, and the products of cracking of the oil used for the production of vacuum in the diode; hydrogen can make an appreciable percentage of the plasma. For a wide range of experimental conditions (/1 = 0. 1 - 1 0 kA/cm), the plasma density near the cathode is 1 015-1 016 cm-3 and quickly decreases in going deeper in the discharge gap. The plasma with a high density, n = 1 018- 1 020 cm-3, which is necessary for self-maintenance of ectons, is localized near the cathode within 0 . 1 mm The pressure of the magnetic field (B - 1 04 Gs) is considerably greater than the pressure of the cathode plasma (B2/8rr » n1) even at a distance of 0. 1 mm from the cathode. After the occurrence of EEE, the cathode plasma appears in a magnetic field and starts moving both transverse to and along this field. It should be noted that the plasma processes were investigated in detail for a cylindrical MICD with a uniform magnetic field (Fig. 23. 1 , b). Therefore, it is convenient to consider the physical phenomena in an MICD of simple geometry as an example. To elucidate the role of the cathode plasma in the breakdown transverse to the magnetic field, the diode gap closure time t5 and the time delay to the .

.

422

Chapter 23

appearance of cathode plasma were measured at different points in radius down to the anode with the help of the collector technique (Baksht et a/. , 1 977). For tubular graphite and aluminum cathodes, the breakdown transverse to the magnetic field develops as the cathode plasma approaches the anode (Bugaev et a/. , 1 98 1 ). The anode current before the closure of the diode gap was measured to be about 10% of the beam current. The time delay to the appearance of current toward the anode decreased with decreasing the electrode gap spacing d and for a current of 150 A and d = 0.65 em it was - tsf2. Under these conditions, the velocity of the cathode plasma, v1. , averaged over the most part of the gap, and the rate of closure of the diode, dlt5, coincide to within the measurement error. Thus, the anode plasma, which can be formed if electrons reach the anode, has only a slight influence on the breakdown of the diode. Similar results were obtained for MICD's with plane graphite and copper cathodes (Baksht et a/., 1 977). Additional supporting evidence for the dominant role of the cathode plasma in the breakdown of a diode is experiments (Bugaev et a/., 1991) in which a change of the cathode geometry, with other things being equal, changed the value of dlt5 • Thus, for d = 6 mm, V = 300 kV, and B � 10 kGs, dlts was 5 · 1 05 crn/s for a plane cathode and < 2· 1 05 crn/s for a point cathode. For the latter type of cathode (d = 3 mm, B = 1 2 kGs), dlt5, as follows from Table 23. 1 , varied with cathode material. Table 23. 1. Material

AI

w

Mo

Cu

c

d/t5, 1 05 cm/s

2.3

2.6

2.7

3.6

6.6

With the help of a drift tube, the dependences ts(/b) and ts(rc) were investigated (Bugaev et a/. , 1 983). The first one was obtained at a fixed voltage ( V = 240 kV) and a fixed magnetic field (B = 24 kGs) for rc = 2.0 em and d = 0.5 em. The increase in beam current from 0.6 to 3.5 kA resulted in an insignificant (-1 5%) increase in diode closure time. Experimental check of the effect of rc on ts was carried out at a constant B = 24 kGs, d � 1 em, and a linear beam current density !J2nrc � 0.09 kA/cm. As rc was increased from 2 to 4.5 em, the closure time increases from 1 .4 to 1 .8 �s. The dynamics of the cathode plasma motion transverse to the magnetic field in a cylindrical MICD depends on the cathode geometry and material, on the magnetic field, and on the plasma density and direction of its propagation (toward the anode or toward the axis of the diode) (Baksht et a/., 1 977). The plasma is essentially nonuniform: intense bursts are observed on the oscillograms of the collector current and PMT signal. Collector measurements for a graphite cathode have shown that the dynamics of the radial motion of the cathode plasma is different for

ANNULAR ELECTRON BEAMS

423

magnetic fields lower or greater of an optimum Bopt at which v_1_ averaged over the electrode gap is a minimum. For B < Bopr. the radial velocity of the plasma, originally equal to 2· 1 06 cm/s, decreases and then increases a little. For B > Bopr. it increases with distance from the cathode. In the case B � Bopr. the plasma velocity in the gap is approximately constant. For metal cathodes (Al, Cu) and B > Bopr. it increases with distance from the cathode. It seams that in this case, as well as for a graphite cathode at B > Bopt. the region where the plasma velocity decreases is closer to the cathode. It should be noted that at residual gas pressures over 0. 1 Pa the velocity of propagation of the plasma front from cathode to anode does not depend on magnetic field (B 6-27 kGs) and is invariable on a radius. The velocity of motion of the cathode plasma along the magnetic field, '11! • was measured with the help of a photoelectric technique (Bugaev et a!. , 1 99 1 ), microwave interferometry (Nikonov et a!. , 1 983 ), and capacitive voltage dividers (Bugaev et al., 1 99 1 ). With an eight-millimeter-band microwave interferometer (Nikonov et al. , 1 983), it was possible to measure plasma densities n 2: 1 0 1 1 cm3 and thus follow the motion of low-density peripheral layers. Capacitive voltage dividers arranged along a drift tube are usually used to measure the potential difference between the electron beam and the drift tube, �Vb, which is lower than the voltage applied to the diode. As the cathode plasma approaches a capacitive voltage divider, the amplitude of the signal of the divider increases to a value corresponding to the voltage across the diode. By the inflection in the oscillogram of the signal from the capacitive gage, the time is determined at which the plasma carrying the potential of the cathode approaches the gage. The velocity of propagation of the collector plasma along the magnetic field was also measured using a photoelectric technique (Bugaev et al. , 1 99 1 ) and microwave interferometry (Nikonov et al. , 1 983). Despite the rather small number of techniques used, the experimenters were managed to distinguish the contributions of the cathode and collector plasmas to the breakdown of a diode and to follow the expansion of the cathode plasma transverse to and along the magnetic field. The current pulse duration of the beam formed in an MICD can also be limited by the breakdown along the magnetic field. The mechanism of the vacuum breakdown of the cathode--collector gap and the motion of the cathode plasma along a uniform magnetic field were studied by Bugaev et al. ( 1 99 1 ) and Nikonov et al. ( 1 983). The longitudinal vacuum breakdown in diodes with tubular cathodes (C, AI) of external radius rc = 3.0 em (d 2.6 em) is best investigated. A voltage pulse of amplitude 200 kV and duration -3.5 J.lS was applied to the diode: the beam current was about 1 .5 kA. The distance was varied with the help of a movable collector. The magnetic field was varied in the limits 3-27 kGs; the residual gas pressure

=

=

Chapter 23

424

was 10-3-1 0- 1 Pa. To examine the propagation of the cathode plasma and the formation and expansion of the collector plasma use was made of a system of five capacitive voltage dividers, placed sequentially in the drift tube, and a photoelectric technique. With the help of these techniques, the time delay td to the occurrence of the cathode plasma at various distances from the cathode and the time of closure of the cathode-collector gap were measured. 3

10

20

z

[em]

30

40

Figure 23.5. Time delay to the appearance of the cathode plasma, td, measured by a PMT (1-4) and capacitive voltage dividers (5), as a function of the distance from a graphite cathode and the time of closure along the magnetic field (6) as a function of the cathode--collector separation. B = 1 8 kGs, p = 3· 1 0-3 Pa. F = 1 00F0 (1), 3F0 (2), 1 .5F0 (3), and F0 (4)

All measurements were performed with graphite cathodes and a collector in a magnetic field of 1 8 kGs. From the results obtained (Fig. 23.5), it follows that the td values measured by two methods agree to each other and to the closure times for various cathode-collector separations [ lc lt11 � (1-1 .6) · 1 07 crnls]. The increase in residual gas pressure from 10-3 to 1 0- 1 Pa resulted in a 20-30% increase in 111 Uc = 20 em), and td increased as well. Measurements by the photoelectric technique have shown that the time delay to the occurrence of the cathode plasma at collectors made of graphite and stainless steel was equal, respectively, to 1 .2 and 0.25 J.lS, and the velocity of its propagation along the magnetic field was about 5 · 1 05 cm/s in both cases. The power density of the beam at a collector was -10 MW/cm2• The velocity of the collector plasma measured by a microwave interferometer under similar experimental conditions (Nikonov et al. , 1 983) was ( 6-7) · 1 05 cm/s. At megavolt voltages across the diode and the beam power density at a collector equal to about 1 GW/cm2, the influence of the collector plasma on the breakdown along the magnetic field was found to be unappreciable (Bugaev et al., 1 99 1). Thus, the breakdown of the cathode­ collector gap in a uniform magnetic field is determined by the propagation of the plasma formed at the cathode during explosive electron emission.

ANNULAR ELECTRON BEAMS

425

1 .00 "'

� .;:: 0.75 ,_...,

20

40 z [em]

60

Figure 23.6. Time delay to the appearance of the cathode plasma as a function of the distance from the cathode. /b = 1 0 kA, V= 0.9 MB (J) and 20 kA, 1 .3 MV (2)

The velocity of the cathode plasma front increases with current and reaches v 11 � 1 08 cm/s for Ib � 1 0 kA. As the current is further increased, v 11 does not increase; however, the region of accelerated motion of the plasma near the cathode becomes smaller. The measurements of the time delay to the occurrence of the cathode plasma at various distances from the cathode for Jb � 1 0 kA are given in Fig. 23.6. Thus, it is possible to distinguish two components in the motion of cathode plasma along a magnetic field: a hydrodynamic expansion with a constant velocity of (2-2.6)· 106 cm/s and an accelerated motion.

4.

FORMATION OF ELECTRON BEAMS

Let us consider the principal characteristics (current, potential, and structure) of annular electron beams formed in cylindrical (ra R) MICD' s (see Fig. 23 . 1 , b) with a uniform magnetic field. Investigations have shown (Gleizer et al. , 1 975; Voronin et al. , 1 978) that the beam current depends on magnetic field. As the magnetic field is increased, the current increases for B < Ber, reaches a maximum at B � Ben decreases for B > Ben and becomes practically independent of magnetic field for B � (2-3)Bcr· For B < Ben the beam current is lower than the maximum current because of the arrival of electrons at the anode. At B :::::: Bcr , the thickness of an annular beam is a maximum and its external radius is close to the radius of the drift tube. The basic contribution to the beam current is made by the electrons emitted from the cylindrical surface of the plasma cathode transverse to the magnetic field. For B » Ben the external radius of the beam is equal to the external radius of the cathode plasma and the main contribution to the beam current is made by the electrons emitted from the face surface of the plasma along the magnetic field. ==

Chapter 23

426

In solving the problem on the formation of an REB in an MICD, two models were used that supposed that the beam current is determined, respectively, by the throughput of the drift tube (Voronin and Lebedev, 1 973; Nechaev and Fuks, 1 977) and by the region of formation of the beam, i.e., by the diode (Fedosov et al. , 1 977; Fedosov, 1 982). We now consider the second model since it better agrees with experiment. The problem was solved for a cylindrical MICD with a tubular cathode of wall thickness he and an infinitely strong guide magnetic field. The approximation of an infinitely strong magnetic field obviously holds if (Fedosov et al. , 1 977)

E « .Jr - I B

(23.4)

'

where r = eER/mc 2 + 1 ; � = v0 /e ( v0 being the velocity of electrons in the ra. The electron flow in a diode under these drift channel), and R conditions is described by the Poisson equation

f).y

=

e 4njy me -1 ' 3

z \/r;--; Y

=

=

y 1+

e\jl me 2 '

(23.5)

where j is the beam current density depending only on radius and \jf is the potential. The boundary conditions are: y = r = 1 + e V/me2 at the anode and y = 1 at the cathode. Besides, the emissivity of the cathode is assumed infinite. Multiplying (23.4) by dyldz , integrating over the internal space of the diode (except the volume occupied by the cathode), and using Eq. (23.5) for the drift space and the boundary conditions, we obtain Yb ra Y b ( Y b + 1) - 2r = -In - rc Y b - 1

(-dy )2 (1 + 2 ) dr

2

y

rdr .

(23.6)

Here, y b = 1 + e\jlblme 2 is the relativistic factor at the external boundary of the electron beam in the drift space, and the integration on the right side is carried out over the beam thickness at z = +oo . It should be noted that (23.6) is a consequence of the laws of conservation for the energy and the Z-{;Omponent of a pulse in the system. For a rather thin-walled beam we have rhcl rc ln (ralrc ) « I , the right side in (23.6) can be neglected, and we obtain Yb

[

=

.Jo.25 + 2r - o.5 .

]

(23.7)

Using (23.5), we find the current of a thin-walled annular beam in the drift space:

ANNULAR ELECTRON BEAMS

427 (23.8)

Substituting Yb determined by expression (23.7) into (23.8), we obtain the current of the beam formed in an MICD with a thin-walled tubular cathode. The above theory was developed by Fedosov (1 982), and we refer to the space charge current determined by formula (23.8) as Fedosov's current. Let us compare the results obtained for MICD's to the characteristics of a beam with a limiting transportation current lnm· The potential of a nonrelativistic beam (kinetic energy of electrons) formed in an MICD is given by 'l'b � 2V/3 . The beam current thus is equal to lum i.J2 . For a relativistic beam, Yb � J2f , and for the limiting current we have Y b = W . The current an ultrarelativistic beam in an MICD tends to its limiting value. In MICD' s, alongside with tubular cathodes, plane cathodes are also used. Plasma is formed in the main at the side cylindrical surface of such a cathode, while its face surface does not emit and the electric field at this surface is nonzero, and thus an annular electron beam is formed in the diode. For an MICD with a thin-walled tubular cathode, a method for the calculation of the REB parameters at an arbitrary external magnetic field was proposed (Fuks, 1 982) based on the Brillouin model of a beam (Nechaev et a/. , 1 977). In contrast to the work by Nechaev et al. (1977), who used the assumption that the beam current reaches its limiting value in the transportation channel, Fuks (1 982) solved the problem of the formation of an REB taking into account the laws of conservation of momentum flux and moment of momentum for the electric and magnetic fields and for the beam electrons. The experimental data of Bugaev et al. (1991) are in better agreement with the results of these calculations than with the predictions of the model by Nechaev et al. ( 1977). For numerical simulations of beams formed in MICD's with a uniform magnetic field, the method of large particles (Jones and Thode, 1 980) or the method of tubes of current (Gorshkova et al., 1 980) was used. The general conclusion is that the limiting beam current is not achieved in transportation. We now consider in more detail the results of numerical calculations for different diodes with the same voltage V 360 kV (Bugaev et a!., 1 99 1). Calculations were performed for tubular cathodes of thickness he = 2 mm with a rounded radius of 1 mm and for plane cathodes with a rectangular or 2-mm radius rounded edge. The external radii of the cathode and cathode holder were usually equal, and the length of the cathode-anode coaxial cavity was (3-10)-d. For comparison, calculations were performed for an MICD with a cathode whose radius, rc = 3.0 em, was larger than that of the cathode holder ( 1 .2 em); the length of the cathode was 3.0 em, and the

=

428

Chapter 23

electrode separation was 2.6 em. Other things being equal, no difference was revealed for the above two cases. In a cylindrical MICD with a plane cathode having a rectangular edge, an increase in magnetic field increases the current density of the beam and improves its annular shape (Fig. 23.7) since the main current is transferred along the external wall of the beam. The (slight) widening of the beam at the internal wall is less than that at the external one. When a cathode with a rounded edge is used, the beam at the external wall is practically not widened and the distribution je(r) is more graded. The current density at the internal wall of the beam is somewhat increased irrespective of the type of cathode. In what follows, we consider experiments that were performed to compare measurements of the current Jb and potential \jib of thin-walled annular beams formed in MICD's with a strong guide magnetic field with the above results of analytical and numerical calculations. 1 .2 "'s

�

4

(a)

(b)

o.9

�� 0.6 ·�

-�

O L-_L__L_�___L__L_� 2.8

2.88

r [em]

2.96

3.04

0 lr--2.8

2.88

r'""';"1..., 2.96 r [em]

Figure 23. 7. Radial distribution of the electron beam current density in a cylindrical MICD with a rectangular-edge plane cathode for B = 6 (a) and 1 8 kGs (b); ra = 5.6 em; rc = 3 em, and V = 360 kV (calculations)

Let us first discuss the measurements of the beam potential, which substantially vary depending on whether or not the limiting beam current is achieved. The potential of a thin-walled annular beam is \jib = V - � Vb, where � Vb is the potential difference between the beam and the drift tube. The value of � Vb was determined using a capacitive voltage divider or from the energy of negative ions accelerated in the gap between the beam and the drift tube (Bolotov et al. , 1 980). In the experiment (Bugaev et al. , 1991), a cylindrical MICD with a thin-walled tubular cathode (ra = 5.6 em, rc = 3.0 em, he = 1 mm, V = 500-650 kV, B = 6-27 kGs) was used. Measurements were carried out directly after the pulse rise time C tr � 75 ns) when the voltage (current) peaked. In this case, the cathode plasma moved transverse to and along the magnetic field for small distances, and a thin-walled annular beam was formed in the diode. The distance between the cathode and the voltage

ANNULAR ELECTRON BEAMS

429

divider, equal to 1 6.5 em, was greater than the length of the beam formation zone, - 1 .5ra (Fig. 23.8). No effect of the magnetic field on the measured characteristics ('!'b, Jb) was revealed for B = 6-27 kGs. With the measurement error -30%. The ratio 'l'biV � 0.5 differed from its theoretical value [Eq. (23.7)] by no more than 10%. Note that in the case that a limiting current was achieved 'l'biV was about 0.25. The ratio of the beam current to its limiting value was approximately equal to 0. 7. The beam current calculated by formula (23.8) for the measured V and 'l'b differed from the measured Jb by no more than 25%. Comparison of the measured current of a thin-walled beam, Jb, with hcaJc calculated by formulas (23.7) and (23.8) for a cylindrical MICD with a thin­ walled tubular cathode (he = 1 mm, B = 2 1 kGs) is given in Table 23.2. Table 23.2. V, MV

ra, Cm

rc, em

Ib

fb calc• kA

/b /h calc

1 .5

8.6

3.0

1 1 .6

1 1 .6

1 .00

1 .57

5 .6

3.0

20.5

20.7

0.98

2.36

5.6

3.0

24.0

34.9

0.69

2.70

8.6

3.0

1 3.6

24.4

0.56

It can be seen that at a diode voltage V :$ 1 .6 MV the measured beam current Jb is practically equal to the calculated h calc> while at V > 2 MV we have Jb < h calc This is due to the screening action of the electron flow that is emitted from the top of the reflector (see Fig. 23.2) with an electric field at the reflector E � 1 00 kV/cm and moves between the cathode and the anode. .

Marx generator

�

� � 14 'ilm====�

Figure 23.8. Experimental setup for investigations of the dynamics of expansion of the cathode plasma on the Gamma accelerator: chopping spark gap, 2, 8 - capacitive voltage dividers, 3 vacuum insulator, vacuum chamber, 5 - cathode holder, 6 reflector, 7 cathode, 9 drift tube, - ring collector, - shunt, 12 - conical collector, 13 - solenoid with alignment coils, and Rogowski coils

-

10 14-

4-

111

-

430

Chapter 23

The formation of annular beams in an MICD with a plane cathode was investigated experimentally (Bugaev et a/., 1 99 1 ) The photographs of the plasma in the diode, collector measurements of the distribution of the beam current density in radius, je(r), and beam "autographs" obtained in this experiment allow the conclusion that plasma is formed at the edge of the cathode. At the end face, under the conditions of the experiment ( V = 370-470 kV), there are individual EEE centers whose number decreases with distance from the external edge of the cathode. Thus, at the axis of the diode, the current onto the collector was absent throughout the voltage pulse ( tp ::::: 3 J.!S). Preliminary experiments showed that when a graphite cathode was used, the beam current increased and the beam were more uniform in azimuth. The uniformity also increased with magnetic field. All this is associated with the conditions of plasma formation at the cathode. Note that in all experiments described only graphite was used. The measurements for tubular and plane cathodes of MICD's and numerical calculations are in good agreement. Comparative beam current measurements were carried out under identical conditions for tubular and plane cathodes in a cylindrical MICD (Bugaev et a/., 1 99 1 ; Straw and Clark, 1 979). To eliminate the electron emission from the end face of the cathode, the voltage across the diode was low: V = 1 00-1 20 kV (Bugaev et a/. , 1 99 1). In the experiments (ra = 3 .0 em, re = 2.2 em, he = 1 mm), measurements were carried out after the voltage pulse rise time (tr ::::: 50 ns) in a magnetic field B = 1 8 kGs. The current from the plane surface of the plane cathode was absent. In this case, the current in the diode with a plane cathode was less than that in the diode with a tubular cathode by 25%. In the diode with ra = 2.35 em, re = 0.64 em, he = 1 mm, and V = 2 MV, the beam current from the tubular cathode was greater than that from the plane one by 7%. The limiting current was calculated for an indefinitely thin-walled annular beam. Investigations of MICD's with a uniform magnetic field have shown that the expansion of the cathode plasma cannot be decelerated by merely increasing the magnetic field. The velocities of the plasma transverse to and along the magnetic field increase with the voltage across the diode and for V- 1 MV they reach -106 and -108 cm/s, respectively. These high velocities complicate the production of REB's with a current pulse duration fp � 1 J.!S in MICD's of this type. Here, the increase in beam energy is due to the increase in dimensions of the region of REB formation. An increase in pulse duration fp is achieved by using a nonuniform magnetic field increasing from cathode to anode (Dolgachev and Zakatov, 1 983). Accelerators based on MICD's are described in Chapter 28 where we discuss the operation of high-power microwave generators. .

ANNULAR ELECTRON BEAMS

43 1

REFERENCES Bakshaev, Yu. L., Blinov, P. I., Golgachev, G. P., and Skoryupin, V. A., 1 979, Acceleration of lons in a Magnetically Insulated Diode, Fiz. P/azmy. 5: 1 29- 1 3 1 . Baksht, R. B., and Mesyats, G . A., 1 970, Effect o f a Transverse Magnetic Field on the Electron Beam Current at the Initial Stage of a Vacuum Discharge, Izv. Vyssh. Uchebn. Zaved. , Fiz. 7: 144- 146. Baksht, R. B., Bugaev, S. P., Koshelev, V. I., and Mesyats, G. A., 1977, On the Properties of the Cathode Plasma in a Magnetically Insulated Diode, Pis 'ma Zh. Tekh. Fiz. 3:593-597. Baksht, R. B., Kudinov, A. P., and Litvinov, E. A., 1 973, Investigation of Some Characteristics of the Cathode Flare Plasma, Zh. Tekh. Fiz. 43: 1 46- 1 5 1 . Bastrikov, A . N., Bugaev, S . P., Kiselev, I . N., Koshelev, V . 1., and Sukhushin, K . N., 1 988, Formation of Annular Microsecond Electron Beams at Megavolt Voltages across the Diode, Ibid. 58:483-488. Bekefi, G., Orzechovski, T. J., and Bergeron, K. D., 1975, Electron and Plasma Flow in a Relativistic Diode Subjected to a Crossed Magnetic Field. In Electron Research and Technology: Proc. Intern. Top. Electron Conj Beam Res. Techno/. , Albuquerque, NM, Vol. 1, pp. 303-345. Belomytsev, S. Ya., Korovin, S. D., and Mesyats, G. A., 1 980, The Screening Effect in High­ Current Diodes, Pis 'ma Zh. Tekh. Fiz. 6: I 089-1092. Bolotov, V. E., Zaitsev, N. 1., Korablev, G. S., Nechaev, V. E., Sominsky, G. G., and Tsybin, 0. Yu., 1 980, Examination of the Possibility of Diagnosing High-Current Relativistic Beams by the Ion Current Method, Ibid 6: 1 0 1 3 - 1 0 1 6. Bugaev, S. P., Kanavets, V. 1., Koshelev, V. 1., and Cherepenin, V. A., 199 1 , Relativistic Multiwave Microwave Oscillators (in Russian). Nauka, Novosibirsk. Bugaev, S. P., Kim, A. A., Klimov, A. I., and Koshelev, V. I., 1 980, On the Mechanism of the Vacuum Breakdown and Cathode Plasma Expansion Along the Magnetic Field in Foilless Diodes, Zh. Tekh. Fiz. 5:2463-2465. Bugaev, S. P., Kim, A. A., Klimov, A. I., and Koshelev, V. I., 198 1 , On the Mechanism ofthe Propagation of the Cathode Plasma Transverse to the Magnetic Field in Foilless Diodes, Fiz. Plazmy. 7:529-539. Bugaev, S. P., Kim, A. A., Koshelev, V. 1., and Khryapov, P. A., 1 983, Experimental Investigation of the Motion of the Cathode Plasma Transverse to the Magnetic Field in Magnetically Insulated Diodes, Ibid. 9 : 1 287-1 29 1 . Burtsev, V. A., Vasilevsky, M. A., Gusev, 0. A., Roife, I. M., Seredenko, E. V., and Engelko, V. 1., 1979, A Microsecond High-Current Electron Beam Accelerator, Prib. Tekh. Eksp. 5:32-35. Close, R., Palevsky, A., and Bekefi, G., 1 983, Radiation Measurement from an Inverted Relativistic Magnetron, J. App/. Phys. 54:4147-4 1 5 1 . Dolgachev, G . I . and Zakatov, L . P., 1 983, On the Possibility of Increasing the Lifetime of a Magnetic Insulation, Pis 'ma Zh. Tekh. Fiz. 9:964-967. Dreike, P., Eichenberger, C., Humphries, S., and Sudan, R., 1976, Production of Intense Proton Fluxes in a Magnetically Insulated Diode, J. App/. Phys. 48:85-87. El'chaninov, A. S., Zagulov, F. Ya., Korovin, S. D., and Mesyats, G. A., 1 9 8 1 , On the Stability of Operation of the Vacuum Diodes of High-Current Relativistic Electron Beam Accelerators, Zh. Tekh. Fiz. 51: 1 005-1 007. Fedosov, A. 1., 1 982, Candidate's Degree Thesis Electron Flows in Magnetically Insulated Foilless Diodes and Lines (in Russian). Inst. of High Current Electronics, Tomsk. Fedosov, A. 1., Litvinov, E. A., Belomytsev, S. Ya., and Bugaev, S. P., 1 977, On the Calculation of the Characteristics of the Electron Beam Formed in a Magnetically Insulated Diode, Izv. Vyssh. Uchebn. Zaved , Fiz. 10: 134- 135.

432

Chapter 23

Friedman, M. and Ury, M., 1 970, Production and Focusing of High Power Relativistic Annular Electron Beam, Rev. Sci. Instrum. 4 1 : 1 334- 1 335. Fuks, M. 1 . , 1 982, Formation of a High-Current Relativistic Electron Beam in a Magnetically Insulated Coaxial Diode, Zh. Tekh. Fiz. 52:675-679. Gleizer, I. Z., Didenko, A. N., Zherlitsyn, A. G., Krasik, Ya. E., Usov, V. P., and Tsvetkov, V. 1., 1 975, Production of an Annular Relativistic Electron Beam in a Magnetically Insulated Coaxial Gun, Pis 'ma Zh. Tekh. Fiz. 1 :463-468. Gorbachev, S. 1., Zakharov, S. M., Pikuz, S. A., and Romanova, V. M., 1 984, C02-Laser Interferometry of the Explosive-Emission Plasma in a Microsecond High-Current Diode, Zh. Tekh. Fiz. 54:399-4 0 1 . Gorev, V . V., Dolgachev, G . 1., Zakatov, L . P . , Oreshko, A . G., and Skoryupin, V . A., 1 985, Dynamics ofthe Magnetic Insulation Breakage in an Electron Diode, Fiz. Plazmy. 1 1:782-786. Gorshkova, M. A., Il'in, V. P., Nechaev, V. E., Sveshnikov, V. M., and Fuks, M. l., 1 980, The Structure of the High-Current Relativistic Electron Beam Formed by a Magnetically Insulated Coaxial Gun, Zh. Tekh. Fiz. 50: 1 09- 1 14. Jones, M. E. and Thode, L. E., 1 980, Intense Annular Relativistic Electron Beam Generation in Foilless Diodes, J Appl. Phys. 50:5212-5214. Koshelev,V. I., 1 979, On the Expansion of the Cathode Plasma in a Tran�verse Magnetic Field, Fiz. Plazmy. 5:698-70 1 . Kova1ev, N. F., Nechaev, V. E., Petelin, M. 1., and Fuks, M. 1., 1 977, On the Stray Currents in Magnetically Insulated High-Current Diodes, Pis 'ma Zh. Tekh. Fiz. 3:41 3-4 1 6. Lovelace, R. N. and Ott, E., 1 974, Theory ofMagnetic Insulation, Phys. Fluids. 17:1263-1268. Luckhardt, S. C. and Fleischmann, H. H., 1 977, Microsecond-Pulse Insulation and Intense Ion Beam Generation in a Magnetically Insulated Vacuum Diode, Appl. Phys. Lett. 30: 1 82-1 85. Martin, T. H. and Clark, R. S., 1 976, Pulsed Microsecond High-Energy Electron Beam Accelerator, Rev. Sci. Instrum. 47:46-463. Mesyats, G. A., 1 974, Generation of High-Power Nanosecond Pulses (in Russian). Sov. Radio, Moscow. Mesyats, G. A. and Proskurovsky, D. 1., 1989, Pulsed Electrical Discharge in Vacuum. Springer-Verlag, Berlin-Heidelberg. Nechaev, V. E. and Fuks, M. 1., 1977, Formation of Annular Relativistic Electron Beams in Magnetically Insulated Systems (Approximate Calculations), Zh. Tekh. Fiz. 47:2347-2353. Nikonov, A. G., Roife, I. M., Saveliev, Yu. M., and Engelko, V. 1., 1 983, On the Operation of a Magnetically Insulated Diode with a Long Pulse Duration, Ibid. 7:683-690. Orzechovski, T. J. and Bekefi, G., 1 976, Current Flow in a High-Voltage Diode Subjected to a Crossed Magnetic Field, Phys. Fluids. 19:43-5 1 . Stinnett, R. W., Allen, G. R, Davis, H . P., Hussey, T . W., Lockwood, G. J., Palmer, M . A., Ruggles, L. E., Widman, A., and Woodall, H. N., 1984, Cathode Plasma Formation in Magnetically Insulated Transmission Lines. In Proc. XI ISDEIV, Berlin, Vol. 2, pp. 397-400. Stinnett, R. W., Palmer, M., Spielman, R., and Bengtson, R., 1 982, Small Gap Magnetic Experiments in Magnetically Insulated Transmission Lines. In Proc. X ISDEIV, Columbia, sc, pp. 2 8 1 -285. Straw, D. C. and Clark, M. C., 1 979, Electron Beams Generated in Foilless Diodes, IEEE Trans. Plasma Sci. 26:4202-4204. Voronin, V. S. and Lebedev, A. N., 1973, Theory of Magnetically Insulated High-Voltage Coaxial Diodes, Zh. Tekh. Fiz. 43:25 9 1 -2598. Voronin, V. S., Krastelev, E. G., Lebedev, A. N., and Yablokov, B. N., 1 978, On the Limiting Current of a Relativistic Electron Beam in Vacuum, Fiz. Plazmy. 4:604-6 1 0. Voronin, V. S., Zakharov, S. M., Kazansky, L. N., and Pikuz, S. A., 198 1 , A Microsecond Monoenergetic High-Current Electron Beam with a Stabilized Current, Pis 'ma Zh. Tekh. Fiz. 7 : 1 224- 1 227.

Chapter 24 DENSE ELECTRON BEAMS AND THEIR FOCUSING

1.

THE DIODE OPERATION

In this chapter, we consider the diodes intended for the production and focusing of dense high-current relativistic electron beams (REB 's) with a pulse duration fp ::; 1 o-7 s. Reviews of the studies in this field are given by Tarumov ( 1990), Gordeev ( 1990), and Mesyats ( 1994). By dense high­ current REB's we imply such beams whose current is limited by the self magnetic field. This field can be used to focus the beam. The operation of this type of diode is strongly influenced by the cathode and anode plasma layers, and, unlike in the diodes described in the previous chapter, the anode plasma is present practically continuously due to the intense energy flux onto the anode. A feature of these devices is a strong electric field between the electrodes. This results in favorable conditions for a great number of emission centers and ectons occurring on the cathode resulting in the formation of uniform cathode plasma. To produce rectangular pulses, it is necessary to have a pulse rise time tr « tp, i.e., tr < 1 o-s s. The rate of rise of the electric field in a diode, dE/dt, is generally approximately equal to Vltrd � 1 0 1 4 V/s at a voltage V - 1 06 V and the cathode-anode separation d � 1 em. With these high values of dE/dt, there is no need to use multipoint cathodes: ectons are produced in sufficiently large numbers due to cathode surface microirregularities. The conventional cathode material in diodes of this type is graphite. If it is necessary to obtain a uniform high-current REB, a strong guide magnetic field is applied. In this case, the beam current is entirely limited by

434

Chapter 24

the space charge field, and the electron trajectories are nonnal to the equipotential surfaces in the gap. Let us elucidate under which conditions the self magnetic field of the beam must be taken into account. Let there be a planar diode with an axisymmetric electron beam. We compare the characteristic (electric, Fe, and magnetic, Fm) forces that act on the electrons in the diode. To estimate Fm, we assume that the beam radius R is equal to the radius of the emission area and that the emission current density is detennined by the "3/2-power" law for a planar diode. For the boundary of the beam, where Fm is a maximum, we then obtain F.

e

_

eV

.

d ' (24. 1 )

where V is measured in megavolts. I f the beam radius i s larger than the diode gap spacing, the ratio FmiFe is considerable even for a nonrelativistic case, and, hence, the self magnetic field substantially affects the beam structure. For a relativistic case, we use the expression for the current density in a planar diode of infinite area. Then we obtain

Fm R ; F. � d e

(24.2)

that is, for a relativistic case, in order that the influence of the self magnetic field of the beam on the motion of electrons could be neglected, it is necessary that the beam radius be much less than the gap spacing of the diode. From (24. 1 ) it follows that for e V!mc? > d/R the diode current is limited by the self magnetic field of the beam. In this case, the trajectories of electrons are crossed orbits radially converging to the diode axis. Let us dwell on the role of the anode plasma. As shown in Chapter 3, this plasma is generated due to the bombardment of the anode surface by the electron beam. Mesyats ( 1 994) detennined the reduced energy necessary for the production of an anode plasma layer in a diode with plane-parallel graphite electrode. For this purpose, the time dependence of the electron beam perveance was investigated experimentally. The time delay to the onset of anode plasma fonnation was detennined by the deviation of the perveance plot from the theoretical curve corresponding to the "3/2-power" law. The appearance of the anode plasma can also be fixed by the beginning

DENSE ELECTRON BEAMS AND THEIR FOCUSING

435

of anode luminescence, which is detected on electron-optical records (Mesyats, 1 994). The reduced energy of the electron beam delivered to the surface layer of the graphite anode by this moment was about 0.4 kJ/g. This is an order of magnitude lower than the energy necessary for the evaporation of graphite. Hence, the anode plasma was formed from the gases absorbed in al. ( 1 975), with the graphite. In the experiment performed by Goldstein the help of various direct techniques, the specific energy going for the formation of plasma at the surface of an aluminum anode was determined. It has been established that desorption and ionization of gases from the anode surface layer need an energy of 1-3 kJ/g. The anode plasma consists basically of H+ and Hi ions and contains some amounts of C+, c+2 , 0+, and aluminum ions, which appear later (at the 55th-65th nanoseconds), when the diode is already bridged with a dense plasma.

et

DIODES WITH PLANE-PARALLEL

2.

ELECTRODES

Let us first consider diodes with no external magnetic field. If a diode is formed by round plane anode and cathode of radius R and the electrode separation is d, then, provided that the cathode emissivity is unlimited and the pulse duration fp « d /( Vc + Va ) , where Vc and Va are the cathode and the anode plasma velocity, respectively, the current I is determined by the "3/2power" law that can be written as 1

.J2 = 9

mc3/e

mc3 (�)2 3/2 ( R )2 ' e mc d

(24.3)

where = 1 7 kA. The "3/2-power" law implies that the motion of electrons in an acceleration gap occurs on trajectories normal to equipotential surfaces. However, for � d/R , the Lorentz force acting on electrons is comparable to the electric force, and the self magnetic field of the diode current appreciably bends the electron trajectories at the edge of the diode. As a result, the voltage dependence of the current deviates from the "3/2power" law. The critical diode current fer at which this takes place can be estimated by equating the Larmor radius of an electron of energy to the gap spacing d:

eV/mc2

eV

where y is the relativistic factor; fer is measured in kiloamperes.

(24.4)

Chapter 24

436

There are some models aimed at giving an explanation to this effect for currents I > fer· In terms of the parapotential model (Gordeev, 1 990), it is supposed that electrons move along conical potential surfaces with a common vertex located at the center of the anode. The balance of electric and magnetic forces acting on an electron is responsible for the parapotential character of the motion. In this case, the electron current can be determined from the formula

R d)y ln (y + �y2 - 1 ) , kA.

I = 8.5 ( !

(24.5)

This model is based on the assumption that a near-axis electron current exists in a diode. Other ways of determining the current of relativistic electrons in a diode with a strong self magnetic field were proposed by Goldstein et al. (1 974), Breizman and Ryutov (1 975), Rukhadze et al. (1 980), and Davidson (1974). Based on the ideas of one-fluid hydrodynamics, the laminar theory of a diode, which implies no assumptions of the shape of equipotential surfaces and of the existence of a near-axis current, was developed by Breizman and Ryutov (1975). According to this theory, the electron current is given by

I = 8.5(

Rld)yll2 1n( y + �y2 - 1 ) , kA,

(24.6)

y

and the diameter of the electron beam at the anode is times smaller than at the cathode. Breizman and Ryutov (1975) performed their calculations for the diode geometry in which the acceleration gap is increased toward the edge of the cathode. In such a diode, electron trajectories never intersect; therefore, the use of the equations of one-fluid hydrodynamics is justified. For » 1 , the results obtained by Breizman and Ryutov (1975) fit better to the parapotential model than to the laminar one. Tarumov (1 990) compared the predictions of the parapotential and laminar theories with experimental results. Figure 24. 1 gives the ratio 1/q as a function of the voltage between the electrodes for data obtained on various accelerators. The quantity q is referred to as an aspect ratio. For the current I, the peak beam current was taken. The voltage of the accelerators ranged from 0. 1 to 1 .4 MV, the cathode radius was 1 5-16 em, and the aspect ratio lied in the range 1 .25-22.4. The current-voltage characteristics of high­ aspect-ratio diodes were investigated on the OWL II accelerator (Di Capua et al. , 1 976). To moderate the influence of the plasma motion on the diode current, rather large electrode gaps were used: from 0. 73 to 1 .46 em. The use of a cathode with a deep of radius Ri in the central part (Fig. 24.2) moderates the influence of the cathode plasma on the operation of the diode.

y

= Rid

DENSE ELECTRON BEAMS AND THEIR FOCUSING 70 � 50

�

<:::!'<

o-1 o- 2 e- 3 c- 4 1>. - 5

•-9 1. -10

0.2

0.4

437

&1 - 6 )( - 7

+-8

:::::; 30 10 0

0.6

0.8

1 .0

1 .2

1 .4

1 .6

V (MV] Figure 24. 1. Comparison of diode current measurements (dots) and predictions (curves). The measured values of current I and voltage V refer to the peak current (dl/dt = 0): 1 - SNARK, 2, 3 - PIML, 4, 9, 10 - OWL II, 5, 6 - PULSERAD 738, and 7, 8 - Gamble I. The dashed line depicts the current calculated by the laminar theory A

(b)

C

di

do

do

Figure 24.2. Diode geometry: a plane cathode, b - conical cathode, R - external radius, Ri - radius of the deep in the cathode, do, di - gap spacings -

Figure 24.3. Evolution of the operation mode of a diode: Ic-L - Child-Langmuir current, T - transitory region. The dashed line shows the current and voltage variations in a pulse

The current-voltage characteristic of this type of diode shows four consecutive phases (Fig. 24.3): (1) the phase of limited emission (I) where the diode current is close to zero until a plasma is formed at the cathode; (2) the phase with no pinching of the beam (II) where the diode current is approximately described by the "3/2-power" law; (3) the phase of pinching of the electron beam (Ill) where the diode current is described approximately by expression (24.5) for a parapotential current lpp; (4) the phase of "short­ circuiting" of the diode (IV) where the voltage across the diode falls with increasing current.

438

Chapter 24

The study of Di Capua et al. (1976) has shown that the diode current in the pinching phase is the same for plane (Fig. 24.2, a) and conical (Fig. 24.2, b) cathodes. If the plasma motion in the acceleration gap is negligible, the operation of the diode with a pinched electron beam is well described by the parapotential theory. The anode plasma is a source of accelerated ions whose current is also space-charge-limited. The space charge of ions neutralizes the space charge of electrons, and the magnetic field of the total (electron and ion) current results in strong pinching of the electron current. As electrons come in the anode plasma, the electric force ceases to act on them and they are reflected, due to the magnetic force, from the anode plasma back toward the cathode. Calculations show that stationary conditions are eventually attained under which the electron flow is focused, while the ion flow remains laminar (Poukey, 1 975). The ion-to-electron current ratio is in inverse proportion to the ratio of the mean times required for ions and electrons to travel through the electrode gap. Since the characteristic length of the trajectory of an electron crossing the gap is approximately equal to the diode radius R, and for ions it is equal to the gap spacing d, if the aspect ratio is large enough, the ion current may become higher than the electron current. An example of diodes in which the ion current is over the electron one are so-called pinch reflex diodes used for the production of intense ion flows (Cooperstein et al. , 1 979). Now we consider the operation of diodes with an external longitudinal magnetic field. The theory of a diode with round plane electrodes immersed in an external longitudinal magnetic field is given by Gordeev (1 990). For a strong magnetic field, the relativistic extension of the "3/2-power" law is applicable for the diode current owing to magnetization of the electrons. Their current in the diode, in the absence of ions from the anode and with the external magnetic field Hz satisfying the condition

Hz >> Her =

mc 2 (y - 1) 2 eR f(y) '

--

is given by

I = 8.5 (Rid) 2 f(y) ,

f(y) =

{

2 ,fi (y - 1)3 12 y

9

for y - 1 « 1,

for y » 1 .

(24.7) (24.8)

The function f(y) for an electron diode is presented in Fig. 24.4 by curve 1, and for the case where the anode of the diode is a source of ions with "infinite" emissive power it is given by curve 2.

DENSE ELECTRON BEAMS AND THEIR FOCUSING

439

7 6 5 ......,

4 3 2 I 0

I

2

3

4 y

5

6

7

Figure 24.4. Plot of the function.f{y)

Figure 24.5. Electron current density distribution over the beam radius

Arzhannikov and Koidan ( 1980) performed an experiment to investigate the current-voltage characteristics and the current density distribution for a high-current diode immersed in a strong external longitudinal magnetic field. A graphite cathode with the gap smoothly increasing with radius, d d(r) (Fig. 24.5, the dashed curve), was used. The intensity of the longitudinal magnetic field in the diode was Hz = 42 kGs, the diode voltage early in the pulse was -0.9 MV, and the diode current was -30 kA. The maximum ratio HJHz (Hb being the self field of the beam) was about 0.07. Radial distributions of the current density are given in Fig. 24.5. The solid curve shows the distribution calculated in the planar diode approximation, i.e., for je - lld2 (r) . It can be seen that the experimental current density distribution is different from this one and an edge effect is observed. Figure 24.6 presents the current-voltage characteristic of a diode in comparison with theoretical curves for a pure electron diode (solid curve) and a diode with ions (dashed curve). To compare experiment with theory, the voltage dependence of the beam current was presented as

=

Iba� -

mc3 2ef(V) '

(24.9)

--­

=

=

where a 1 is the geometric factor, which was determined from the condition that the value of Iba 1 coincides with the theoretical value calculated by formula (24.7) for V 1 MV (t 1 0 ns). Note that the dashed curve in Fig. 24.6 was constructed under the assumption that the plasma at the anode had an "infinite" ion emissivity. It can be seen that early in the voltage pulse, the current is close to its theoretical value only for the pure electron diode, and comes nearer to the line corresponding to the diode with ions. For the diode with j > 6 kA/cm2 (rc 1 em, d 0 . 5 em) the transition to the branch

=

=

Chapter 24

440

=

with ions comes at t > 40 ns after the beginning of the voltage pulse, which corresponds to V � 0.45 MV, while for the diode with j � 1 .5 kA/cm2 (rc 2.0 em, d = 1 .0 em) it comes only at t > 50 ns (V � 0.2 MV). 7 6 5

�4

<:; 3 �

2

0

o.-4

�/

0" I

I

'1

I

I /o

I

I I I

I

0

o- 1 ·- 2

•

30 0.25

0.50 V [MV]

t [ns] 0.75

10 1 .00

Figure 24. 6. Current-voltage characteristic of a relativistic diode in a strong magnetic field. Hz = 42 kGs (Bz = 4.2 T); an approximate time scale: rc = 1 em, d = 0.5 em {1) and rc 2 em and d = 1 .0 em (2) =

3.

BLADE-CATHODE DIODES

For the production of electron beams of high brightness, diodes with a blade cathode are used. The brightness of a beam is defined as Vi /92 , where 8 is the electron scattering angle. We first consider the operation of this type of diode with an external magnetic field. Figure 24.7 shows an experimental arrangement on the generation of a high-current thin slice REB in a magnetic field in the diode of the Ural accelerator (250 kV, 100 kA, 80 ns) (Babykin et a/. , 1 982) created at I. V. Kurchatov Institute of Atomic Energy. The stainless-steel blade cathode used was made as an annular disk of internal diameter 14.0-14.4 em, external diameter 18.4 em, and thickness 0.5, 1 .0, or 2.0 mm. The cylindrical anode was a strip of stainless-steel foil of thickness 0.2 mm fixed on a thin­ walled stainless-steel tube and covering a circular slit in the tube through which the x rays generated by the electron beam at the anode could enter the anode tube. Inside the anode tube, symmetrically on both sides of the circular slit, coils creating a magnetic field Hrc of acute-angled geometry were placed. Figure 24.8 shows the impedance of the diode, Z, as a function of time and magnetic field. It can be seen that Z weakly depends on the field Hrc ·

DENSE ELECTRON BEAMS AND THEIR FOCUSING

44 1

Figure 24. 7. Experimental arrangement for the production of a thin high-current disk REB in a magnetic field of acute-angled geometry on the Ural accelerator: 1 - magnetic lines, 2 metal can, 3 camera obscura, 4 - magnetic field coils, 5 annular circuit covered with the anode foil, 6 cathode disk (blade), 7 - current shunt, and 8 - voltage divider -

-

-

9

15

8

7

g

......, 10 N

.0 .J:::

5 0 20 40 60 80 1 00 t [ns]

Figure 24.8. Time dependence of the diode impedance Z for different Hrc in experiments with a blade cathode on the URAL accelerator for d0 = mm, h0 = mm, Hrc kGs (curve 2) (curve 1) and =

3

6 j_ 5 4 3 2 1 0

......,

5 13

0.5

3

6

9

Hrc [kGs]

12

15

Figure 24. 9. Beam width h0 as a function of magnetic field Hrc in experiments with a blade cathode on the URAL accelerator for d0 mm. 1, 2 - curves of (hb - h0) oc 1/H;c for two values of h0 =

5

442

Chapter 24

The width of the beam at the anode, hb, was determined from the x-ray pictures obtained with the help of a camera obscura. The beam width decreased with increasing magnetic field, and at Hrc = 1 3 kGs clear signs of beam filamentation could be seen. Beam filamentation was also testified by erosion traces on the anode. In Fig. 24.9, the beam width is plotted as a function of Hrc for different h0• For high Hrc, the beam width asymptotically tends to h0 • In a diode with a blade cathode immersed in an external longitudinal magnetic field, the electron beam is formed at the surface of the cathode plasma formed as a result of a complex motion of electrons which drift along the side surface of the blade in crossed electric and magnetic fields and are accelerated toward the anode due to the longitudinal electric field component En . The impedance of an annular blade diode with h0 « d can be estimated as follows: The electric field near the side surface of a blade, within the limits of the cycloid of drift, is known to have a nonzero tangential component En at a distance of the order of d from the blade edge, and therefore the formation of an electron beam will occur from the blade side surface of area Sc � 2 2rr.Rc cd at an average distance from this region to the anode d � 1 5 d Using the well-known expression for the impedance of a planar diode that follows from the "3/2-power" law: Z = 430d2 I V 1 1 2 Sc , where V is the diode voltage measured in megavolts and Z is the diode impedance measured in ohms, and substituting the values of Sc and d, we obtain a relation for the estimation of the impedance of an annular blade diode: ·

.

.

(24. 1 0) A rigorous theory of a blade-cathode diode immersed in a strong external longitudinal magnetic field, developed by Gordeev ( 1987), gives the following expression for the diode impedance: (24. 1 1)

The asymptotic values of the coefficient x are: x(y) = 1 for y » 1 and X(Y) = 0.36 for y � 1 . For any y, the value of x(y) is determined from the interpolation relation x(y) = 1 - 0.64/y. It should be noted that for 0 . 1 � V � 3 MV formulas (24. 1 0) and (24. 1 1 ) give values of Z which differ by no more than 25%. For a diode where an anode plasma is present, the above formulas must be corrected by introducing a factor a that takes into account the increase in diode current due to the neutralization of the space charge of electrons by ions extracted from the anode plasma; that is, Z* = Zla must be used for the

DENSE ELECTRON BEAMS AND THEIR FOCUSING

443

diode impedance. The value of a depends on the diode voltage (lgnatenko, 1 962) and geometry, on the anode plasma density, and on whether or not a magnetic field is present. For a planar diode with the anode plasma having an "infinite" emissive power and for eV/mc2 < 0.2, we have a « 1 .86. It monotonicly increases with y and for y = 5 it reaches 2.05. The value of a should be calculated in each particular case. A mathematical simulation of a diode with an annular blade cathode, placed in a longitudinal magnetic field Hz = 30 kGs and having Rc = 1 .27 em, ho = 1 .4 mm, d0 = 2.5 mm at V = 600 kV, shows that the account of the anode plasma ions results in an increase in diode current from 39.8 to 59.2 kA (a = 1 .5) (Barker et al., 1 980). When comparing experimental data with calculations of the impedance of a diode, one should bear in mind that in experiments on the Ural accelerator the formation of plasma at the edge of the cathode blade occurred 1 00-1 20 ns before the application of a pulsed voltage. The diode current, within 5-l 0 ns after its appearance, rose to 20-30 kA at a voltage of 1 50-200 kV and remained at this level for 10-15 ns. This mode corresponds to an electron current in a diode with no anode plasma. Thereafter, within 30 ns, the diode current, with the voltage slightly falling, reached a maximum of about 60 kA for do = 5 mm or 90 kA for d0 = 3 mm. The more than twofold increase in current and the presence of a maximum can be accounted for by the ion flow occurring in the diode due to the formation of anode plasma under the bombardment of the anode by accelerated electrons, by the reduction of the effective gap, and by the monotonic decrease in diode voltage. An example of a blade-cathode diode with an external magnetic field is the diode of the MS accelerator (Gordeev et al. , 1 982) (350 kV, 1 70 kA, 60 ns). The cathode was made as a plate of length 27 or 10 em and thickness 0.3 em. The cathode material was stainless steel or graphite. The anode was a stainless steel plate of thickness 0.8-1 mm or an aluminum foil sheet of thickness 1 0 J.lm. The gap spacing d0 between the edge of the cathode blade and the anode was varied from 0.5 to 7.5 mm. The impedance of a high-current diode with a plane blade of length /, taking into account the blade part facing the anode, without an external . magnetic field is well described by the relation, obtained from formula

(24. 1 1),

z z, [ 1 + f(y)lzp, ld J 1 ' =

where

(24. 1 2)

444

Chapter 24

is the imn_edance of a diode with a blade cathode of length l and h0 « d; f(y) = 2-f [ x(y) t (y + 1)1 1 2 , and hp1 is the width of the plasma cathode ( h = ho + 2 vct ). Calculation of the impedance of the MS diode with l = 10 em, d = 3.5 mm, h0 3 .0 mm for a maximum current ( 1 20 kA, 330 kV) by formula (24. 1 2) and the cathode and anode plasma velocities Vc equal to 1 · 1 06 cm/s under the assumption that a dense anode plasma is formed within 1 5 ns after the onset of current passage, for a = 1 .9 gives 3.0 n, which is close to 2.75 n obtained experimentally. Tarumov (1 990) took x-ray photographs of the anode luminosity in a diode with a blade cathode of l = 1 0 em and d = 0.35 em. Measurements showed that the angular spread of electrons increased with time. Initially, it was not over 1 0°-20°, 40 ns later it started increasing, and reached about 60° at the 60th-70th nanosecond. Examination of the x-ray pictures shows that early in the operation of the diode, within 30 ns, the radiation was uniform along the cathode blade. However, after the 40th nanosecond, the luminosity was observed to become nonuniform, the nonuniform regions being about 1-3 mm in size and slightly extended across the cathode blade. A significant achievement was the use of a diode with an 1 8-blade cathode (Sanford et al. , 1 986). The diode was capable of producing 1 .5-TW REB 's of voltage about 1 .0 MV and current 1 .8 MA with an effective power pulse duration of 1 7 ns. For the production of REB 's with the above parameters, the SPEED accelerator (Seamen et al. , 1 983) was used. The 1 8-blade diode, which had the geometry of a frustum, was connected to a generator with an output resistance of 0.4 n through a convolution system consisting of 1 8 parallel magnetically insulated lines. The diode geometry was dictated by the goal of creating a powerful x-ray source for uniform irradiation of objects of total area 500 cm2 • Noteworthy is the very low total inductance of the energy supply system between the symmetric acceleration tube and the cathode blades (2. 1 5±0.2 nH) that ensured a very short pulse of REB power, whose effective duration was 1 7 ns. Figure 24. 1 0 shows the time dependence of the diode impedance. Three phases in the impedance evolution were observed: the formation of a cathode plasma and the operation of the diode in the mode of current passage according to the "3/2-power" law (/); the plateau in the diode impedance, characteristic of the current passage in the mode of pinching of the electron beam (II), and gradual failure of the acceleration mode because of the bridging of the diode gap with a dense plasma (Ill). The limiting diode impedance measured at the instant the power peaked with the gap spacing varied along a blade from 3 to 6 mm was 0.60 n and remained high enough throughout the pulse. It should be noted that the x-ray pulse waveform was similar to that of the REB pulse. Framing photography of the x-ray

=

DENSE ELECTRON BEAMS AND THEIR FOCUSING

445

luminosity of the anode with the help of a camera obscura and an image converter tube (ICT) show that early in the pulse the luminosity along the cathode blades was rather uniform, while later the electron beam pinched and its trace moved along the blades toward the axis of the diode. 2.0 1 .6

g:

N

Q)

,.....,

2:)

1 .2

�

0.8 0.4 0

6

12

18 t [ns]

24

30

Figure 24. 1 0. Electron current density distribution over the beam radius

Vacuum diodes of annular geometry with symmetric power supply are widely used for the generation of high-power pulsed x rays (McClenahan et al. , 1 983; Ware et al., 1 985). The advantage of these high-current diodes is the small ion component of the diode current. A diode of this type consists of an inner and an outer cylindrical anode, connected by a plane anode, and a cylindrical cathode. Symmetric energy supply to the diode can be realized with an accelerator having a symmetric acceleration tube, such as the SPEED machine, or with the help a vacuum convolution adapter between a single coaxial and a symmetric output, as, for example, in the Black Jack accelerator (Ware et al. , 1 985). Since backward currents flow both inside and outside the cathode, the electron beam does not experience pinching toward the diode axis, and forms an annular beam. The ion current in such a diode is not over several percent of the total diode current. McClenahan et al. ( 1 983) reported on the generation of REB' s by the HYDROMITE accelerator (2 MV, 40 ns, 4.8 Q) with a double coaxial diode. With a convolution adapter, the output power of the generator was divided into two flows that were necessary for the operation of the diode. It turned out that the current division factor depended on the diode impedance: for low-impedance modes, from 30% to 40% of the total current passed through the inner coaxial diode, while for higher impedance modes the currents of both diodes were approximately equal. In convolution, approximately 113 of the total current was lost irrespective of the diode impedance.

446

Chapter 24

X-ray photographs of the luminosity of the plane anode testify to a rather uniform annular electron beam, whose average diameter was equal to the average diameter of the annular cathode, and to radial pinching of the beam with internal and external electrons moving outward and inward, respectively. The diode impedance strongly depended on the gap spacing between the face of the cathode and the plane anode. The most powerful diode with an annular cathode and symmetric power supply was used in the Black Jack machine (Ware et al. , 1 985). The cathode diameter was 25 em. For a gap spacing of 1 .3 em and a voltage of about 2. 1 MV, a diode current of about 2.1 MA was achieved. With 1 .5 MJ of energy stored in the Marx generator, the energy delivered to the electron beam was 250-300 kJ.

4.

FOCUSING OF ELECTRON BEAMS

=

From relation (24.3) we have for the diode impedance Zd oc V 112 (Ridt2 • Hence, the smaller the aspect ratio q Rid, the higher the impedance. Therefore, diodes with a small aspect ratio are sometimes called high­ impedance diodes. First experiments on REB focusing in high-current diodes of this type are described by Morrow et al. ( 1 971) and Bradley and Kuswa (1 972). In these experiments, diodes having dielectric rod or tubular cathodes of diameter 2-6 mm and more and length 20-40 em were used; the gap spacing between the cathode tip and the plane metal anode was 0.5-5.0 em. The voltage applied to the diode was varied from 1 .0 to 3.5 MV. In the experiments on the FX- 7 5 system (Morrow et a/. , 1 971) at a diode voltage of 3.5 MV, the electron beam of current 40 kA and duration 30 ns was focused to a diameter of about 2 mm. The diode current density in these experiments reached several megaamperes per 1 cm2 • The diodes impedance was tens of ohms, and the diode current was less than or equal to the Alfven current JA = 1 7�y (kA), where � = v0 1c , y = (l - v�lc2 t 1 12 , v0 is the velocity of an electron, and c is the velocity of light. As established experimentally, early in the voltage pulse, the electron beam emitted from a cathode of small diameter diverged and formed on the anode a spot of diameter about 10 mm with a rather low current density. Schlieren photographs of the plasma luminosity in a cathode-anode gap (Bradley and Kuswa, 1 972) showed that the REB pinching in the diode occurred shortly before the bridging of the gap with the visible plasma. As a result, the beam was focused on the anode to a small spot of diameter about 1-2 mm with a current density over 1 MA/cm2 • According to holographic interferograms (Mix et al., 1 973), at the moment of pinching of an electron beam at the axis of the diode, there exists a plasma of density about 10 1 7 cm3

DENSE ELECTRON BEAMS AND THEIR FOCUSING

447

between the cathode and anode plasmas that provides neutralization of the space charge of the focused electron beam. Numerical simulations of the processes occurring in high-current diodes with currents I < fer (Poukey et al. , 1 973) have shown that the angles of incidence of electrons on the surface of the anode are small (normal incidence, see Fig. 24. 1 1 , a). With increasing diode current, the angles of incidence of electrons on the anode increase due to the increasing action of the self magnetic current equal to len and the electron trajectories change essentially, namely, the laminar electron flow in the acceleration gap goes over into a flow with crossed electron orbits (Fig. 24. 1 1 , b). For I > Im the Larmor radius of electrons whose energy corresponding to the diode voltage becomes equal to or less than the cathode-anode gap spacing, and the electrons start drifting from the external boundary of the beam to the diode axis. A consequence of this is pinching of the electron beam, resulting in its self-focusing on the anode. (a)

(b)

0.635 cq

j

Figure 24. 11. Calculated stationary trajectories of electrons in a diode with plane round electrodes: (a) laminar electron flow (f < fer), diode voltage V 200 kV, Zea!e = 1 1 .9 0; (b) electron focusing with the help of a current-carrying plasma at the axis (f > fer), diode voltage V = 250 kV, wire current = 70 kA, diode current 50 kA. The dashed line depicts the boundary of the anode plasma =

=

The self-focusing of high-current REB's in diodes with round plane electrodes and a large aspect ratio Rid was described by Di Capua et al. ( 1 976) and Jonas ( 1 974). It was noticed that the position of the focal spot of a self-focused beam not necessarily coincided with the diode axis, and focusing often occurred at the end of the current pulse when a significant portion of the pulse energy had been expended. Besides, numerical simulations of the pinching of an electron beam due to ExH drift (Poukey et al., 1 973) have shown that a significant electron charge is built up at the

448

Chapter 24

diode axis that appreciably displaces the near-axis equipotential lines in the electrode gap toward the anode. This will result in a focused flow of electrons toward the anode, interfering with their motion to the diode axis and thus reducing the degree of self-focusing. In this connection, the self­ focusing of REB' s with the help of a preliminary created plasma channel along the diode axis was investigated (Jonas et a/. , 1 973, 1 974). This idea is explained by the sketch in Fig. 24. 1 2 that shows a cylindrical diode with a large-area cathode, whose impedance is about 1 0, and a resistive current­ carrying plasma in the axial region of the diode, produced by an exploded thin wire stretched between the cathode and the anode (Jonas et a/., 1 973). In the experiment on the Nereus accelerator (300 kV, 80 kA) (Mix et al. , 1 973), laser holograms of the diode gap were taken after the explosion of a tungsten wire of diameter 1 2.7 J..Lm and length 3.2 em stretched between a deep in the cathode and the anode at an anode-cathode separation of 0.38 1 em. For example, from the hologram obtained in 25 ns after the occurrence of a current pulse in the diode it can be seen that the cathode, anode, and wire surfaces are covered with dense plasma. Despite the fact that the plasma electron density along the wire was no less than 1 0 1 9 cm3 , the diode was not short-circuited within 35-40 ns after the occurrence of the beam current pulse. Measurements of the current density distribution carried out with the help of a Faraday cup and x-ray pictures taken by a camera obscura in experiments on the SLIM accelerator (Jonas et a/. , 1 973) have shown that the current of accelerated electrons was 80 kA at a voltage of 250 kV and the conduction current in the plasma formed after the explosion of a wire was 1 50 kA; the maximum current density of the electron beam at the anode was 5 · 1 06 A/cm2 • 1

I

Figure 24. 12. Schematic of the focusing of an electron beam in a diode with the help of a current-carrying plasma: 1 cathode, 2 anode, 3 resistive plasma, 4 pinch, 5 beam current, and 6 conduction current of the plasma -

-

-

-

-

-

DENSE ELECTRON BEAMS AND THEIR FOCUSING

449

Another way of producing plasma at the axis of a diode, allowing one to control the dimensions, density, and degree of ionization of the plasma, was the use of a laser beam passed through a hole in the cathode (Jonas et a/. , 1 974). The laser plasma increased the REB current density in the focus 5-6 times and made it possible to achieve on the Nereus accelerator a current density over 2 MA/cm2 with a highly reproducible focusing effect. Figure 24. 1 1 , b gives an example of calculations of the electron trajectories in a diode with a cathode of diameter 5.0 em and a resistive plasma present at the diode axis. For these calculations, experimentally determined parameters were used: the diode voltage equal to 250 kV, the conduction current in the axial plasma 70 kA, and the electron beam current 50 kA. It has been revealed that explosive electron emission occurs in the main from the side regions of the cathode and most of the electrons emitted from these regions penetrate into the plasma formed by the explosion of the wire and are focused on the anode. The magnetic field of the conduction current suppresses the emission from the near-axis region of the cathode, and this explains the rather high impedance of this type of diode. Experimental results show that the focusing of an electron beam with a current I considerably exceeding fer is substantially improved in the presence of the plasma formed by the explosion of a wire at the diode axis, and this is confirmed by numerical simulations. This plasma performs two important functions. First, the conduction current in the plasma induces a rather high azimuthal magnetic field providing an ExH drift motion of electrons toward the wire plasma, and, second, the plasma provides neutralization of the space charge of electrons near the axis, and thus the magnetic field inside the plasma promotes the focusing of the electron beam. Numerical simulations have also shown that after the explosion of the wire stable propagation of an electron beam with I > h inside the plasma is possible if there is a longitudinal electric field Ez (Poukey and Toepfer, 1 974). An appreciable achievement in the work on focusing high-current REB' s in diodes was the use o f hollow cathodes with a conical end facing a plane anode and with a large aspect ratio (Blaugrung et al., 1 975). With the help of this type of cathode, even early in the current pulse, a thin-walled beam is formed which implodes to the axis at a rate of 1 to 5 rnrnlns depending on the anode material. As a result, a stable pinch of diameter no less than 3 mm at the anode is formed. The main advantage of this type of cathode is that it provides a short rise time of the power pulse of the REB focused on the anode, whereas for diodes with plasma injection or with a current channel along the diode axis the rise rate of the REB power in the focal spot was determined by the time of rise of the power in the diode, which was about 20-30 ns. In a diode with a hollow cathode having a conical end, this time was as short as 1 ns, so that the REB power in the focal spot was close to

Chapter 24

450

zero even before the beam pinching. This type of diode allows one to obtain a stable pinch at the center of the anode. With an optimum choice of the cathode dimensions, more than 2/3 of the diode current can be focused to a spot of area 0. 1 cm2 on the anode. Experiments with the use of hollow cathodes having a conical end were carried out on the Gamble I accelerator (750 kV, 500 kA, 70 ns) with the total energy of the electron beam equal to 8-9 kJ and on the (more powerful) Gamble II accelerator ( 1 MV, 670 kA, 50 ns) with the REB total energy equal to about 3 5 kJ. The hollow cathode with a conical end of external diameter 84 mm and internal diameter 39 mm with a taper angle of 6° was used and the cathode-anode gap spacing was 3.7 mm (Fig. 24. 13), which made it possible to reduce the diode impedance to 3 Q. This diode configuration provided stable focusing of the beam at the diode axis with a spot diameter no more than 3 mm The current density in the focal spot reached 1 .6 MA/cm2 and the REB power density was 1 0 1 2 W/cm2 • Within 3 ns, the power rose to 1 0 1 1 W, the current to more than 200 kA, and the voltage to about 700 kV. .

Figure 24. 13. The diode geometry and a schlieren photograph of the luminosity of a scintillator placed behind the anode (titanium saturated with hydrogen) in experiments on REB focusing: 1 - cathode, 2 - anode, 3 - scintillator of thickness 0.5 mm, and 4 - neutral filter (D = 0.5)

In Fig. 24. 1 3 , the implosion of a hollow electron beam into a pinch of small diameter is shown. It can be seen that initially a thin-walled annular electron beam of wall thickness less than 3 mm was formed whose radius was somewhat larger than the internal radius of the hollow conical cathode. The hollow beam, being constantly accelerated, imploded to the center of the anode. For an aluminum anode, the initial implosion rate was 0.8 mm/ns. The average implosion rate of the beam was 1 . 7 mrnlns between the radii 1 0 and 1 5 mm and 3 .6 mrnlns for radii smaller than 1 0 mm, so that the beam imploded into a dense pinch at the center of the anode within about 40 ns after the beginning of the pulse. During the subsequent 50 ns, the dense pinch continued to exist, chaotically migrating within 1 mm about the diode

DENSE ELECTRON BEAMS AND THEIR FOCUSING

45 1

axis. These displacements might be in part affect the average pinch diameter determined from integrated x-ray pictures taken with a camera obscura. Therefore, the instant average diameter of the focal spot on the anode (spot width at a half maximum of x-ray intensity) was less than 3 mm, and the average current density was appreciably above 1 MA/cm2• Framing photography of the luminosity of a scintillator placed behind the anode, performed with an ICT, showed that the imploding hollow electron beam was circularly symmetric. An experiment with a brass anode coated with a very thin (�1 J..tm) aluminum layer showed that the rate of implosion of an electron beam depended on the material of the anode surface layer. According to estimates, the electron energy delivered to the anode by the imploded electron beam was too low to cause evaporation of the anode metal. It was supposed that the motion of electrons in a diode is influenced by the low-density ion flow emitted by the anode surface and that the implosion rate depends on the rate of formation and velocity of motion of these ions. It has been revealed that the rate of implosion of an electron beam monotonicly increased with the atomic number of the material of the anode surface layer from 1 · 1 09 cm2/s for carbon to 3.5 · 109 cm2/s for tantalum and gold. Blaugrung et aL ( 1 975) suggested that the ion flow leaving the anode appears due to ionization of the gases desorbed from the anode heated by the electron beam. Within about 1 ns, the gas is ionized by both the initial electrons of the beam and the electrons reflected from the anode. The greater the atomic number of the anode material, the more rapidly its surface layer is heated, since the specific losses of the electron energy in the material increase, resulting in a more intense gas desorption. Experiments on the Gamble II accelerator have shown that the surface rate of implosion of an annular electron beam, d(rrR2 )/dt , monotonicly increases with beam current, and this is in conformity with the notions about the nature of implosion. Thus, in the opinion of Blaugrung et a/. ( 1975), the implosion of a hollow high-current electron beam and the formation of a dense pinch occur due to the surface heating of the anode, the desorption of gas, and the formation of an ion flow directed toward the cathode. Goldstein et a/. ( 1975) have shown that the presence of an ion sheath expanding from the anode surface is the necessary and sufficient condition for the formation of a pinch due to the implosion of a hollow cylindrical electron beam. According to Goldstein et a/. ( 1975), the dynamics of formation of a dense pinch at the axis of a diode with a hollow cathode having a conical end, as well as for a solid round cathode, is as follows: Early in the process, before the appearance of an anode plasma, only a laminar flow of electrons formed from the cathode plasma, well described by the laminar theory of high-current diodes (Goldstein et a/. , 1 975), is observed in the diode. This model is known to

452

Chapter 24

predict a weak compression of the electron beam and agrees with experimental observations of the early phase of a slow implosion of a hollow beam. At a later stage, anode plasma is generated due to electron bombardment. The electrons coming in the plasma ion sheath at a slip angle will be reflected back in the diode gap due to the action of the magnetic field and a moderated action of the electric field. The reflected electrons will move radially toward the diode axis until they reach the anode region where plasma is absent. Here, the enhanced electron flow bombards the anode, forming a rather dense ion sheath that promotes the radial motion of the electron flow. This ion sheath is formed within a rather short time (�1 ns), and this just accounts for the fast electron beam implosion observed in experiment. Since the magnetic field has no influence on the ions formed, they move parallel to the diode axis, and the ion current makes an appreciable fraction of the total diode current. The ion-to-electron current ratio 1/le for the conditions of a stationary flow of electrons and ions in a diode with a large Rld and strong pinching of the electron beam is given by (Tarumov, 1 990)

[

m J. 1 R ___.!._ � - - 2(y - 1)le 2 d m;

]

112

'

(24. 1 3)

where m; is the mass of an ion. Thus, if the accelerated ions are protons with energy e V = 2 MeV and Rld = 20, we have 1/le = 0.65. Spense et al. ( 1 97 5) arrived at the conclusion that to initiate the focusing of electrons to the diode axis, not only the diode current should exceed a critical current (I � fer), but also the energy input to the anode material should surpass some critical level (300-450 Jig for copper and brass and 450-650 Jig for graphite). Comparing the current-voltage characteristics of the diodes of the Camel and OWL II accelerators, these authors suggested that the longest time of existence of the mode of focusing is achieved by the earliest and simultaneous fulfillment of these two conditions. In conclusion, we mention the sharp focusing of a high-current REB in the diode of the PROTO I accelerator (3 MV, 800 kA, 24 ns) attained as a result of careful optimization of the shape and dimensions of the cathode having a conical end (Jonas, 1 978). The conclusion of this work is that to produce high current densities ( � 10 MA/cm2) and attain highly efficient focusing, it is necessary to use the least allowable cathode diameter and cathode-anode gap spacing by lowering the prepulse voltage. In this experiment, the average power density of the electron beam in the focal spot reached 1 0 1 3 Wlcm2•

DENSE ELECTRON BEAMS AND THEIR FOCUSING

453

REFERENCES Arzhannikov, A. V. and Koidan, V. S., 1980, The Microstructure of an Electron Beam and the Current- Voltage Characteristic of a Relativistic Diode in a Strong Magnetic Field (in Russian). Preprint No. 80-73, Inst. of Nuclear Physics, Siberian Division, USSR AS, Novosibirsk. Babykin, V. M., Rudakov, L. 1., Skoryupin, V. A., Smimov, V. P., Tarumov, E. Z., and Fanchenko, S. D., 1 982, Inertially Confined Fusion Based on High-Current REB Generators, Fiz. Plazmy. 8:90 1 -914. Barker, R. J., Goldstein, S. A., and Lee, R. E., 1 980, Computer Simulation ofIntense Electron Beam Generation in a Hollow Cathode Diode. NRL' Memorandum Rept. 4279. Sept. 5. Blaugrung, A. E., Cooperstein, G., and Goldstein, S. A., 1 975, Processes Governing Pinch Formation in Diodes. In Proc. I Intern. Topical Conf Power Electron and Ion Beam Research and Technology, Albuquerque, NM, Vol. 1, pp. 233-246. Bradley, L. P. and Kuswa, G. W., 1 972, Neutron Production and Collective Ion Acceleration in a High-Current Diode, Phys Rev. Lett. 29: 144 1 - 1 445. Breizman, B. R. and Ryutov, D. D., 1 975, On the Theory of Focusing of Relativistic Electron Beams in Diodes, Dokl. AN SSSR. 225: 1308- 1 3 1 1 . Cooperstein, G., Goldstein, S . A., Mosher, D., et al., 1979, Generation and Focusing of Intense Light Ion Beams from Pinched-Electron Beam Diodes. In Proc. III Intern. Topical Conf High Power Electron and Ion Beam Research and Technology, Novosibirsk, Vol. 2, pp. 567-575. Davidson, R. C., 1 974, Theory ofNonneutral Plasmas. Benjamin, London. Di Capua, M., Creedon, J., and Huff, R., 1976, Experimental Investigation of High-Current Relativistic Electron Flow in Diodes, J. Appl. Phys. 47: 1 887- 1 896. Goldstein, S. A., Davidson, R. C., Lee, R., Siambis, J. G., 1 975, Theory of Electron and Ion Flow in Relativistic Diodes. In Proc. I Intern. Topical Conf. Power Electron and Jon Beam Research and Technology, Albuquerque, NM, Vol. 1 , pp. 2 1 8-232. Goldstein, S. A., Davidson, R. C., Siambis, J. G., and Roswell, Lee, 1 974, Focused-Flow Model of Relativistic Diodes, Phys. Rev. Lett. 33: 147 1 - 1 474. Gordeev, A. V., 1987, On the Current of a Relativistic Blade Diode in a Strong Longitudinal Magnetic Field, Pis 'ma Zh. Tekh. Fiz. 13: 4 1 0-4 1 7. Gordeev, A. V., 1 990, Theory of High-Current Diodes. In Generation and Focusing ofHigh­ Current Relativistic Electron Beams (in Russian, L. I. Rudakov, ed.), Energoatomizdat, Moscow, pp. 1 82-192. Gordeev, A. V., Zazhivikhin, V. V., Korolev, V. D., et al., 1 982, Magnetic Self-Insulation of Vacuum Lines. In Problems of Physics and Technology of Nanosecond Discharges. Nanosecond Generators and Breakdown in Distributed Systems, Moscow, pp. 9 1 - 1 1 1 . Goldstein, S . A., Swain, D. W., Hadley, G. R., and Mix, L. P., 1 975, Anode Plasma and Focusing in REB Diodes. In Proc. I Int. Topical Conf High Power Electron Beam Research and Technology, Albuquerque, NM, Vol. 1 , pp. 262-283. Ignatenko, V. P., 1 962, Ion Neutralization ofthe Space Charge of Relativistic Electron Flows, Zh. Tekh. Fiz. 32: 1 428- 1432. Jonas, G., 1 974, Electron Beam Induced Pellet Fusion: Sandia Rept. SAND-74-5367. Present. IV Nat. School Plasma Phys., Novosibirsk, USSR. Jonas, G., 1 978, Developments in Sandia Laboratories Particle Beam Fusion Programme. In Plasma Phys. and Control. Nucl. Fusion Res. (Vienna, IAEA 1978). In Proc. VII Intern. Conf., Innsbruck, Austria, Vol. 3, pp. 1 25-133.

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Jonas, G., Poukey, J. W., Prestwich, K. R., Freeman, J. R., Toepfer, A. J., and Clauser, M. J., 1 974, Electron Beam Focusing and Application to Pulsed Fusion, Nucl. Fusion, 14:73 I -740. Jonas, G., Prestwich, K. R., Poukey, J. W., Freeman, J. R., I 973, Electron Beam Focusing Using Current-Carrying Plasmas in High v!y Diodes, Phys. Rev. Lett. 30: I 64-I 67. McClenahan, C. R., Backstrom, R. C., Quintenz, J. P., et a!., I 983, Efficient Low-Impedance High Power Electron Beam Diode. In Proc. V Intern. Topical Conf High Power Electron and Ion Beam Research and Technology, San Francisco, CA, pp. I 47-I 50. Mesyats, G. A., I 994, Ectons (in Russian). Nauka, Ekaterinburg, Vol. 3. Mix, L. P., Kelly, J. G., Kuswa, G. W., Swain, D. W., and Olsen, J. N., I 973, Holographic Measurements of the Plasmas in a High-Current Field Emission Diode, J. Vac. Sci. Techno!. 10:95 I -953. Morrow, D. L., Phillips, J. D., Stringfield, R. M., Jr., Doggett, W. 0., and Bennett, W. H., I 97 I , Concentration and Guidance of Intense Relativistic Electron Beams, Appl. Phys. Lett. 19:44 I -443. Poukey, J. W., I 975, Z < I Q Pinched Electron Diodes. In Proc. I Intern. Topical Conf High Power Electron and Jon Beam Research and Technology, Albuquerque, NM, Vol. I , pp. 47-254. Poukey, J. W. and Toepfer, A. J., I 974, Theory of Superpinched Relativistic Electron Beams, Phys. Fluids. 7: 1 582- I 59 1 . Poukey, J. W., Freeman, J. R., and Yonas, G., I 973, Simulation ofRelativistic Electron Beam Diodes, J. Vac. Sci. Techno!. 6:954-958. Rukhadze, A. A., Bogdankevich, L. S., Rosinsky, S. E., and Rukhlin, V. G., I 980, Physics of High-Current Relativistic Electron Beams (in Russian). Atomizdat, Moscow. Sanford, T. W. L., Lee, J. R., Halbleib, J. A., Quintenz, J. P., Coats, R. S., Stygar, W. A., Clark, R. E., Faucett, D. L., Webb, D., and Heath, C. E., I 986, Electron Flow and Impendance of an I 8-Blade Frustum Diode, J. Appl. Phys. 59:3868-3880. Seamen, J. F., Van Devender, J. P., Johnson, D. L., et a/., 1 983, SPEED, a 2.5 TW, Low Impedance Pulsed Power Research Facility. In Proc. IV Pulsed Power Conf, Albuquerque, NM, pp. 68-70. Spense, P., Triebes, K., Genuario, R., and Pellinen, D., I 975, REB Focusing in High Aspect Ratio Diodes. In Proc. I Intern. Topical Conf Power Electron and Jon Beam Research and Technology, Albuquerque, NM, Vol. I , pp. 346-363. Tarumov, E. Z., I 990, Production and Focusing of High-Current Relativistic Electron Beams in Diodes. In Generation and Focusing of High-Current Relativistic Electron Beams (in Russian, L. I. Rudakov, ed.), Energoatomizdat, Moscow, pp. 1 22- I 8 1 . Ware, K., Loter, N., Montgomery, M., et a/., I 985, Bremsstrahlung Source Development on Black Jack 5'. In Proc. V IEEE Pulsed Power Conf., Arlington, VA, pp. 1 I 8 - I 2 1 .

PART 9. HIGH-POWER PULSE SOURCES OF ELECTROMAGNETIC RADIATION

Chapter 25 HIGH-POWER X-RAY PULSES

1.

HISTORICAL BACKGROUND

First experiments on the production and application of high-power x-ray pulses were performed early in the last century. In these experiments, lightning discharges received by an antenna in the form of a wire stretched over insulators were used to generate high-voltage pulses of 1 2- 1 5 MV that were supplied to a vacuum discharge tube. In this way, high-power pulsed x-rays capable of penetrating a 20-cm thick lead plate were obtained. However, systematic studies aimed at developing high-power x-ray pulse devices were started between the late 1 930s and the early 1 940s by Steenbeck ( 1 93 8) and by Kingdon and Tanis ( 1 938). The latter authors used the spark of an auxiliary discharge between a mercury cathode and an ignitor electrode to obtain an electron source. X-ray tubes were filled with low­ pressure mercury vapor. An important step in the development of pulsed x-ray technology was the creation of sealed-off and demountable high-vacuum tubes. First cold­ cathode vacuum tubes intended to generate pulsed x-rays were developed by Miihlenpfordt ( 1 939) and Slack and Ehrke ( 1 94 1 ). The sealed-off three­ electrode tube described by Slack and Ehrke ( 1 94 1 ) had a plane tungsten anode and a focusing cathode head with a slot in which the cold cathode was mounted. The edges of the slot acted as an ignitor electrode. The demountable two-electrode tube with a conical tip anode and a conical hollow cathode with sharp edges developed by Miihlenpfordt ( 1 939) operated under continuous evacuation. Its modified version contained an ignitor electrode. Subsequently, tubes of this type were improved (Tsukerman and Manakova, 1 957; Fiinfer, 1 953) in order to produce more

458

Chapter 25

stable intense x-ray pulses. In particular, a dielectric was introduced in the space between the ignitor electrode and the cathode to stabilize the excitation of an igniting spark and to increase the amount of the spark plasma. Much work was performed to study the effect of the shape of the anode and cathode on the parameters of x-ray pulses. The pulse duration of x-rays produced by such tubes was 1-1 0 J.!S. Subsequently, two-electrode vacuum x-ray tubes came into use in pulsed x-ray technology. Based on studies performed by Dyke and co-workers (Martin et a/. , 1 960), sealed-off multipoint pulsed tubes with field emission (FE) were developed. In order to obtain microsecond x-ray pulses, Tsukerman and Manakova ( 1 957) used two-electrode vacuum tubes and were the first to design x-ray apparatus with a voltage of up to 1 .5 MV, which was record voltage at that time. They also believed that field emission occurs in tubes of this type. However, investigations that have been performed since that time suggest that, besides, another type of emission, called explosive electron emission (EEE) (Mesyats and Proskurovsky, 1 97 1 ), takes place in this case (see Chapter 3). The evolution of concepts concerning this type of emission is associated with two closely related trends: the study of FE mechanisms for the limiting current density and the transition of FE to a vacuum arc, on the one hand, and the study of the development of a vacuum breakdown between macroscopic electrodes, on the other hand. After a thorough analysis of the EEE phenomenon, the dynamic current-voltage characteristics of x-ray tubes and the parameters of x-ray pulses could be calculated and the mechanisms of the material removal from cathode and anode could be understood. This makes it possible to design tubes with a long service life, taking into account prescribed pulse parameters. An important stage in the development of pulsed x-ray technology was the creation of high-power generators of nanosecond x-ray pulses (Tsukerman et a/. , 1 97 1 ; Martin, 1 996). Such generators are based on two­ electrode explosive-emission tubes with a high-power nanosecond pulse generator as a power supply. Powering x-ray tubes with such pulses makes it possible to reduce considerably the overall dimensions of the devices due to a significant increase in the electric strength of their insulation. The advances in this field were also determined to a considerable extent by achievements in the generation of high-voltage nanosecond pulses (Vorob'ev and Mesyats, 1 963). In modem x-ray devices, tubes with EEE are mainly used for the production of high-power pulses. During the first years following their creation, pulsed devices were widely used for studying fast processes, but at present, such devices are employed for flaw detection of weld joints in industrial metal structures under nonstationary conditions, in medical

HIGH-POWER X-RA Y PULSES

459

diagnostics, in the x-ray diffraction analysis of substances, in location, and in other fields of science and technology. The components of industrial devices (high-pressure spark gaps, pulsed capacitors, and primary switches) are being improved continually. Investigations aimed at a considerable reduction of pulse duration and an increase in power of pulsed x rays are being continued. Laboratory prototypes of subnanosecond x-ray pulse generators have already been developed. An important event in pulsed x-ray technology was the creation of superpower nanosecond devices with an energy of accelerated electrons of 1 06 -107 eV and a current of up to 1 06 A. A review of publications in this field is given by Mesyats et al. (1 983). A lot of the credit must go to Martin ( 1996) who pioneered the creation of superpower x-ray generators, which are used both for x-raying and for studying the effect of superpower radiation on various objects. This facilitated the development of high-current beam technology. However, his work remained unpublished for many years. In this chapter, we will consider only two types of high-power nanosecond x-ray pulse generator. The first type includes small-size systems with a pulse power of 1 07-109 W, voltage of 1 00-500 kV, and pulse duration of 1 0-9-1 0-8 s. The other type includes superpower x-ray devices with a pulse power of 1 0 1 1 -10 1 3 W, voltage of up to 107 V, and duration of 1 0-8-10-7 s. The former are used in research work, flaw detection, medicine, for sterilizing microorganisms, etc., while the latter are used in x-ray diffraction analysis of high-energy density explosive processes and for studying the effect of superpower radiation on various objects.

2.

ON THE PHYSICS OF X RAYS

X rays are electromagnetic oscillations in the wavelength range 1 0- 1 0-5 nm. They are excited by bombardment of a solid target with a high­ energy electron beam. In modern devices used for the production of high­ power x-ray pulses, the maximum electron energy reaches 30 MeV. Electrons penetrating into the target are scattered, i.e., deflected from the initial direction of motion, and lose their energy. For an electron energy W � 10 MeV, the energy lost by electrons goes into ionization and radiation. Ionization losses are due to inelastic collisions of electrons bombarding the target with its atoms. In this case, the electron energy is spent for excitation and ionization of atoms and for the excitation of collective plasma oscillations of free electrons in the target material. In each individual collision with an atom, an electron spends an energy of the order of 1 0 eV for ionization. However, in some events the lost energy can be as high as several and even some tens of electron-volts. This is the

Chapter 25

460

case where a high-energy electron of the beam ionizes a target atom in one of its inner shells. As the vacancy formed is closed with an electron from an outer shell, an x-ray photon is emitted. The photon energy s equals the change in the energy of the atom corresponding to this transition. X radiation emitted by an atom upon the replacement of electrons removed from inner shells by electrons from outer shells is known as characteristic radiation. Radiation losses are associated with the deceleration of electrons in the Coulomb field of atomic nuclei. Deceleration is motion with a negative acceleration; in accordance with classical electrodynamics, charged particles moving with acceleration emit electromagnetic waves in the surrounding space. Hence, electrons bombarding a target must lose some part of their energy in the form of electromagnetic radiation. This is the way by which x-ray bremsstrahlung having a continuous spectrum is generated. The spectrum contains photons whose energies range from zero to �>max = W0 , where W0 is the initial kinetic energy of the electron. A photon of energy �>max is characterized by a wavelength Amin = licleV. In this relation, 1i is Planck's constant, c is the velocity of light, e is the electron charge, and V is the potential difference that accelerates electrons. Substituting the numerical values of 1i , c, and e into the formulas for A min , we have

A min = 1 .24/ V ,

(25.1)

where V is measured in kilovolts and Amin in nanometers. The average energy lost for radiation per unit path length can be determined from the relation

-

( dW ) dx

rad

= n WI:rad ,

(25.2)

where n is the number of atoms in 1 cm3; WI = W + mec2 , mec2 = 0 .5 1 1 MeV is the rest energy of an electron, and rad is the radiation loss cross section (in cm2) (Heitler, 1 954), which strongly depends on the degree of screening of the Coulomb field of nuclei by atomic electrons. For relativistic energies m0 c2 < WI < 1 3 7 mec2 z-I 1 3 at which the screening can be neglected, we have

(25.3) For

WI > 1 37mec2Z- 1 13

(complete screening), we have

rad = 5.8 · 1 0-28 Z(Z + �) [ 4 ln (1 83Z-113 ) + 2/9 J ,

(25.4)

HIGH-POWER X-RA Y PULSES

46 1

where Z is the atomic number and � = 1 .2-1 .4 is a correction taking into account the bremsstrahlung in the field of atomic electrons (this correction is equal to unity in the previous formula). For low electron energies, the radiation loss is much smaller than the ionization loss; for a certain energy W = Wcr, the bremsstrahlung and ionization losses become equal, while for W > Wcr the radiation loss is dominant. The value of the critical energy Wcr (in MeV) is determined by the following approximate relation:

(25.5) For example, Wcr � 1 1 MeV for tungsten (Z = 74), which is widely used as the target material for pulsed x-ray tubes. As the electron energy is increased, the ionization loss first decreases and then slowly increases. The minimum losses for tungsten and aluminum targets correspond to W � 1 and 1 .5 MeV, respectively. The radiation loss is practically independent of the electron energy in the energy range W < mec2 and monotonicly increases with W in the range of high energies. Thus, a beam of accelerated electrons bombarding a target excites two types of x rays simultaneously, viz., bremsstrahlung with a continuous spectrum and characteristic radiation with a line spectrum. The origins of these rays are basically different: bremsstrahlung is emitted by the bombarding electrons themselves, while characteristic radiation is emitted by target atoms ionized in their inner shells as they revert to the normal state. For high electron energies, the bremsstrahlung power is considerably higher than the characteristic radiation power. Therefore, we can refer to a pulsed device as a powerful source of bremsstrahlung pulses. However, by an appropriate choice of experimental conditions (acceleration of electrons to comparatively low energies, use of low-Z targets, and filtration of radiation), it is possible to obtain characteristic radiation with a pulse power exceeding that of the accompanying bremsstrahlung. Pulsed characteristic radiation is used, for example, in x-ray diffraction analyses. In order to generate bremsstrahlung, bulk and thin targets are used. In a bulk target, the kinetic energy of electrons is absorbed completely or almost completely (in contrast to a thin target in which a passing electron loses an insignificant part of its energy; in thin targets, nonradiative bremsstrahlung and multiple scattering processes practically do not occur). Targets of commercial x-ray tubes (including pulsed tubes) can be classified as bulk targets. Figure 25. 1 shows the wavelength dependence of the spectral intensity for a bulk target. As the accelerating voltage is increased, the spectral intensity of radiation at a given wavelength grows. Simultaneously, the spectral composition of the radiation changes: the spectrum shifts toward shorter wavelengths.

462

Chapter 25

�

7

40 ���----���-

o ��-L�--L---�--� 0.02

0.04

0.06 A. [run]

0.08

0.1

Figure 25. 1. Wavelength dependence of spectral intensity on for different electron­ accelerating voltages

The same spectral intensity curves converted to those in terms of energy are approximated quite correctly by the expression (Blokhin, 1 957)

fe = const (Emax - E) ,

(25.6)

/{; = kolZ(emax - e) ,

(25.7)

which is valid for the entire spectrum except a narrow region adjoining its boundary Emax . This conclusion is in good agreement with the theory of continuous spectrum developed by Kramers (Blokhin, 1957). Using classical notions and the correspondence principle, we can calculate the energy distribution of the bremsstrahlung flux excited in a bulk target. The corresponding expression in a slightly modified form convenient for applications is

where Pe is the spectral density of the radiation flux, k0 is the proportionality factor, I is the electron current onto the target, and Z is the atomic number of the target material. It can be seen from this expression that an increase in atomic number (as well as an increase in current), other conditions being the same, leads to a proportional increase in Pe , while the spectral composition of the radiation remains unchanged. Using relation (25.7), we can find the bremsstrahlung power:

P=

J:max P de e

where b = k0 e 2 /2 .

= bJZV 2 ,

(25.8)

HIGH-POWER X-RA Y PULSES

463

The bremsstrahlung spectrum is described by formula (25.6) only for relatively low electron energies (approximately up to 1 00 keV), although this formula is often used for approximate calculations in the range of much higher energies. In pulsed x-ray apparatus, the tube current and voltage vary in time during a pulse; therefore, the spectral intensity of the radiation is also a function of time. The formula

� (t) = const [ Emax (t) - e ] l(t)

(25.9)

clearly shows that a change in voltage leads to a synchronous change in the energy range of the spectrum since its instantaneous boundary is displaced in accordance with the equality Emax (t) = e V(t) .

(25 . 1 0)

The spectral intensity averaged over the period of voltage variation,

_ 1 l (e) = -

sT-l& (t)dt ,

T o

(25. 1 1 )

can be determined if we know the functions Emax (t) and J(t) appearing in the expression for � (t) . Since these functions are different in form for different apparatus, we will consider qualitatively some general features of the pulsed radiation spectrum I (e) . For this purpose, we compare the composition of a radiation generated at a constant voltage V with that of a radiation generated at a periodic pulsed voltage of arbitrary waveform with amplitude Va = V. In both cases, we initially assume that the currents are constant and equal in magnitude. Since Va = V, the maximum photon energy Emax is the same for pulsed and constant voltages. However, in effect, the radiation generated at a constant voltage corresponds to shorter wavelengths as compared to the radiation generated at a pulsed voltage. This difference is due to the fact that radiation in the latter case appears, during a larger or smaller time interval, at instantaneous values of the applied voltage smaller than its amplitude value. In reality, this difference in the spectral composition of radiation is very substantial. The matter is that the current passing through a pulsed tube is not constant. A high instantaneous current passes through the tube when the voltage, having reached its maximum, decreases. However, the current at the maximum voltage is relatively low. Thus, during a certain time interval, when the voltage is low and the current is high, the tube generates a high-intensity long-wave radiation. This explains the fact that under identical conditions, the bremsstrahlung in pulsed devices is depleted in short wavelengths as compared to the radiation generated by apparatus operating at a constant voltage.

464

Chapter 25

The efficiency of conversion of the power released by an electron beam at a target to the bremsstrahlung power is characterized by the radiant efficiency 11 = b0ZWo . According to experimental data, we have b0 equal to (0.8±0.2) · 1 0-6 keV- 1 for W < 200 keV. The linear dependence of 11 on W0 breaks down at higher energies, and the efficiency increases at a lower rate. In the low-energy range, the radiation efficiency has very low values (from a fraction of one percent to a few percent). In a bulk target, almost the entire kinetic energy of electrons converts, through some intermediate processes, to heat. With increasing W0, the fraction of energy lost for radiation increases, and the efficiency becomes higher. For a very high energy, the efficiency reaches tens percent. For example, for a lead target the efficiency is 60% for W0 = 40 MeV and 75% for W0 = 1 00 MeV. 3.

CHARACTERISTICS OF X-RAY PULSES

In order to calculate the parameters of radiation pulses generated by an x­ ray apparatus, we must know the current-voltage characteristic (CVC) of the pulsed tube. For tubes with explosive-emission cathodes, the cathode plasma affects the shape of the CVC. In our earlier publication (Litvinov and Mesyats, 1 972), we proposed to calculate the CVC's of EEE x-ray tubes using the idea that the current in the system formed by the front of the moving cathode plasma and the anode is space-charge-limited (Flynn, 1 956). It was assumed that the plasma conductivity is much higher than the conductivity of the tube. It is difficult to obtain an exact solution to the system of partial differential equations describing the passage of electrons in the regime of space-charge-limited current for an arbitrary geometry of electrodes and plasma blobs. For this reason, we will use approximate methods for the case of nonrelativistic electrons. In our earlier calculations (Litvinov and Mesyats, 1 972), we employed a method where the electrostatic capacitance of a diode with an arbitrary system of electrodes is equated to the capacitance of a plane cylindrical or spherical capacitor, for which the form of the "3/2-power" law is known. The dimensions of an equivalent system of simple geometry are determined and used in subsequent calculations of the current. The basic assumption in this method is that the shape of equipotential surfaces is the same whether or not a space charge is present, and only the potentials of these surfaces are different. This method was widely used in calculations of the CVC ' s of electron tubes. With this method, it was found that for the case of a spherical plasma cathode formed by the explosion of the tip of a point on a plane surface, the current I can be determined from the formula

HIGH-POWER X-RA Y PULSES 1=

37 · 1 o-6 V 3 1 2 vt d - vt

----­

465 (25. 12)

this fonnula is valid for vt « d , where v is the velocity of the cathode plasma and d is the length of the cathode-anode gap. For other types of diode, the current-voltage characteristic can be expressed in the general fonn

(25 . 1 3) where A is a constant coefficient depending on the geometrical parameters of the diode and F is a function of the ratio vtld . For a plane cathode with a large number of emission centers, for vt « d , the current-voltage characteristic is independent of vt/d : 1=

2.33 · 1 0-6 v-3 12 s d2

(25.14)

Figure 25.2 gives fonnulas for detennining eve's for various plane-anode diode configurations (Mesyats, 1 974). The condition vt « d is met practically for all nanosecond x-ray tubes; therefore, we can assume that it holds in all cases. The main practical scheme for the production of x-ray pulses is based on discharging a capacitor of capacitance C through an x-ray tube. Depending on the capacitance, two typical cases of the discharge may take place: (1) the capacitor discharge time is smaller than the time dlv it takes the cathode plasma to close the gap; (2) conversely, this time is longer than d/v. The second case is not used in x-ray apparatus as a rule, since strong erosion of electrodes takes place due to the energy remaining in the capacitor upon closure of the gap. For this reason, we will consider the cases where vt « d . For vt « d , the eve can be written in the fonn (25.13) for almost all diodes considered above. If we disregard the inductance of the discharge circuit, the system of equations that describe the pulse parameters for the case of a capacitor discharging through a diode with a eve of the fonn (25 . 1 3) becomes (Mesyats, 1974)

(25 . 1 5)

466

Chapter 25

The functions F (vt!d) and the values of A for different diode configurations are given in Fig. 2 5 .2. The system of equations (25 . 1 5) can be reduced to the equation dx

d't

=

-Bx312 F( 't) '

where x = VIV0 , across the tube).

(25. 1 6)

't vt/d , B AdVJ12 /Cv ( V0 =

=

Diode type

being the initial voltage

F(vt!d)

A

Condition Spherical cathode

!

3.no-5

vt!d

vt

«

7.32· 1 0--6

(vtld)2 (1 - vt/d)2

vt

�

d/2

Cathode formed by several spheres

.(((//(/// ///(/(/(/ �

d

a

vt/d 1 - vt/d

G_--B� rc = vt 77777777/77.

(l - vtld)2

vt

« d,

a « d,

a "" d

.JS » d

Cylindrical cathode

1 .47 · 1 0-5 ..!.. d

vt!d

vt

«

d

Toroidal cathode

R

rc = vt

9.23 · 10-5 d

vtld

vt

«

d

Figure 25.2. Form ofthe function F(vt!d) for various configurations of vacuum diode

Solving Eqs. (25. 1 5), we can find the time dependences of the current and voltage for an x-ray tube. For the simplest case of a point cathode and a plane anode, for which F('t) == 't , the current and voltage are described by the formulas 64B't

(25. 1 7)

HIGH-POWER X-RA Y PULSES

467

where y = ld /Cv V0 The time corresponding to the peak current and the current itself, in view of formulas (25 . 1 7), are given by •

JCd = 2 ; �5AvVJI2 0.52 VJ14 (ACv)� 2 lmax = d l/ 2

tmax

(25 . 1 8)

The time corresponding to the maximum x-ray power flux, which, in accordance with Eq. (25.8), is proportional to IV 2 , and the power flux itself can be determined as

tmax = 2

Cd 5Av VJI 2

'

Rmax - V 13 1 4 1AvC/d \1

.

(25. 1 9)

Tne x-ray pulse duration at half maximum is given by

o.88JCd tP -- -,=== . �A V1 12 v

(25.20)

If we write the condition fp « d/v , which is assumed to be met in the derivation of these formulas, in the form tP < 0.3 d/v , we must set B :2:: 1 2 for the above relations to be valid. If the eve of an x-ray tube is independent of time, we can write the following relations for the discharge of a capacitor through a diode with plane-parallel electrodes:

V-

Vo A v,3 1 2 A v,1o 12 1= o P (1 + 't)3 ' (1 + 'tf ' (1 + 'tf '

(25.21)

where 't = t/9 ; e = 2CIA.jVo ; A = 2.33 · 10-6 S/d2 , and S i s the area o f the cathode. The radiation pulse duration measured at half maximum is fp

�

1

9.56 · 1 04 Cd-2 S VJ 2 -:-;::--

-

(25.22)

if the voltage is measured in volts and capacitance in farads. Sometimes, energy storage lines are used in generators of nanosecond x-ray pulses. If such a line is discharged into a diode with a time-dependent eve, the equation for the diode current the can be written as

1 F(vtld) = -----=-:=­ A(Vo - IZ0 )3 1 2 '

(25.23)

468

Chapter 25

where Z0 is the wave impedance of the line. The x-radiation flux can be determined from the relation P � I (V0 - IZ0 ) 2 , and its maximum value is 2 1 given by Pmax � V0 Z0 • The energy in an x-ray bremsstrahlung pulse is WP = .b Pdt . It can be shown that for the case of a line discharging into a diode the time characteristics of the x-ray pulses are proportional to d/v and the energy WP oc (V�IZ0 )d . This can be verified experimentally. Figure 25.3 shows the x-ray pulse duration (at 0. 1 ofthe pulse amplitude) (Mesyats, 1 974) and the radiation energy in a pulse on the length d of the diode vacuum gap which confirm the theoretical predictions that for a line discharging into a diode we have WP oc d and fp oc d . 200

10

1 60

8

�

6 .._6

80

4

40

2

0

.;

�

]: 120

3 d [MM]

2

4

?I::.

c..

5

Figure 25. 3. Dependence of x-ray pulse duration and radiation pulse energy spacing d

WP

1 .2 1 .0

� �

�

0.8 0.6 0.4 0.2 0

0.4

0.8 d 1 12 [mm -1 12]

1 .2

-

Figure 25.4. Dependence of the peak electron current in an x-ray tube on d -112

on gap

HIGH-POWER X-RA Y PULSES

469

As follows from relations (25. 1 8), the current pulse amplitude in a diode into which a capacitor is discharged is Im oc d - 11 2 This was confirmed in an experiment (Mesyats, 1 974) (Fig. 25 .4) where a capacitor (C = 30 pF, V0 = 1 80 kV) was discharged into a diode with a point cathode and a plane anode. For superpower x-ray diodes with relativistic electron beams, the CVC's must be calculated based on the data given in Chapter 24 of this monograph. •

4.

HIGH-POWER PULSED X-RAY GENERATORS

4.1

X-ray tubes

In modem pulsed x-ray apparatus, sealed-off two-electrode tubes with a cold cathode are used as a rule. The role of the target in pulsed diodes is played by the anode. X-ray tubes with an electron beam extracted to the atmosphere are also used. In this case, the target is located outside the tube. In domestic industrial pulsed x-ray apparatus, x-ray tubes with explosive­ emission cathodes (EEC's) are used (Mesyats et al., 1 983). Let us consider the design of such tubes in greater detail. Pulsed tubes have a coaxial or planar electrode system. Tubes of the coaxial type are manufactured with a conical anode made of tungsten in order to obtain intense bremsstrahlung. Usually, a tungsten rod of diameter 3-8 mm is used. The cone angle is 1 0°-30°, and the radius of curvature of the top is 0.5-1 mm . In tubes of planar configuration, transmission anodes having the shape of thin plates made of tungsten, tantalum, and other heavy metals are used. Commercial pulsed tubes with EEC are manufactured with tungsten or tantalum blade cathodes. Such cathodes have the shape of a disk or several disks, one or several coaxial tubes with sharp edges, a ribbon coiled into a spiral, etc. Electron emission is initiated as the blade edge explodes under the action of a high-density field emission current. The insulating part of the envelope of a pulsed tube is made of high-a glass or ceramics. In domestic standard tubes, the envelope is made of molybdenum glass. The residual gas pressure in sealed-off tubes is 1 o-4-1 o-s Pa. One of the main parameters of x-ray tubes is the size of the radiation source (focal spot). The actual focal spot of a tube is the region on the surface of the anode (target) in which electrons are decelerated. The larger its area, the lesser the anode heating, all other factors being the same. The projection of the actual focal spot in the direction of the working radiation beam axis onto a plane normal to this axis is called the effective focal spot, or merely the focal spot. Its size determines the geometrical blurring of the boundaries of the shadowgraph formed in the radiation beam passed through

470

Chapter 25

the object under examination. In order to obtain a sharp contrast of the image, one must use a tube with a sharp (i.e., small-size) effective focal spot. A sharp focal spot can be provided in a rather simple way by using a conical anode in the tube (Tsukerman et al., 1 97 1 ). Figure 25.5 shows a schematic diagram of the IMA5-320D pulsed x-ray tube with a coaxial EEC designed for a voltage of 320 kV and intended for x-raying of materials. The tube is used in MIRA-3D apparatus. Blade cathode 3 shaped as a disk is made of 20 J..tm-thick tungsten foil. The inner edge of the disk serves as the emitting surface of the cathode. Anode 2 is made of a tungsten rod of diameter 4 mm with one end sharpened to form a cone. The cone angle is 1 4°, and the tip radius is 0.6 mm. The cathode-anode separation is 2. 7 mm . The anode is soldered to a steel rod lead 7 connected to a small flange 9. A large flange 4 is electrically connected to the cathode. To this flange, a 0.2-mm thick Kovar extraction window 1 in the form of a hemispherical dome is soldered. Owing to such a shape of the window, the tube is suitable for panoramic x-raying of hollow obj ects. The steel screen 6 on which the cathode is fixed is rigidly connected with the large flange through ring 5. The main purpose of the screen is to prevent deposition of tungsten vapors formed during a discharge in the tube on glass insulator 8. The x-ray tube is evacuated through an exhaust tube 1 0 (thin-walled copper pipe). The working medium of the tube is transformer oil. 1

2

3

4

5

6

7

8

9

10

Figure 25.5. Schematic o f the IMA5-32D pulsed x-ray tube: 1 - window; 2 - anode; 3 cathode. The remaining notation is given in the text

In the 1 00-kV IMA6-D tube (Belkin and Aleksandrovich, 1 972) intended for directional x-raying of objects and having a similar design, a plane extraction window made of 1 -mm thick beryllium sheet is used. Beryllium is characterized by a small attenuation coefficient for long-wave radiation; therefore, such a window filters the radiation emitted by the tube only

HIGH-POWER X-RA Y PULSES

47 1

slightly. For example, the long-wave component of radiation with a photon energy W = 5 keV is attenuated approximately to half its initial intensity. A glass window of the same thickness almost completely absorbs radiation with W � ( 1 0- 1 2) keY. Owing to the relatively small operating voltage and the presence of a beryllium window in the tube, it can be used to obtain high-contrast photographs of articles made of aluminum, plastics, and other light-atomic-weight materials. The tube is used in medical diagnostics equipment. Tubes with conical anodes (Mesyats et al. , 1 983) are characterized by a small cathode-anode separation ( 1 .5-3 mm), and the cathode is made as a nickel disk. The tube stably operates at a voltage of 1 00-200 kV and is characterized by a small size of the effective focal spot (0.4 mm). The CGR firm (France) manufactures 200-2000-kV pulsed tubes with a conical anode and a blade cathode consisting of several thin plates whose emitting edge has a rounded radius of 5 !lffi. The plates are fixed inside a cylindrical screen embracing the anode normal to its surface. Pulsed x rays are used to examine the structure of crystal bodies. For x-ray diffraction experiments, monochromatic radiation is required in most cases. Usually, use is made of practically homogeneous characteristic K radiation of an x-ray tube or its Ka line, which is separated, for example, with the help of a selectively absorbing filter. X-ray diffraction analysis is based on the phenomenon of coherent scattering of radiation from the object under examination. Since long-wave radiation is required for this purpose, the characteristic radiation emitted by a pulsed x-ray tube intended to x-ray diffraction analysis must be long-wavelength radiation. It can be obtained if the anode is made of a material with relatively small atomic number, e.g., copper or molybdenum. Jamet and Thorner ( 1 976) described the design of a pulsed sharp-focus tube with a conical copper anode intended for crystallographic and other studies where the characteristic radiation of copper is used. Its cathode is made as a disk with sharpened edges. A distinguishing feature of the tube is the presence of a thin ( 1 25 !lffi) beryllium extraction window mounted at a small distance from the tip of the anode. The window transmits the characteristic radiation of the K series of copper ( W � 8 keV) with negligible attenuation. Owing to a small gap between the window and the anode, the object can be placed close to the actual focal spot. Decreasing the spacing between the object and the focal spot increases the intensity of radiation incident on the object. In order to carry out structural analysis by the Laue method, a tube with a tungsten anode is used. Pulsed tubes of planar design are characterized, as a rule, by a large size of the focal spot. However, they can also be sharp-focus devices. By way of an example, we consider a small-size sharp-focus IMA2- 1 50D tube with a

472

Chapter 25

blade-edge cathode (Fig. 2 5.6) used for x-raying of materials (Mesyats et al., 1 983). The tube is a unit of the MIRA-2D apparatus. Cathode 3 is a tungsten tube of diameter 2 mm and wall thickness 0.2 mm, mounted on a mushroom­ shaped electrode 4 intended to protect the glass insulating part 6 of the vacuum envelope from condensation of metal vapors on it and to support an exhaust tube 7. The extraction window 1 made of Kovar and having a thickness of 0.2 mm is soldered to a metal casing 5. The transmission tungsten anode 2 of thickness 0.02 mm is soldered directly to the extraction window. The cathode-anode separation is 4.5 mm.

� a a

Figure 25. 6. Schematic of the IMA2- 1 50D planar pulsed x-ray tube: 1 - extraction window; 2 anode; 3 - cathode. The remaining notation is given in the text -

An important distinguishing feature of tubes with a transmission anode (which is usually grounded) is the possibility of placing the object in the immediate vicinity of the extraction window, i.e., at a distance of the order of a tenth of a millimeter from the focal spot. Table 1 lists the parameters of the tubes described above and of some other types of pulsed tubes. All the tubes have a blade-edge cathode and (except IMA2- 1 50D) a conical anode. Table 25. 1. Parameter

IMA2- 1 50D

IMA-320D

IMA-6

IMA-7

Voltage amplitude, kV

1 50-200

320

1 00

600

Effective focal spot diameter, mm

2.1-2.8

5-6

2.3-3.0

2.3-3.0

Pulse repetition rate, s-1 , not higher than

50

15

Length, mm

40

120

60

230

Diameter, mm

30

62

38

73

Mass, g

60

200

70

900

HIGH-POWER X-RA Y PULSES

473

In some pulsed x-ray devices, three-electrode cold-cathode tubes are used. The third (trigger or ignitor) electrode is mounted at a small distance from the cathode. When a trigger voltage pulse of relatively low amplitude is supplied to this electrode, an auxiliary discharge is ignited between this electrode and the cathode, which initiates a discharge in the high-voltage anode circuit. By introducing the third electrode, it becomes possible to reduce the anode voltage and to control the instant of occurrence of an x-ray flash, which can be synchronized with the corresponding phase of the process under investigation. This improves the reproducibility of the flash parameters (intensity, spectral composition, and duration) in repetitive operation. The current in the tube can be controlled by shifting the instants of voltage application to the trigger electrode and to the anode relative to each other (Mesyats et al. , 1 983). In laboratory pulsed setups, demountable tubes operating under continuous evacuation are used. In spite of the obvious disadvantages associated with the requirement of continuous evacuation, these tubes also have certain important advantages over sealed-off tubes, e.g., the possibility of using very thin windows made of various materials, including those preventing considerable heating. The electrodes and other design elements can be replaced when disabled; anodes made of various materials can be used for the production of characteristic radiation of a required wavelength, and so on. 4.2

Compact pulsed x-ray apparatus

As shown in previous chapters, explosive electron emission (EEE) and ecton effects are used in bulky high-power pulsed electron beam accelerators. For a long time, the prevailing opinion was that EEE can be used only in large-scale exotic devices for which special premises with radiation shielding are required. However, the advances in high-current pulse electronics using EEE have made it possible to design very compact accelerators with an electron energy of up to 500 keV, which could compete with conventional electron-beam devices. The compactness of these devices 0 is attained in two ways: ( I ) by shortening the pulse duration to 1 0- 1 -I0-8 s and (2) by reducing the accelerating voltage and by increasing the current to obtain the required pulse power, which is usually in the range 1 07-109 W. Let us first consider commercial apparatus. In most cases, a generator with a Tesla transformer is used as the source of pulsed voltage. The smallest apparatus of the MIRA series, MIRA- 1D, whose operating voltage is 1 00 kV, is intended for x-raying of thin-walled steel articles and articles made of plastics and light metals. It is mainly used in electronics and aircraft instrument-making industry. The MIRA-2D and

474

Chapter 25

MIRA-3D devices are mainly used to control the welding quality in petroleum and gas pipelines. In contrast to MIRA- 1D, the primary storage capacitors in these devices are enclosed in the same casing with the high­ voltage unit. This makes it possible to make the high-voltage cable connecting the remote control panel with the x-ray unit as long as 20-30 m, thus ensuring radiation safety of operators almost without any special protective shielding. Both devices have a uniform directional pattern within a cone angle of -1 50°, which makes them suitable for panoramic x-raying of circular joint welds. The MIRA-4D and MIRA-50 devices comprise three functional units. The third unit contains primary storage capacitors connected in a Marx circuit to increase the charge voltage, which is 40-50 kV in this case. Since the actual transformation ratio for high-voltage Tesla transformers of this type is not over 1 5-20, this charge voltage provides a peak voltage of 500 kV across the spark gap. The technical characteristics of flaw detectors of the MIRA series are given in Table 25.2. The choice of a model is dictated by the thickness and material of the test object and by the required quality of x-ray photographs. Table 25.2. Parameter

MIRAlD

MIRA2D

MIRA3D

MIRA4D

MIRA5D

Maximum thickness of steel accessible for x-ray diffraction analysis, mm

10

20

40

60

1 00

Amplitude of voltage across x-ray tube, kV

1 00

1 50

200

350

500

Radiation pulse exposure dose at 0.5 m from anode, mR (Cikg)

0.2 (5· 1 0-8)

0.8 (2· 1 0-7)

2 (5· 1 o-7)

4 (1 0--{i)

8 (2· 1 0--{i)

Pulse repetition rate, Hz

20-25

1 0- 1 5

4-5

2-3

1 .5-2

Focal spot diameter, mm

2

3

3

4

4

Cone angle of the working radiation beam, deg.

30

1 50

1 50

1 50

1 50

Working life ofthe device, number of pulses

5 · 1 06

5 · 1 06

1 06

0.5 · 1 05

0.5 · 1 05

Power input, W

300

400

600

800

1000

Mass of the x-ray unit, kg

2

4

10

25

40

Type of x-ray tube

IMA-6

IMA21 5 0D

IMA5320D

IA-6

IA-6

X-ray pulse duration at half maximum, ns

10

15

20

20

20

In the Inspector apparatus manufactured in the United States, a spiral transformer is used as the voltage pulse generator. The total mass of the

HIGH-POWER X-RA Y PULSES

475

apparatus is not over 6.5 kg. The radiation exposure dose in a pulse is about 8· 1 o-7 C/kg (3 mR) at a distance of 0.5 for a maximum voltage of - 1 50 kV across the x-ray tube. The focal spot diameter is not over 1 .5 mm. Short x-ray pulses are required for solving many physical problems involved in fast luminescence, x-ray location, radiation-induced defect testing, x-ray diffraction analysis, etc. For example, in physics research it is important to measure time characteristics of ionizing radiation detectors. For this purpose, two devices (KVANT and IRA-3) based on the same principle (Fig. 25.7) have been developed (Mesyats et al., 1 983). The main distinguishing feature of their design as compared to the above devices is the method of pulsed charging of the storage capacitor. Capacitor C1 is charged from the supply line (220 V, 50 Hz) through rectifier D 1 and limiting resistor R1 to a voltage at which dynistor D2 is actuated. As this takes place, capacitor C1 discharges through the primary winding of pulse transformer Tr1 The potential difference appearing across the secondary winding charges storage capacitor C2 through rectifier D3 to a certain voltage. The time constant of the C1 R 1 circuit is chosen so that the dynistor is actuated 5-6 times during a half-period of the supply line voltage. Gradually, during several seconds, the storage capacitor is charged to the amplitude value of the output voltage of the pulse transformer. A triggered three-electrode spark gap SG 1 starts the high-voltage generator formed by the resonance Tesla transformer Tr2, spark gap SG2, and x-ray tube RT. The pulsed power supply used for the storage capacitor has made it possible to reduce considerably the overall dimensions and mass of the charging transformer, which operates at an elevated frequency in this case. The advantage of this circuit is the possibility of using dry batteries as the power supply. Owing to the fact that the dynistor is actuated practically at the same output voltage, the voltage across the capacitor C2 is stable. Structurally, the KVANT and IRA-3 apparatus are designed as a portable x-ray unit connected with the remote control panel through a 5-m cable. X-ray tubes of the IMA 1 - 1 50P type with a large focal spot and peaking spark gaps that operate at 1 00 kV (KVANT) and 1 50 kV (IRA-3) are used in these devices. The KVANT and IRA-3 apparatus can be used for calibration of detectors and x-raying of plasti� articles and electronic device elements. While pulsed x-ray examination in physics (e.g., for fast processes) can be regarded as a conventional tool, its application in medicine is in its initial stage. Owing to the development of new and improvement of the existing models of commercially manufactured pulsed devices, they can be used not only in classical medical diagnostics, but also for solving some specific problems (e.g., for locating alien objects in human body, fractures, etc. under field conditions and in wards). •

476

Chapter 25

Figure 25. 7. Schematic circuit of the KVANT and IRA-3 apparatus

The Scanditronics company produces three models of x-ray devices. Their technical characteristics as given in the commercial pamphlets are presented in Table 25.3. In these devices, voltage is controlled by varying the gas pressure in the spark gaps of the generator and dry air is used as the insulating medium. The control panel is unified for the entire batch. A distinguishing feature of the Scandiflash devices is that the tube is continuously evacuated by a small ionic pump and has interchangeable electrode units. Owing to the small duration of the x-ray flash, sharp photographs can be obtained even at hypersonic velocities. Table 25.3. Parameter

Scandiflash 300

Scandiflash 600

Scanditlash 1200

Amplitude of voltage across x-ray tube, kV

1 00-300

250-600

500-1200

Pulse current

1 0 000

10 000

1 0 000

High-voltage unit dimensions: diameter, mm length, mm Mass, kg

700 600 1 50

800 885 300

800 1 205 450

Radiation pulse exposure dose at 0.5 m from focal spot of the tube, mR (C/kg)

35 (9· 1 0-6)

75 (2· 1 0-5)

1 80 (5· 1 0-5)

Radiation pulse duration at half maximum, ns

20

15

10

In the latest developments of high-power compact x-ray pulse generators, the Tesla-transformer-based power supply system was radically improved. The transformer has an open ferromagnetic core, which makes it possible to attain the maximum charge voltage within the first half-wave of the Tesla transformer voltage. The design of a generator of the Radan series is described in Section 4 of Chapter 14 (see Fig. 1 4.5). X-ray devices using open-circuit pulse generators based on SOS diodes and magnetic switches were developed by Filatov et al. ( 1 996) (see Chapter 20). The generator, whose mass is 1 5 kg, produces across the x-ray tube a 1 20-kV voltage pulse of duration 1 5-25 ns at a pulse repetition rate of

HIGH-PO WER X-RA Y PULSES

477

1 03 Hz in the burst mode. In earlier x-ray devices, the pulse repetition rate was not over 1 00 Hz. Such devices are very promising for medical diagnostics.

5.

SUPERPOWER PULSED X-RAY GENERATORS

Nanosecond superpower pulsed x-ray generators (megavolt operating voltage, · electron current of hundreds and more kiloamperes, and pulse duration of tens of nanoseconds) were developed in the 1 960s for x-ray diffractometry. Similar generators were developed soon after in many laboratories for studying the effect of high-power pulsed x-rays on various objects. The design of these generators intended for x-ray diffractometry and for irradiation is basically the same. They differ only in the structure of the diode since x-ray diffractometry requires small-diameter electron beams. There are no other types of laboratory sources of x rays having a comparable power. Important advantages of these generators include the small pulse duration, high radiation dose, and a comparatively low cost. Almost all existing generators are designed according to a universal scheme. A coaxial energy storage line filled with liquid insulator (transformer oil or water in most cases) is charged from a source of high voltage (Marx generator), a Tesla transformer, a line transformer, or a Van de Graaff electrostatic generator, which was used in early sources to charge a coaxial line insulated with compressed SF 6 (Denholm, 1 965). As the switch operates, the line is discharged through an acceleration tube. The main elements of the tube are a diode and an insulator. An intense electron flux is created due to explosive emission. The pulse formed in a generator with a liquid storage line is fed to a demountable x-ray tube whose diode produces an electron beam and forms an x-ray flux. A vacuum transmission line containing a peaker formed by a two-electrode vacuum spark gap and a dielectric inserted between the electrodes is often connected between the diode and the storage line (Bernstein and Smith, 1 973). The peaker is required for removing prepulses and, in addition, for shortening the pulse rise time. In the region between the liquid insulation and the vacuum, a vacuum insulator is placed which is made as a hollow cylinder coaxial with the storage line. The insulator usually consists of identical dielectric rings (made of acryl, epoxy resin, or polyethylene) separated by grading metal rings required for a uniform distribution of the electric field over the insulator surface. The inner surface of each dielectric ring is inclined to the axis by 45°, forming a truncated cone. With such a tilt, the flashover electric field is a maximum. The experience of operation of Hermes I and Hermes II generators showed that,

Chapter 25

478

in the voltage range from 1 to 12 MV, the breakdown electric field (in kV/crn) is determined as (Martin, 1 969)

E

(25.24) where d is the length of the insulator (in ern) disregarding the thickness of the grading rings and t is the time of voltage action (in ns) . This relation was established empirically by J. C. Martin (Mattin, 1 996) for an insulator of diameter 60 ern under a voltage of up to 5 MV. For the insulator to hold off a large number of pulses, the value of E must be 20% lower than the values given by relation (25.24). Kotov et al. (1 986) carne up with a vacuum insulator supplied with metal screens. The effect of the screens on the insulator performance is explained by Fig. 25.8. A thin-walled cylindrical metal screen is mounted on the positive electrode. The end face of the screen is in the immediate vicinity of the region where the negative electrode is in contact with the insulator. The screen performs several functions. To eliminate the interaction between primary electrons and the dielectric surface, it collects the electrons generated at the triple junctions of the cathode and the electrons corning in the gap between the end of the screen and the negative electrode. In addition, the screen protects the dielectric surface from electromagnetic radiation, charged particles, and rnacroparticles flying from the vacuum diode space. The use of the screens made it possible to almost double the average breakdown voltage and to considerably improve the reliability of the insulator. I (b)

1�/ 11/ ...... 1/

nro

I

e

Vacuum

///

y /

+

Figure 25.8. Influence of a screen on the performance of an insulator: (a) insulator without a screen; (b) insulator with a screen protecting the dielectric surface from primary electrons e­ and from electromagnetic radiation tiro

With a vacuum transmission line, it is possible to physically separate the x-ray source from the pulse generator, to avoid the contamination of the insulator surface by the evaporated cathode and anode materials, and to transport the beam. The electric field in the inner conductor of the coaxial line is usually high enough to cause explosive electron emission from this

HIGH-POWER X-RA Y PULSES

479

conductor, which usually serves as a cathode. Under standard conditions, explosively emitted electrons incident on the anode heat it, causing evaporation of its material and thus promoting the development of the vacuum discharge. If a strong magnetic field is applied to a vacuum gap, the electrons from the cathode plasma fail to reach the anode and return to the cathode. In this case, the discharge operative time increases and is actually determined only by the time of closure of the electrode gap by the cathode plasma. The diode design is governed by the purpose of the apparatus (irradiation or x-ray diffractometry). However, in all cases the energy of the electron beam must be converted to the x-radiation energy as completely as possible. For this purpose, high-atomic-number targets of specified thickness are used. When a generator is used for irradiating large surfaces, the effect of beam compression by the self magnetic field (pinch effect) must be eliminated (see Chapter 24) and the electron beam should be directed normally to the target. For this purpose, a toroidal cathode of radius R is used. The cathode-anode separation d is chosen so that the space-charge-limited current is larger than the critical current of the pinch effect. The electron beam emitted by such a cathode has a concentric intensity distribution at the target which consists of two regions where the intensity peaks. One region has the shape of a ring whose diameter approximately corresponds to the diameter of the torus, while the second has the shape of a spot at the center. The central region of peak intensity usually affects the target more strongly. For x-ray diffractometry, it is necessary to have a small-diameter focal spot on the target. The beam is constricted due to the pinch effect and small diameter of the cathode as well as due to the use of special focusing electrodes, which do not emit electrons and create an electric field of required configur�t1on. When the pinch effect takes place, a large fraction of electrons hit the target not along the normal, but at a considerable angle to the target surface. This reduces the x-radiation intensity in the direction away from the electron beam. For an axisymmetric beam, the transverse-to­ longitudinal electron velocity ratio is approximated as

:�

( )vz

I � 1 7�y

'

(25.25)

where I is the beam current in kiloamperes. For example, for the beam generated by the Pulserad 1480 device at a voltage of 9 MV and a current of 200 kA, the transverse-to-longitudinal velocity ratio is 0.8-1, which corresponds to a 38° mean angle of incidence of electrons with the normal. Therefore, the intensity of x radiation in the forward direction is about one tenth of its highest possible value.

480

Chapter 25

The shape of the cathode and the presence of prepulses considerably affect the beam pinching and the reproducibility of the pulse parameters. The conical tip of the cathode makes it possible to draw up the electrons emitted later from the conical surface by the magnetic field of the beam of initial electrons emitted by the tip. The prepulses arriving at the diode during pulsed charging of the energy storage line lead to the explosion of cathode microprotrusions and to the formation of plasma prior to the arrival of the main pulse. This reduces the impedance of the diode and decreases the efficiency of energy transfer to the diode. This effect is eliminated by including peaking spark gaps both in liquid and in vacuum lines and by using conical cathodes with rounded tips. The lower the amplitude of the prepulse voltage, the smaller the cathode-anode separation that can be used and the sharper the beam focus on the target that can be attained. The choice of the material and thickness of a transmission target is considered in detail by Mesyats et al. (1 983). Recall that the target thickness is always smaller than the electron mean free path; for this reason, a thick plate of low-Z metal (usually, iron or aluminum) is placed behind a tungsten target to decelerate the electrons passed through the target. A problem with the target is its destruction, which necessitates overhaul of the diode. The mechanism of destruction is the cleavage or fragmentation of the metal. To prevent this, the target is usually made not as a solid plate, but as a stack of foils. For example, in the Aurora machine, a stack of tantalum foils of thickness 50 J.lll1 is used. The target becomes mechanically more stable to the action of the electron beam due to enhanced attenuation of acoustic waves and due to ductility of the material. In addition to the simple type of superpower pulse generators based on Marx generators and liquid coaxial lines, systems with inductive energy storage and current interruption by wire or plasma opening switches as well as systems using line transformers and Tesla transformers have been developed. Such systems were considered in Chapters 14 through 16. In early pulsed x-ray tubes, the voltage pulse amplitude was not over 500 kV. A pulsed source of x-ray flashes (Litvinov and Mesyats, 1972) operated at a voltage of up to 1 .5 MV across the tube with a flash duration of 0.2 J.lS. The power supply of the x-ray tube was a Marx generator capable of storing about 1 kJ of energy. The apparatus was intended to take x-ray photographs of rapidly moving objects. An important advantage of the source was the small size of the effective focal spot, whose diameter was not over 3 mm . Such a spot could be obtained owing to the conical anode used in the tube. A device with a similar circuit design was used in studying the mechanism of damage to a target by a high-power pulsed electron beam. The Marx generator stored more than 30 kJ of energy; the voltage pulse amplitude was 3 MV, and the current in the tube was 20 kA.

HIGH-POWER X-RA Y PULSES

48 1

In view of the large period of oscillations in the discharge circuit of a Marx generator, the x-ray flash duration in generators of this type is hundreds of nanoseconds. To produce shorter pulses, the high-voltage source must charge an intermediate energy store, which would subsequently be discharged into a load through a special switch. The role of the intermediate store can be played by a low-inductance capacitor filled with insulating liquid or by a line. For example, in the x-ray generator developed by Denholm (1 965), such a line was formed of coaxial metal cylinders filled with high-s gas; the line was charged from an electrostatic Van de Graaff generator. The breakdown of the spark gap between the inner cylinder and the electrode connected with the cathode of the x-ray tube made it possible to obtain voltage pulses of amplitude 2.3 MV and duration 20 ns. In the generator described by Abramyan ( 1 970), a Tesla transformer was used to charge a line. A pulsed x-ray tube, an energy storage line, and the transformer were contained in a steel tank of diameter 1 .8 m and length 5 m. A capacitor bank was discharged through a trigatron into the primary winding of the transformer. Oscillations were excited in the secondary winding. As the line voltage peaked, the switch operated and the line discharged into the tube. The tank was filled with a mixture of nitrogen and sulfur hexafluoride at a pressure of 1 .4 · 1 06 Pa. The anode of the switch was a 1 -mm thick tantalum plate and the cathode was a metal rod. The capacitor bank of the primary circuit accumulated 1 5 kJ of energy at a voltage of 28 kV. For a pulse duration less than 50 ns, the voltage across the tube was 7 MV and the electron current through the tube was up to 20 kA. High-power x-ray sources were also developed in which an energy storage line was charged from a Marx generator capable of storing 0. 1 -5 MJ. One of this series was the Hermes II system that generated a 1 2-MeV electron beam with a current of 1 70 kA and a pulse duration shorter than 1 00 ns (Martin, 1 969). The main elements of this machine were a pulsed Marx generator, a double pulse-forming line (DPFL), a switch, and an acceleration tube. All high-voltage elements were placed in a steel tank of diameter 6. 7 m and length 26 m filled with transformer oil. The Marx generator was assembled from 1 86 capacitor stages each containing two parallel-connected 1 00-kV, 0.5-JlF capacitors. The energy stored in the generator was about 1 MJ and the output voltage was about 1 8 MV. The capacitance of the Marx generator was 5 .4 nF and the capacitance of the Marx-charged storage line was 5.6 nF. The inductance of the discharge circuit was 80 mH, and the total resistance of each stage was 1 .5 kn. The spark gaps of the Marx generator had the third, ignitor electrode and were placed in individual nylon cases filled with compressed nitrogen. The Marx generator charged the DPFL to a maximum voltage of 1 6.3 MV within 1 .5 JlS. The DPFL was formed by three coaxial cylinders. The outer cylinder

482

Chapter 25

of diameter 4.9 m served as a tank, which was a continuation of the tank of the voltage pulse generator. The impedance of the outer and inner lines was 1 1 and 22 n, respectively. The role of the switch in the system was played by a nontriggered spark gap immersed in oil. The insulator of the acceleration tube was a stack of epoxy rings separated by aluminum grading rings. A considerable problem aroused during the development of the machine was associated with the prepulses that were formed at the diode due to capacitive coupling in the course of charging of the DPFL even before the operation of the oil switch as well as due to the presence of a ground inductor. These prepulses determine the explosive processes at the cathode that lead to the formation of ectons and plasma, reducing the diode impedance and, as a result, the energy of the accelerated electrons. In order to eliminate the effect of prepulses on the diode performance, it is necessary, first, to reduce their amplitude and, second, to remove sharp protrusions from the cathode surface. In the Hermes II machine, the prepulse voltage amplitude was reduced through the control of the triggering delay time for the spark gaps of the voltage pulse generator by choosing an optimum position of the trigger electrodes. Another problem encountered during the development of this machine was associated with the damage to the target by the afterpulses that appeared due to the energy remaining in the Marx generator and in the DPFL. An effective method for eliminating afterpulses is to connect the central electrode of the DPFL, through an oil spark gap, to a resistor whose resistance is equal to the wave impedance of the outer line of the DPFL. The Hermes III accelerator, one more machine of the series developed and built at SNL, which generates an electron beam of current 800 kA and pulse duration 40 ns at an accelerating voltage of 20 MV, is intended to produce high-power pulsed x-rays in experiments with large radiation doses. It can provide a dose rate of 5·1 01 2 R/s in a cylindrical tank with a base area of 500 cm2 and a height of 15 em (Ramirez et a!. , 1 987). As mentioned above, the main distinguishing feature of this system is the use of a magnetically insulated coaxial line for summation of voltages from 20 inductive sections with the help of a line transformer. This machine was described in detail in Chapter 14 of this monograph, which is devoted to the design of high-power pulse transformers and their use in nanosecond pulsed power technology. The Aurora system (Bernstein and Smith, 1 973) remained for a long time the most powerful pulsed x-ray generator. The design of this machine is conventional. A Marx generator charges a liquid energy storage line, which is subsequently discharged through a liquid spark gap into an x-ray tube. The energy to the tube is supplied through a vacuum coaxial line. The design parameters of the system are: voltage 1 5 MV, current 1 .6 MA, and pulse

HIGH-POWER X-RA Y PULSES

483

duration 125 ns. Hence, the electron beam power is 24 TW and the pulse energy is 3 MJ. The length, height, and width of the machine are 4 1 , 1 8.3, and 1 5.2 m, respectively. To reduce the wave impedance, a parallel connection of four 20-Q DPFL's is used. All the lines are charged from the same Marx generator to a total energy of 5 MJ. The four storage lines of the Aurora are connected with four acceleration tubes. Each tube has an insulator, a coaxial transmission line, and a diode. The vacuum coaxial line terminates in a diode. The inner cylinder of the line, whose diameter is 53 em, goes over into the cathode having the shape of an elliptical toroid with the minor diameter equal to 5 . 1 em, while the outer cylinder goes over into the anode made as a metal plate. The anode­ cathode separation is 45 em. Like the inner cylinder of the line, the cathode is made of aluminum, while the anode is stacked from 50-).l.m-thick pieces of tantalum foil. The anode tantalum plate of total thickness 2.5 mm is electrically fastened to an aluminum plate with the help of an inductive energy store and an opening switch to decelerate the electrons passing through the target and to counterbalance the atmospheric pressure. Devices with inductive energy storage and current interruption with the help of a large number of parallel-connected conductors are described in Chapter 1 5. Some of them, such as VIRA, IGUR- 1 , IGUR-2, and IGUR-3, are used for the production of high-power pulsed x rays. The IGUR-3 machine is the most powerful among these devices (Diankov et a/. , 1 995). A high-voltage pulse is formed in it with the help of an inductive energy store and a current interrupter with electrically exploded conductors. A Marx generator with a voltage of 1 .4 MV and a stored energy of 300 kJ serves as the driver. The maximum bremsstrahlung dose rate at a distance of 1 m from the diode window is 1 0 1 0 R/s for a voltage of 6 MV across the x-ray tube, a current of 55 kA, and a pulse duration of 25 ns. Systems of this type are low­ cost and simple to service. To produce high-power pulsed x rays, Barinov et a/. ( 1 997) used systems with plasma opening switches (see Chapter 1 6). The primary energy store was a 1 -MV, 1 6-kJ Marx generator; it was discharged through a plasma opening switch into an x-ray tube. As a result of the operation of the plasma opening switch, the voltage across the tube reached 3 MV at a pulse duration of 1 00 ns. The mean x-ray dose rate at a distance of 0.5 m was -1 kGy/s. The electron beam power in the x-ray tube was, on average, 20 kW at a pulse repetition rate of up to 4 Hz. Linear pulsed electron accelerators are also used to produce high-power pulsed x rays. For example, pulsed accelerators developed by Pavlovsky et a/. ( 1 970) produced an electron beam of energy up to 30 MeV with a current of up to 1 03 A. Electrons were directed to an appropriate target, as a result of which high-power pulsed x rays were generated.

484

Chapter 25 LONG-WAVE X-RAY GENERATORS

6.

High-power sources of long-wave x rays are used for studying the behavior of physical and biological objects exposed to radiation. Long-wave x-rays is the term applied to radiation with a wavelength lying in the range 5 · 1 0-2 nm < 'A. < 1 0 nm. In order to generate long-wave bremsstrahlung x-rays, the x-ray tube must operate at a low accelerating voltage. In this case, however, the radiant efficiency is very low since the electron beam power goes almost entirely into the heating of the target. Therefore, the quest for new, more effective sources of such radiation becomes of practical importance. A dense high-temperature plasma may serve as a source of this type. The radiation emitted by a dense plasma consists of several components. First, this is radiation with a continuous spectrum resulting from the deceleration of electrons in the field of nuclei or from recombination capture of electrons on unoccupied atomic levels. Second, this is radiation with a line spectrum, which occurs due to transitions of electrons from level to level in partially stripped ions. The total power of bremsstrahlung and recombination-induced radiation is the power Pc (in W/m3) of continuous radiation (Griem, 1 964): pc

=

(

1 5 · 1 0-26 J:el l 2 nz ne z 2 ·

+

z 2 Vz-l T.e

)•

(25.26)

where Te is the electron temperature in eV; nz is the concentration of ions of charge z in cm-3; ne is the electron concentration in cm-3; z is the mean effective charge of the plasma, and vz-1 is the ionization potential of an ion of charge z - 1 In accordance with (25 .26), the continuous radiation power exhibits weak temperature dependence, but strongly depends on the mean charge of plasma ions. Hence, the value of Pc for light elements (He, Be, C) is comparatively low since the maximum attainable ion charge z is very small for them. The value of Pc for heavy metals is considerably larger. The quantity z in tum is a complex function of the plasma specific energy, pressure, and temperature. The value of z for a multicomponent plasma is calculated using a computer as a rule. Such calculations show that the plasma starts intensely radiating at a temperature of 100-200 eV; at higher temperatures, the increase in absolute yield of continuous radiation slows down. The same applies to the ratio of the radiated energy Pet to the specific energy W0 stored in the plasma, i.e., the plasma radiator efficiency

.

=

Ttc /{t/ Wo . W0

The time dependence of Ttc can be plotted using the tabulated values of = f(n, T) (Kalitkin and Kuz'mina, 1 978) taking into account the fact

HIGH-POWER X-RA Y PULSES

485

that the characteristic lifetime for a high-density hot plasma is t � 1 o-9 s. The dependence plotted in this way shows that llc has a peak in the temperature range 1 00-500 eV; therefore, it seems to be inexpedient to produce a plasma with a temperature of the order of 1 0 keV for using them as a source of long-wave radiation. The dependence of the spectral intensity of the radiation of plasma on the photon energy (Fig. 25.9) has a clearly manifested short-wavelength limit associated with recombination continuum and shifts toward short wavelengths with increasing temperature (Mosher,

1974).

Radiation with a line spectrum is significant in the short-wavelength part of the spectrum, especially for optically thin plasma sources. The peak of the line radiation corresponds to resonance lines of the ions present in the plasma; according to Griem ( 1964), the power of this radiation (in W/m3) is given by pJ

- 3 · 5 . IQ-I 9 r,-vzn n

-

e

z

e

( )

exp -

Ei T ' e

(25.27)

where Ei is the energy of excitation of the resonance level of an ion of charge z. 0 1 0 .------, (a) w- 1

�

1 0-2

3 w-

---'---'--"--....1.1 w-4 '1 1 02 1 03 1 04 1 05 10 e [eV]

Figure 25.9. Dependence of the spectral intensity on the photon energy at different plasma temperatures for copper (a) and tungsten (b)

As follows from the foregoing, any method of production of high-density hot plasma can also be used for the production of long-wave x rays. In this sense, all methods suitable for inertial confinement fusion (laser beam, ion and electron relativistic beams, and magnetohydrodynamic cumulation) can be used to produce high-power pulsed x rays. However, the application of a particular method of inertial heating may be restricted by some factors. For example, in some technological applications, the radiation with an energy W > 20 -30 keV must be eliminated; in view of the large attenuation

486

Chapter 25

coefficient for long-wave radiation, the geometry of the source must be such that the objects to be irradiated could be placed in the immediate vicinity of the source, and so on. The method of production of high-density hot plasmas by magnetohydrodynamic (MHD) implosions of thin-walled cylindrical shells is promising for the generation of pulsed long-wave x rays. The advantages of this method acquire a special significance in connection with the development of high-power nanosecond pulse technology and the possibility to attain high values of dl/dt. Let us consider this method in detail. The idea of the generation of an intense x-ray flash with the help of MHD implosions of shells was proposed by Turchi and Baker ( 1 973). It can be seen from Fig. 25. 1 0 that the geometry of such a scheme of plasma production resembles z pinching. The load placed in vacuum may be a metal foil cylinder, a cylindrical thin wire array, or a cylindrical shell consisting of weakly ionized plasma. To cause an axial current to flow through such a load, a capacitive energy store providing high (up to 10 1 3 A/s) dl/dt is used. The current rapidly ionizes and heats the shell to a temperature of several electron-volts. As a result of the action of Lorentz forces arising due to the interaction of the current with the self magnetic field, the shell starts imploding with the radial velocity reaching 107 cm/s. In the course of acceleration, the electric energy of the store converts to the kinetic energy of the imploding plasma. During the implosion, the kinetic energy converts to thermal energy, producing a dense hot plasma that radiates the major part of its energy as a short x-ray flash.

Figure 25. 10. Principle of producing hot plasmas with the help of MHD compression of a plasma sheath (a) and a qualitative time dependence of the plasma energy (b)

In plasma shell implosions, the major part of the store energy initially converts to magnetic field energy. Indeed, as the temperature increases, the plasma resistance decreases, preventing Joule heating of the plasma shell; at

HIGH-POWER X-RA Y PULSES

487

the same time, the inductive resistance of the plasma shell increases during its motion. For the axial current, the rate of variation of the shell inductance is described by the expression

dL = .:... �0hv(t) ...:. dt 2nr(t) ' __:_:___

(25.28)

where fl o = 4rt · 1 o-7 Him; h is the shell height; v(t) is the velocity of motion of the plasma, and r(t) is the radius. For a shell with typical parameters: h :::d O em, r = 1 em, and v = 5· 1 06 crn/s, the ratio dL /dt is of the order of several ohms, which is much larger than the resistance of a plasma column of the same size. Thus, conditions are created under which a comparatively cold plasma is accelerated to a high velocity during a larger part of the current pulse, while the plasma heating occurs during the implosion within a very short time (see Fig. 22. 1 0). The time of heating of a shell is determined by the ratio of the thickness of the shell to its velocity; hence, to attain a high temperature, the velocity of the shell must be high. The required velocity can be obtained by using a high-power electric generator well matched to the load. Matching the load and the generator for systems with MHD implosions of shells is a complicated problem. Its solution requires the knowledge of the equation of state for the shell material and its relation to the electrical and thermal conductivities. Baker et a!. (1978) described the Shiva experimental setup generating high-power pulsed long-wave x-rays due to MHD implosions of shells. A battery with a total stored energy of 400-700 kJ was discharged through a cylinder of diameter 1 0-7 em and height 1-2 em made of aluminized plastic with a 5-f..!m-thick coating. The maximum peak current in this case was 7-1 2 MA at a rise time of 1-1 .5 f..!S; the velocity of motion of the shell was 1 5-20 Crn/flS. The x radiation emitted by the dense plasma of the imploded shell was detected with the help of semiconductor detectors placed behind filters of various thicknesses and by a spectrograph. The total x-ray yield was 50-100 kJ (about 1 5% of the stored energy). The spectral composition of this radiation corresponded to that of blackbody radiation at a temperature of 30-50 eV. The radiation with photon energies above 1 keV consisted mainly of recombination continuum and line radiation of AI XII. The quantum yield of the radiation with photon energies above 1 keV reached 4 kJ for a shell of thickness 5 flS. The radiation pulse FWHM was 90 ns. According to estimates by Baker et a/. (1 978), the electron temperature of the hottest part of the plasma varied from 300 to 400 eV. Very hot dense plasmas were generated by electrically exploding an array of several parallel wires that was the load of a high-current pulse generator

488

Chapter 25

(Stallings et a/., 1 976; Burkhalter et a/., 1 979). Experiments were performed on the Owl II, Python, and Black Jack systems. The energy storage systems of these generators rank far below that of the Shiva machine in total energy storage capability. The exploded wire array consisted of six wires of radius 10 Jlm and length 3-5 em arranged symmetrically in a circle of diameter 4-2 em. The rate of current rise in the load was (5-1 0)- 10 1 2 A/s, and the maximum peak current was of the order of 1 MA. As a result of the implosion of this wire array at a velocity of (1-3) · 1 07 crn!s, a cylindrical column of high-density (up to 1 020 cm-3) plasma with a characteristic size d 0.5- 1 .5 mm was formed at the center of the circle. The size of the plasma column was determined with the help of a pinhole camera. The electron temperature in the plasma was estimated from the relative intensity of lines corresponding to highly charged ions; it was found to be 500-550 eY for aluminum wires and 1 .5-2 keY for iron and titanium wires (Burkhalter et a/., 1 979). The x-ray pulse FWHM was 40 ns. Unfortunately, Burkhalter et a/. (1979) gave no data of direct measurements of the total energy of the x-ray flux; however, this energy can be estimated using formulas (25.27) and (25.28) and experimentally determined values of Te and d. The radiation energy estimated in this way was 1 50-200 J for photons with an energy above 1 keY. Mosher et a/. ( 1 973) obtained on the Gamble generator an x-ray pulse of energy 20 J and full width 50 ns for photons with s > 3 keV. A tungsten wire of length 3.5 em and diameter 1 0-50 Jlffi was used in this experiment. A pulse of duration 60 ns and energy 20-30 J (s > 1 keY) was obtained on the SNOP high-current generator (500 kY, 2.3 Q, 80 ns) (Baksht et a/., 1 980). In this case, a copper wire of length 2-4 em and diameter 20 Jlffi was used. An increase in x-ray yield was attained due to a special spark gap that ruled out the passage of current through the conductor during the charging of the pulse-forming line (Baksht et a/. , 1 980). In recent years, a number of new experiments have been performed with currents of up to 107 A on the Proto, Angara, and GIT-12 machines. Long­ wave x-ray flashes with a pulse energy of up to 105-107 J were obtained.

=

REFERENCES Abramyan, E. A., 1 970, A Short High-Intensity Hard X-Ray Pulse Generator, Dok. Akad. Nauk. 192:76-77. Baker, W. L., Clark, M. C., Degnan, J. H., Kiuttu, G. F., McClenahan, Ch. R., and Reinovsky, R. E., 1 978, Electromagnetic-Implosion Generation of Pulsed High-Energy-Density Plasma, J. Appl. Phys. 49:4694-4706.

HIGH-POWER X-RA Y PULSES

489

Baksht, R. B., Datsko, I. M., Korostelev, A. F., Loskutov, V. V., Luchinsky, A. V., Mesyats, G. A., and Petin, V. K., 1 980, Soft X-Rays in a Nanosecond Explosion of Thin Wires, Pis 'ma Zh. Tekh. Fiz. 6 : 1 1 09- 1 1 12. Barinov, N. U., Belen'ky, G. S., Dolgachev, G. I., Zakatov, L. P., Nitishinsky, M. S., and Ushakov, A. G., 1 997, Repetitive Plasma Opening Switches and Their Application in High-Power Accelerator Technology, Izv. Vyssh. Uchebn. Zaved , Fiz. 12:47-55 . Belkin, N. V. and Aleksandrovich, G. V., 1972, A Two-Electrode Tube Generating Nanosecond Pulsed X Rays, Prib. Tekh. Eksp. 2 : 1 96-1 97. Bernstein, B. and Smith, I., 1973, "Aurora", an Electron Accelerator, IEEE Trans. Nucl. Sci. 20:294-300. Blokhin, M. A., 1 957, Physics ofX Rays (in Russian). Gostekhizdat, Moscow. Burkhalter, P., Davis, J., Rauch, J., Clark, W., Dahlbacka, G., and Schneider, R., 1 979, X-Ray Line Spectra from Exploded-Wire Arrays, J. Appl. Phys. 50:705-7 1 1 . Denholm, A. S., 1 965, High Voltage Technology, IEEE Trans. Nucl. Sci. 12:780-786. Diankov, V. S., Kovalev, V. P., Kormilitsyn, A. I., and Lavrentiev, B. P., 1 995, High-Power Pulse Generators of Bremsstrahlung and Electron Beams based on Inductive Energy Storage, Izv. Vyssh. Uchebn. Zaved , Fiz. 12:84-92. Filatov, A. L., Korzhenevsky, S. R., Kotov, Yu. A., Mesyats, G. A., and Skotnikov, V. A., 1 996, Compact Repetitive Generators for Medical X Ray Diagnostics. In Proc. XI Intern. Conf. on High Power Particle Beams. Prague, Czechia, pp. 909-912. Flynn, P. T. G., 1 956, The Discharge Mechanism in the High-Vacuum Cold-Cathode Pulsed X-ray Tube, Proc. Phys. Soc. 69B:748-762. Fiinfer, E., 1 953, Der Hochvakuumdurchschlag und seine Anwendung beim Rontgenblitzrohr, Zeit. f angew. Physik. 5:426-440. Griem, H. P . , 1 964, Plasma Spectroscopy. McGraw Hill, New York. Heitler, W., 1 954, The Quantum Theory ofRadiation. Clarendon Press, Oxford. Jamet, F. and Thorner, G., 1 976, Flash Radiography. Elsevier, Amsterdam. Kalitkin, N. N. and Kuz'mina, L. V., 1 978, Tables of Thermodynamic Functions ofMaterials for High Energy Concentrations (in Russian). Preprint Inst. Appl. Math., USSR Acad. Sci., Moscow. Kingdon, K. H. and Tanis, H. E., Jr., 1 938, Experiments with a Condenser Discharge X-Ray Tube, Phys. Rev. 53: 128- 1 34. Kotov, Yu. A., Rodionov, N. E., Sergienko, V. P., Sokovnin, S. Yu., and Filatov, A. N., 1 986, A Vacuum Insulator with a Screened Dielectric Surface, Prib. Tekh. Eksp. 2 : 1 38-14 1 . Litvinov, E. A. and Mesyats, G. A., 1 972, On the CVCs of a Diode with a Pointed Cathode in the Explosive Electron Emission Regime, Izv. Vyssh. Uchebn. Zaved , Fiz. 8: 1 58-1 60. Martin, E. E., TroJan, J. K., and Dyke, W. P., 1 960, Stable, High Density Field Emission Cold Cathode, J. Appl. Phys. 31:782-789. Martin, T. H., Guenther, A. H., and Kristiansen, M., eds., 1 996, J. C. Martin on Pulsed Power. Plenum Press, New York. Martin, T. H., 1 969, Design and Performance of the Sandia Laboratories "Hermes-II" Flash X-Ray Generator, IEEE Trans. Nucl. Sci. 16 (Pt 1 ): 59-63. Mesyats, G. A., 1 974, Nanosecond X-Ray Pulses, Zh. Tekh. Fiz. 44: 1 22 1 - 1 227. Mesyats, G. A. and Proskurovsky, D. I., 1 97 1 , Explosive Electron Emission, Pis 'ma Zh. Eksp. Teor. Fiz. 13:7- 1 0. Mesyats, G. A., Ivanov, S. A., Komyak, N. I., and Peliks, E. A., 1 983, High-Power Nanosecond X-ray Pulses (in Russian). Energoatomizdat, Moscow. Mosher, D., 1 974, Coronal Equilibrium of High-Atomic-Number Plasmas, Phys. Rev. 10A:2330-2335.

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Mosher, D., Stephanakis, S. J., Vitkovitsky, I. M., Dozier, S. M., Levine, L.S., and Nagel, D. J., 1 973, X Radiation from High-Energy-Density Exploded-Wire Discharges, Appl. Phys. Lett. 23: 429-430. Miihlenpfordt, J., 1 939, Verfahren zur Erzeugung kurzzeitiger Rontgenblitze. DR Patent No. 748 1 85. Pavlovsky, A. I., Gerasimov, A. I., Zenkov, D. I., Bosamykin, V. S., Klementiev, A. P., and Tananakin, V. A., 1 970, Air-Core Inductive Linear Accelerator, At.Eenerg. 28:432-434. Ramirez, J. J., Prestwich, K. R., Burgess, E. L., et a!., 1 987, The Hermes III Program. In Proc. VI IEEE Pulse Power Conf, Arlington, VA, pp. 294-299. Slack, C. M. and Ehrke, L. F., 1 94 1 , Field Emission X-Ray Tube, J Appl. Phys. 12: 1 65-168. Stallings, C., Nielsen, K., and Schneider, R., 1 976, Multiple-Wire Array Load for High-Power Pulsed Generators, Appl. Phys. Lett. 29:404-406. Steenbeck, M., 1 938, Ober ein Verfahren zur Erzeugung intensiver Rontgenlichtblitze, Wissenschaftliche Verro.ffentlichungen aus den Siemens-Werken. XVII:363-380. Tsukerman, V. A., and Manakova, M. A., 1 957, Short X-Ray Flash Sources for Investigating Fast Processes, Zh. Tekh. Fiz. 27:39 1 -403. Tsukerman, V. A., Tarasova, L. V., and Lobov, S. I., 1 97 1 , New X-Ray Sources, Usp. Fiz. Nauk. 103:3 1 9-337. Turchi, P. J. and Baker, W. L., 1 973, Generation ofHigh-Energy Plasmas by Electromagnetic Implosion, J Appl. Phys. 44:4936. Vorob'ev, G. A. and Mesyats, G. A., 1 963, High- Voltage Nanosecond Pulse Formation Techniques (in Russian). Gosatomizdat, Moscow.

Chapter 26 HIGH-POWER PULSED GAS LASERS

1.

Principles o f operation

1.1

General information

The application of the methods of nanosecond pulsed power technology and electronics has led to a revolutionary breakthrough in gas laser engineering. As a matter of fact, the use of high-power nanosecond electric energy pulses and high-power systems producing initiating electrons (ultraviolet radiation, x rays, electron beams, etc.) makes it possible to create low-temperature plasmas in large volumes ( 1-104 liters) of various gases by discharges operating under high pressures (of the order of several atmospheres and higher). The population inversion in gas atoms or molecules in such plasma is developed as a result of various physical processes, the discharge being of the volume and not constricted type. High gas pressures and large volumes make it possible to attain high energies and powers in laser pulses. In order to simplify notation, we will refer to all high­ power pulsed gas lasers as HPPG lasers. Before HPPG lasers were created, glow discharges were used in gas lasers. Since the gas pressure in a glow discharge is some fractions of or a few mmHg, unwieldy laser devices were required to attain high powers. The prevailing opinion in the literature on gas lasers was that the development of HPPG lasers was a consequence of evolution of laser systems proper. Considerable advances in the gas-discharge physics were disregarded to a certain extent. The author of this monograph firmly believes that the development of HPPG lasers is a direct consequence of advances in the gas­ discharge physics. Among these advances, the discovery of multielectron

492

Chapter 26

initiation in nanosecond discharges and a discharge with direct injection of electrons into the gas, which have led to high-pressure volume discharges, should be mentioned in the first place. These problems were considered in detail in Chapter 6. The principle of operation of a laser is based on the concept of stimulated emission of radiation, which was formulated by Einstein in describing statistical properties of blackbody radiation under thermal equilibrium conditions. By way of a simple example, we consider a two-level atom. Let II) and 1 2) be the nondegenerate ground state and an excited state of our hypothetical atom. We shall consider three processes, viz., absorption, spontaneous emission, and stimulated emission, involving both above states and photons with energy hv equal to the energy gap �e between these two states. These three processes are presented in Fig. 26. I , a and are described, respectively, by the following equations:

I I) + hv

�

1 2) ,

(26. 1)

II) + hv,

(26.2)

l 2) + hv � l1) + 2hv.

(26.3)

12)

�

In a sample containing particles in both states, any of the above processes (absorption, spontaneous emission, and stimulated emission) may take place. In the most general case, the populations of the ground and excited states are in thermal equilibrium, which can be described by the Boltzmann relation:

(26.4) where N1 and N2 are the population densities of the ground and the excited state, respectively, k is Boltzmann's constant, and T is the temperature. Since the absorption cross section is equal to the cross section for stimulated emission, the ratio of the probability of light amplification to the probability of light absorption is determined by the relative population densities of the excited and ground states. This is used to calculate the light amplification (or absorption) factor a (per unit length) by the formula

(26.5) where crst is the cross section for the stimulated transition (or resonance absorption). Thus, in order to attain light amplification (a > 0), we must find

HIGH-POWER PULSED GAS LASERS

493

a method for carrying the majority of atoms to the excited state (Ni > N1 ). If we confine our analysis to positive temperatures, such a situation leads to violation of the requirements of statistical mechanics defined by relation (26.4). This violation can be eliminated if we recall that relation (26.4) presumes the existence of thermal equilibrium in the sample, which is not always the case in actual practice. Consequently, methods must be found by which population inversion can be realized. (a) Pumping

12 )

(b)

hv -::;. Sp
Pumping

11)

Absorption 11)

Figure 26. 1. Simplified diagram of laser levels for a two-level (a) and three-level atom (b)

In the case of two-level systems, population inversion is most commonly developed if the laser medium originally contains no particles that could participate in lasing. Particles in an excited state are selectively produced, for example, by an electrical discharge. If the lower level I I) cannot be emptied rapidly and selectively, the resulting inverse population exists only for a limited time. In the typical case, we obtain a "self-contained" laser in which the inverse population and the gain decrease because of stimulated emission of radiation. In most lasers, particles involved in lasing have three or more energy levels. Such a situation is depicted in Fig. 26. 1 , b. In this case, an inverse population can be obtained in a much easier way. For this purpose, we must only find collisions processes in which the cross section for the excitation I O) � 12) is larger than the cross section for the l o) � I I) process. Furthermore, the creation of an inverse population could be facilitated if the rates of radiative and collision-induced transitions from level I I) to level I O) would be much higher than the rates of the transitions from level 1 2) to level IO) . In the latter case, radiative and collision-induced processes do not limit the lasing time, and we can have a continuous laser. Thermodynamically, the laser excitation mechanism can be treated as energy transfer between two systems with different temperatures: laser particles initially have a low temperature, while the temperature of pumping particles is high. Obviously, we are not interested in equilibrium properties of the systems, but we must have information on the rates of excitation, emission, and relaxation processes.

494

Chapter 26

For an HPPG laser, a bulk plasma must be created which would contain as many as possible atoms and molecules providing for population inversion. Such a plasma is referred to as an active medium. This medium will emit laser radiation if it is in the so-called open resonator proposed by Prokhorov ( 1 958). In this case, the radiation passes many times through the same plasma and leads to the emission of stimulated radiation, which is enhanced due to multiple reflections from the resonator mirrors. In its simplest form, an open resonator consists of two parallel mirrors separated by a distance /, which is much longer than the radiation wavelength A, i.e., I » A. The diameter of the mirrors is also much larger than the radiation wavelength. One mirror, which is partially reflecting, serves to extract the laser beam. 1 .2

Types of gas lasers

The first gas (helium-neon) laser was proposed by Javan ( 1 959) on the basis of detailed analysis of possible mechanisms of activation and deactivation that could lead to population inversion in gas mixtures excited by an electrical discharge. This laser belongs to the class of lasers with direct energy transfer. The basic principle of production of inversion is the excitation of helium atoms upon their collisions with electrons of a gas discharge. This process transfers a small portion of helium atoms from the 1 ground state to the 2 S and 2 3S metastable states. Helium atoms in these excited states can collide with neon atoms, transferring the stored energy to the latter; as a result, two manifolds of energy levels of excited neon are populated selectively: 2p55s in the vicinity of 20.6 eV and 2p54s near 1 9.8 eV. Since the energy exchange reactions do not lead to population of the lower levels of neon, the local inverse population required for lasing is produced between the 2p55s and 2p54p levels (in the range 20.2-20.4 eV), between the 2p5 5s and 2p53p levels ( 1 8.5-19 eV), and also between the 2p5 4s and 2p5 3p levels. The C02 laser is a typical representative of another type of lasers that harness the energy transfer process. There are three types of normal vibrations inherent in a COz molecule: symmetric valence vibrations Y 1 , deformation vibrations v2, and asymmetric valence vibrations v3 • The deformation vibrations are degenerate. Accordingly, the filling of the vibrational levels of a C02 molecule (including not only those with normal frequencies v�, v2 , v3 , but also their overtones and compound vibrations) determines the set of vibrational quantum numbers, v� . V2 , and V3 , that describes the vibrational state of the molecule. Energy levels are denoted by a combination of the quantum numbers V1, Vj , and V3 • The superscript l has been introduced to reflect the degeneracy of the deformation vibrations of frequency v2 • We are interested in the lower vibrational levels of the electron

HIGH-POWER PULSED GAS LASERS

495

ground state, which are depicted in Fig. 26.2 together with a sketch of the types of vibrations of the C02 molecule. The coincidence of the vibrational frequencies v 1 and 2v2 due to the Fermi resonance mixes these levels, and they often appear in kinetic processes as a single state. Consequently, we can expect that the energy transfer upon collisions of N2 (v = 1) and C02 molecules will produce an inverse population between the selectively populated level 00°1 and the lower-lying unpopulated levels. 3

�

'a

VJ _.. o-o-o

-+

V= l

� 2 0

M

w

--'--- V = O

Figure 26.2. Diagram of the lower vibrational levels of C02 and N2 molecules in the ground electronic state

Patel ( 1964) was the first to demonstrate lasing based on this principle. In a glow discharge with a reduced electric field E/p of 5 V/(cm·Torr) in the discharge plasma, from 40% to 80% of nitrogen molecules are excited for an electron energy of 2-3 eV (resonant excitation of vibrations of the N2 molecule in the range of V = 1 -8) and for an electron density of (0.5-5)- 1 0 1 0 cm-3• The excitation cross-section for nitrogen equals 3 · 1 0- 1 6 cm2 . The rate of collisional excitation energy transfer from nitrogen to C02 is (1-2)- 1 04 s- 1 ·Torr-1 . The energy transfer is efficient between the 00°n harmonics of C02 and N2 molecules up to the V 4-5 vibrations of the N2 molecule. Thus, the upper laser level is populated in a C02 laser. As regards the depletion of the lower laser level, it was found that the first excited level 0 1 1 0 of the deformation mode v2 effectively relaxes upon collisions with He atoms. Helium depletes the 0 1 10 level of C02 at a rate of 4· 1 03 s- 1 ·Torr- 1 • In this case, the 00°1 level of the V mode is practically not 3 affected by helium. Subsequently, a large number of alternative schemes were proposed for the excitation of C02 molecules using a discharge initiated or controlled by an electron beam, x rays, ultraviolet radiation, etc. to pump the laser

=

496

Chapter 26

medium. Owing to the high efficiency (- 1 0%) and the ability to operate in the pulsed mode as well as in the CW mode with a high average power ( 1 05-1 06 W), this laser has been studied meticulously. It is worth noting that a C02 laser is a typical molecular laser since its active medium is formed by molecular gases. This laser generates infrared radiation with a wavelength of 1 0.6 Jlm. Another class of molecular lasers includes those with direct excitation of the upper level by electron impact or by some other method. To realize this type of lasing, particle species and excitation processes are required in which the upper laser levels would be populated selectively. The excitation of electronic states of diatomic molecules by direct electron impact makes it possible to create gas lasers with a wide spectrum of lasing wavelengths. In the first laser of this type, developed by Mathias and Parker ( 1 963), the working molecule is that of nitrogen. These researchers observed lasing by the B3 IIg � A 3 I.� transition in the near infrared spectral region. The same year, Heard ( 1 963) attained lasing by the C3 IIu � B 3 IIg ultraviolet transition. Subsequently, lasers generating radiation with wavelengths in the range 3-4 Jlm by the a1 Ilg � a' 1 I.u and w1 8u � a l iig transitions were developed (McFarlane, 1 965). Among lasers of this type, the N2 (C - B) laser is most popular. The upper laser level N2(C3 Tiu) is occupied due to the excitation upon collisions of electrons with N2 molecules being in the X 1 I.; ground state, the cross section of this process being larger than the excitation cross section for the vibrational states of the lower laser level of N2 (B3 08). Lasing occurs mainly by the 0 - 0 transition of the C - B system (second positive system) at a wavelength of 337. 1 nm. This laser has also found wide application in laboratory experiments mainly for pumping high-power pulsed dye lasers. The N2 laser is characterized by a low pulse energy (a few millijoules for a pulse duration of a few nanoseconds) and a low efficiency (about 0. 1 %) due to accumulation of particles during lasing at the lower laser level, i.e., by a rapid decrease in inverse population (bottleneck effect). Directly pumped lasers of another type are those operating by various transitions of the CO molecule (Leonard, 1 965). Infrared generation by the vibrational transitions of the CO ground state was observed for the first time by Patel and Kerl ( 1 964). An infrared CO laser operating in the wavelength range 4.87-6.7 JliD is one of the most efficient lasers; its efficiency is over 20%. The complex kinetics of this laser is determined by excitation by electrons from the upper vibrational levels, leading to lasing at a series of wavelengths through cascade transitions of molecules to the lower vibrational levels. For the production of high-power coherent radiation fluxes in the ultraviolet and visible regions, excimer lasers are of considerable interest.

HIGH-POWER PULSED GAS LASERS

497

The term "excimer" is an abbreviation of the phrase "excited dimer" and refers to a molecule that may exist only in an electron-excited state. This state is comparatively long living and serves as the upper laser level. In the ground state, an excimer molecule decays within a short time ( 1 0- 1 2-10- 1 3 s), testifying to the depletion of lower laser level and the occurrence of a population inversion. As this takes place, lasing occurs by the transitions between the excited bound states and the ground repulsive or weakly bound state of the molecule. In excimer lasers, excited diatomic combinations of two inert gases or of inert gas and halide or oxygen are used. For the well-known excimer laser system where lasing occurs by transitions of the KrF molecule at a wavelength of 248 nm, an efficiency of -1 0% was attained. This system can be scaled to obtain a high output power. Other systems lasing at longer wavelengths in XeF (353 and 483 nm), XeCl (308 nm), HgCl (558 nm), and HgBr (502 nm) show lower efficiency. First reports on excimer rare-gas halide lasers appeared in 1 975 (Mangano and Jacob, 1 975; Searles and Hart, 1 975; Brau and Ewing, 1 975). Lasing in XeBr* (282 nm), XeCl* (308 nm), XeF* (-350 nm), and KrF* (-248 nm) was attained using an electron beam, an electron-beam-controlled discharge, or a fast discharge for the excitation of the laser medium. Excimer lasers are now the most powerful sources of ultraviolet coherent radiation, covering the vuv through visible spectrum (Rhodes, 1 979; McDaniel and Nighan, 1 982; Mesyats et al. , 1 995). They have a very important advantage: these lasers efficiently operate with various methods of pumping, and the pumping systems are universal and can be applied to various working mixtures. The wide spectrum of laser wavelength and high output energies make excimer lasers widely usable in scientific research and technology. One more advantage of excimer lasers is their broad bandwidth allowing frequency tuning over rather wide limits. To attain lasing in excimer rare-gas halides, ternary mixtures consisting of a buffer gas (argon, neon, or helium), a working gas (xenon, krypton, or argon), and a halide carrier (HCl, CCl4 , F 2, NF3 , HBr, etc.) are generally used. The properties of laser radiation are determined by the specifically arranged potential curves of excimer molecules, by the kinetic processes occurring in the plasma upon excitation of the working mixture, and by the light amplification and absorption at the laser wavelength. In addition to lasers with energy transfer, lasers with direct excitation, and excimer lasers, which we discussed above, other gas lasers also exist (such as photodissociation and chemical lasers). We will consider below only two types of gas lasers: C02 lasers and excimer lasers.

498

Chapter 26

2.

METHODS OF PUMPING

2.1

General considerations

First high-power gas lasers were designed as long glass tubes with a longitudinal glow discharge and gas flow (Karlov, 1 983). Longitudinal discharges are the simplest to realize. It is only necessary to connect a series resistor of rather large resistance in the discharge circuit to restrict the discharge current and to compensate the effect of the descending segment of the current-voltage characteristic of the discharge gap. Longitudinal gas flow is required to remove the products of dissociation of the gas mixture. In such systems, the working gas is cooled due to its diffusion to the gas­ discharge tube walls cooled from outside. For the longitudinal configuration of the discharge and gas flow, the maximal power per unit length (50- 1 00 W/m) is independent of the gas­ discharge tube .diameter. Indeed, when the self-excitation threshold of a laser is exceeded significantly, the radiated power is determined by the product of the pumping rate A and the effective volume V of the active medium: P = AVhv .

(26.6)

For a cylindrically configured laser, V = rtD2 l/4 , where l is the discharge length and D is the tube diameter. The pumping rate A = dN(00°1) /dt is determined by the product of the density of molecules in the ground state, N0, the electron density Ne, the cross section for electron impact excitation, cr, and the average velocity of electrons u: (26.7) However, the product Necru has the meaning of discharge current density j; hence, A = N0 j. The product j�/4 gives the value of the total discharge current I, and thus we obtain P = IN0 lhv .

(26.8)

Since N0 is proportional to the total pressure p of the gas mixture, we have P oc:. lpl .

(26.9)

The product of current and pressure is known to be an important characteristic of plasma processes in long tubes. In a stationary glow­ discharge plasma, the conditions are determined by the product pD (Paschen's law). The constancy of pD ensures the constancy of plasma

HIGH-POWER PULSED GAS LASERS

499

conditions. If an optimum pressure is fixed for a certain diameter, the optimum is preserved as long as the value of the product pD remains unchanged. Hence, we have p = const/D and, since I = jrrD 2 /4 ,

Ip oc const · jD .

(26. 10)

On the other hand, the thermal regime is very important for a C02 laser. The amount of heat liberated per unit volume is proportional to the current density j. In a laser of cylindrical geometry, the heat removed from the central part of the discharge channel to its periphery is proportional to liD. In order to maintain a certain optimum thermal regime, the constancy of the product jD is required. Consequently, the product Ip is a constant, and we arrive at the conclusion that under optimum conditions, the output power of a C02 laser with a longitudinal discharge and gas flow is proportional only to the laser length:

P oc l .

(26. 1 1 )

The highest power attained in such a longitudinal configuration was 1 kW for a discharge tube of length 20 m (Karlov, 1 983). Thus, lasers with longitudinal discharge were very big because of the low pressure (of a few Torr) and low electric field (not higher than 10 V/cm). This problem was partly solved by Leonard (1965) who used a transverse discharge instead of a longitudinal one. The operation of pulsed gas lasers was further perfected by passing to the nanosecond range of pulse durations. Shipman ( 1967) used a pulse of duration 4 ns for pumping an N2 laser with a discharge current of 500 kA and di/dt :::::: 1 0 1 4 A/s provided by a low-resistance double strip line. The plasma density was 1 0 1 5 cm-3 at a gas pressure of 30 Torr. However, a major breakthrough in the development of HPPG lasers was the use of methods of pulsed power technology for pumping lasers. This made it possible to develop lasers with a high gas pressure (one atmosphere and higher). As a result, the laser pulse power and energy increased by many orders of magnitude. There exist three basic methods for pumping high­ pressure gas lasers. The first method involves the use of a multielectron­ initiated avalanche volume discharge, which develops between the electrodes of a discharge chamber on application of voltage pulses of duration 1 0-9-1 0-8 s, providing a pulsed electric field E much higher than the de breakdown electric field Edc · We will use the term electric-discharge lasers for devices of this type. This pumping method was developed based on the results of studies of nanosecond discharges in gases (see Chapter 4). The second method is direct pumping of the working gas by a high­ power pulsed electron beam. In this case, the electron beam is injected into

Chapter 26

500

the laser chamber, as a rule, transverse to the laser beam path, and ionizes the gas in the chamber, creating a plasma that serves as the active medium of the laser. It should be noted that no electric field is applied in this case to the electrodes in the chamber, and the entire energy required for plasma production comes from the electron beam. This method basically differs from the above method where electrons only initiate a discharge, while plasma is created due to ionization processes in the gas. Finally, the third method is based on the application of an electric field weaker than the de breakdown field Edc. and electrons, ions, or x rays are injected into the chamber. In this case, the gas discharge is referred to as an electron-beam-controlled discharge. This is a non-self-sustained discharge (see Chapter 4). It is clear that with E > Edc this method is similar to the first method since the injected electrons play the role of discharge-initiating electrons.

2.2

Electric-discharge lasers

Pulsed C02 lasers were the first atmospheric-pressure electric-discharge lasers (Laflame, 1 970). The creation of these lasers marked an important stage in the evolution of quantum electronics. These systems are simple in structure, reliable in operation, and possess high energy parameters. At the early stage of the development of atmospheric-pressure C02 lasers, the medium was excited most often in a transverse system of electrodes, between a solid anode and an array of needles. For a discharge of duration 1 J.LS, the current through the needles was limited by a 1-kn resistor (Laflame, 1 970). Despite the nonuniform excitation of the working medium and the low efficiency, this system, owing to its simplicity, was in wide use. However, the main attention of researchers was subsequently concentrated on lasers in which uniform excitation of the working medium was attained due to preliminary ionization of the working medium. These devices together with lasers of the above type constitute a new class of lasers, viz., electric-discharge or TEA lasers. To excite the working medium in electric-discharge lasers, various electrode systems are used (Fig. 26.3). In the configurations shown schematically in Fig. 26.3, b-e, the required initial electron density in the main gap is provided by ultraviolet illumination of the gap which ionizes uncontrollable and easily ionizable impurity particles and by ignition of an auxiliary discharge whose plasma supplies electrons to the gap. The latter process leads to a redistribution of the electric field strength in the gap, eliminating the need to use specially shaped electrodes. The electrodes of the main discharge are specially shaped for the cases where the initial electron density is created by preliminary ionization of the

HIGH-POWER PULSED GAS LASERS

501

working medium with the ultraviolet radiation of an auxiliary discharge ignited in the vicinity of the main gap (Fig. 26.3, /, g). The electrode shaping can be performed in compliance with recommendations of Rogowski, Bruce, Harrison, Felicci, or Chang (Mesyats et al., 1 995). Owing to the their simple shape, Chang's electrodes are in most common use. The main goal of shaping is to obtain a uniform electric field in electrode systems of finite width. It should be noted, however, that the reduced input energy in a gap with a uniform decreasing field is nonuniform (increasing from the edge to the center). Therefore, simpler (e.g., semicylindrical) electrodes as well as electrodes with a plane central part and rounded edges are also used. The latter electrode configuration provides the most uniform energy distribution in the gap. (b)

� r ;;; � (a)

(g)

(c)

�

(e)

(j)

(h)

(i)

1:c��al

Figure 26. 3. Schematic diagram of devices for initiation of a high-pressure pulsed volume discharge. A anode, C cathode, MG Marx generator -

-

-

An auxiliary discharge, which produces a required initial electron density in the main discharge gap and creates conditions for the initiation of a volume discharge in the gap, plays a very important role in the performance of a laser. Now, many types of discharge have been tested as auxiliary discharges, namely: a) the discharge through a dielectric or the barrier discharge initiated beneath (Fig. 26.3, i) or directly at one of the main (grid) electrodes (Fig. 26.3, b); b) the corona discharge in point-plane (Fig. 26.3, c,.f) or wire-plane (Fig. 26.3, g) electrode configurations; c) the spark discharge;

502

Chapter 26

d) the spark or creeping discharge over the surface of a dielectric (Fig. 26.3, h); e) the diffuse-channel discharge (Fig. 26.3, f), and f) the auxiliary discharge initiated immediately in the main gap (Fig. 26.3, e). In addition, there exist methods for creating the initial electron concentration in the working volume with the help of flows of accelerated low-density electrons, neutrons, 3H particles, x rays, and low-energy electrons filling the working volume. Investigations (Kast and Cason, 1 973) have shown that photoelectrons appear in the working volume of a laser mainly as a result of direct photoionization by radiation with a wavelength of 1 1 5-120 nm or over 1 60 nm. Since such radiation cannot ionize C02, N2 , and He molecules, it is believed that uncontrollable impurities of organic compounds, which are always present in a laser cell, are subject to photoionization. Sometimes, a substance with a low ionization potential (cesium, xylenes, NN dimethyl aniline, tri-N-propylamine, etc.) is added to the working medium to increase the initial electron density. Using such substances gives the following advantages: high values of n0 can be attained more easily, the discharge becomes more homogeneous, and the energy delivered to the gas and the laser efficiency increase. A disadvantage is that the inner surface of the cell and the structural elements inside the cell are contaminated during the operation of the laser. Let us consider some preionization methods depicted in Fig. 26.3 in greater detail. A diffuse-channel discharge (Fig. 26.3, c-./) is used, as a rule, in repetitively pulsed lasers with a small electrode separation (Bychkov et al. , 1 977), where a high preionization level is desirable in view of the short sparking time, considerable effect of the electrode irregularities, and decomposition of the gas mixture, which adversely affects the stability of a volume discharge. It is well known (Mesyats et al., 1 995) that discharges with a discharge channel (n 1 0 17 cm-3) ensure the highest preionization level, while corona discharges make the smallest contribution to the dissociation of C02 (Chang and Tavis, 1 974). A diffuse-channel discharge combines the merits of the above two types of discharge. It is initiated between a solid and a segmented electrode and consists of a large number of diffuse filaments some of which form a channel at the final stage of the discharge. A segmented electrode is made from a series of thin metal foil strips fixed to a thicker insulating base. The sequence of processes occurring in this case is as follows (Bychkov et al. , 1 977): First, explosive emission centers, which are observed as luminous spots, appear on the thin metal electrode. From some centers, diffuse glowing filaments propagate toward -

HIGH-POWER PULSED GAS LASERS

503

the opposite electrode, while other centers operate for a rather long time ( 1 0-80 ns) without any noticeable propagation to the bulk. In a section of length 5 mm, 4-8 diffuse filaments are observed at V = 1 0-20 kV. After 1 0-40 ns (depending on V), a highly conducting channel is formed in the brightest filament in which 20-40% of the energy spent for preionization of a segment is liberated. The electron density in the brightest luminous region near the cathode, measured by the schlieren method, was 3.6· 1 0 1 6 cm-3, i.e., was much lower than in a typical hot channel. 2.3

Electron-beam pumping

This method was proposed by Basov and co-workers for pumping liquid xenon lasers (Basov, 1 964) and was subsequently widely used for exciting the active media of high-pressure lasers. Electron beams of energy 0. 1-1 MeV, current density 1 02 A/cm2, and duration 1 0-8-1 0-6 s are usually

employed. With beams of energy 1 MeV, uniform excitation of a gas at a pressure of tens of atmospheres can be attained with input energy densities ofup to 1 J/cm3, which makes it possible to approach the lasing threshold for various molecule species (Rhodes, 1 979). �

Figure 26. 4. Electron-beam-pumped lasers with transverse pumping (a) and with a coaxial laser chamber and a coaxial cathode (b)

The following two schemes of electron-beam pumping are widely used at present (Fig. 26.4). A high-voltage pulse is applied to a vacuum diode whose cathode operates in the explosive electron emission mode. The operation of diodes of this type was described above. The anode is piece of thin metal foil or Dacron film through which electrons are injected into the laser chamber. In cases where higher working pressures are required, the foil is placed on a support grid on the vacuum side. Figure 26.4, a shows a schematic diagram of transverse pumping with the electron beam injected from one side of the laser chamber. Such laser chambers make it possible to work with pressures of hundreds of atmospheres and are easy to operate. The disadvantages of this pumping scheme are nonuniform excitation of the laser medium and large beam current losses (up to 50-70%) at the support grid. Uniform excitation can be attained in lasers with multisided pumping. In this case, an

504

Chapter 26

electron beam is injected into the laser cell from two or more sides. In the general form, this can be coaxial pumping (Fig. 26.4, b). At the initial stages of evolution of laser technology, longitudinal electron-beam pumping was used (Rhodes, 1 979; Hoffman et al. , 1 976). To conveniently operate the resonator, the electron beam is turned by a magnetic field; to reduce the debunch and losses of electrons at the laser chamber walls, the electron beam is focused by a magnetic field. This pumping scheme is used for electron energies � 1 MeV or for low working mixture pressures. The main drawback of the longitudinal pumping scheme is that the creation of a pulsed magnetic field requires large amounts of energy, which are usually greater than the energy expended for the production of the electron beam. Let us consider the qualitative pattern of the interaction of an electron beam with a high-density cold gas. For the sake of simplicity, we take the gas to be atomic and its pressure to be high enough to assume that the beam energy is transferred to the gas mainly through binary collisions of electrons with atoms. Under these conditions, high-energy electrons of the beam entering the gas experience multiple elastic collisions with atomic nuclei and relatively infrequent inelastic collisions with atomic electrons, resulting in excitation and ionization of gas atoms. Electrons resulting from ionizing collisions and having energies higher than the excitation energy for the lower electron level can also ionize and excite the gas. Therefore, a cascade of ionizing collisions develops in the course of beam injection, and the number of low-energy electrons, ions, and excited atoms increases as in an avalanche; i.e., plasma is formed. The electron beam plasma differs from the electrical discharge plasma in a number of specific properties. For example, the density of charged particles in the electron beam plasma is much higher than the equilibrium density determined by the Saha relation, and the electron temperature is lower than its equilibrium value. For this reason, such electron beam plasma is also referred to as supercooled plasma. The intense recombination processes occurring in such plasma render it a promising laser medium. The characteristics of an electron beam plasma can be determined in much the same way as the characteristics of a discharge plasma, i.e., by solving the kinetic equations for particle densities and radiation together with the Boltzmann equation for the plasma electron distribution function (Evdokimov, 1 982). The physics of the interaction of an electron beam with a gas is described elsewhere (Evdokimov, 1 982; Berger and Seltzer, 1 964; Vorob'ev and Kononov, 1 966). The electrons of a beam entering a gas lose their energy through collisions until their average kinetic energy becomes comparable to the gas temperature. Such thermalized electrons (TE's) play the main role in the ·

HIGH-POWER PULSED GAS LASERS

505

build-up of space charge in a gas gap exposed to an electron beam. The space charge of TE' s may produce strong electric fields (Mesyats, 1 975), the field strength being determined by the TE distribution over the gap width. Calculations show that the absorbed energy distribution (AED) in a gas chamber (and, hence, the rate of generation of active plasma particles, 'I', and the rate of thermalization of electrons, q, strongly depends on many parameters such as the electron energy spectrum of the accelerated beam, the material and thickness of the input foil, the material of the rear wall of the chamber (anode), the gas type and pressure, etc. The foil separating the vacuum diode of the accelerator from the gas chamber is an important structural element of devices intended for gas excitation and ionization by an electron beam. In actual devices, aluminum or titanium foils of thickness 20-50 J.tm are generally used. These foils are "thick" for electrons with energies of 1 00-300 keY, whose extrapolated range in aluminum is 70-400 J.tm, and their effect on the AED may be significant. The reflection of electrons from the anode also affects the absorbed energy distribution, and the larger the atomic number of the material, the greater the number of reflected electrons and their mean energy. Consequently, the AED near the anode in a gas gap can be changed by changing the anode material. It is found experimentally that the delivery of the electron beam energy to the working gas is much more efficient if the laser cell is immersed in a longitudinal (relative to the beam direction) magnetic field of strength H = 1 -4 kGs (Cartwright, 1989). Figure 26.5 shows AED ' s calculated by the Monte Carlo method taking into account the magnetic field (Evdokimov, 1 982) for the output laser amplifier LAM of the Aurora system whose working volume is 1 00 x 1 00x200 em (Cartwright, 1 989). The Ar-Kr-F2 gas mixture was excited by two electron beams injected toward each other through the side walls of the chamber. It can be seen from the figure that the magnetic field increases the total energy stored in the gas cell and improves the uniformity of pumping in the chamber cross section. The rate of gas ionization by an electron beam with a current density j is determined by the absorbed energy distribution D(z) . e ei

\f(z) = 1

(26. 12)

Here, ei is the energy going into the formation of an electron-ion pair. If an electron of energy T0 gives rise to an ionization cascade, which is completely absorbed in the gas after (on the average) Ni ionizing collisions, we have

506

Chapter 26 (26. 13)

i.e., 81 is the energy lost in the generation of one electron by the ionization cascade in the gas. It should be borne in mind that some part of the cascade energy goes into the excitation of electronic and vibrational levels and is lost in elastic collisions; therefore, we have 8; > I .

z

[em]

Figure 26.5. Absorbed energy distribution in the cross section of an amplifier. T0 = 675 keY; the thickness of titanium (1, 3-5) and Dacron (2) foils is 50 J.llll; argon pressure is 1200 rom Hg (1) and krypton pressure is 600 rom Hg (2-5); H = 3 (1-3), 1 (4) and 0 kGs (5)

The energies of formation of an electron-ion pair were measured experimentally. The results of these measurements for pure gases are as follows: Gas

He

Ne

Ar

Kr

e;, eV

42.3

36.6

26.4

24.2

22

36.3

34

35

30.9

32.9

Experiments have shown that 81 is practically independent of the spectral composition of the electron beam, but strongly depends on the gas purity, which is associated with Penning ionization processes.

HIGH-POWER PULSED GAS LASERS 2.4

507

Electroionization lasers

These are high-power gas lasers pumped with an electrical discharge controlled or triggered by an electron beam. This type of discharge, which was run for the first time by Mesyats et al. ( 1 970), was described in Chapter 4. The first pulsed high-pressure laser in which this type of discharge was used was developed by Basov et al. ( 1 9 7 1 ). Later, this discharge was successfully applied to produce lasing in KrF (Mangano and Jacob, 1 975). A typical scheme of a laser excited by an electron-beam-controlled discharge is shown in Fig. 26.6. An electron beam is injected into the discharge gap; a capacitive energy store connected to the anode of the laser chamber can be operated permanently or through a switch to ensure pulsed voltage supply. The electron beam ionizes the working mixture, producing a conducting medium in the entire volume of the gap; the energy store is discharged through the gap, delivering energy to the volume discharge, which is similar to a glow. Two typical laser pumping modes can be distinguished: pumping with a non-self-sustained discharge and pumping with a gas-amplified discharge. e

Figure 26. 6. Schematic of a laser with combined pumping: case {1), insulator (2), anode contact (3), anode (4), mirrors (5), foil (6), and grid (7)

A non-self-sustained discharge in rare-gas-halide mixtures is stable in weak fields, but constricts as the field exceeds a certain limit. It should be noted that the constriction of a discharge in rare-gas-halide mixtures differs significantly from that of a discharge in nitrogen in that the conductivity of the channels is not very high and these channels can coexist with the volume stage of the discharge for a long time. The energy supplied to the gas by a non-self-sustained discharge appears to be comparable, because of the electron attachment, to the energy input from an electron beam.

508

Chapter 26 DESIGN AND OPERATION OF PULSED C02

3.

LASERS

High-power pulsed C02 lasers are pumped, as a rule, by a self-sustained discharge or by an electron-beam-controlled discharge. Lets us consider lasers of the first type. A typical schematic diagram of such a laser is shown in Fig. 26.3 . Like all HPPG lasers, this is a laser with transverse pumping. Figure 26.7 shows schematically the circuit and design of a repetitively pulsed C02 laser. Experiments proved that such a laser can operate at a frequency of up to 20 kHz with an average power density of 34 W/cm3 (Brandenberg et al. , 1 972), generate radiation pulses with an energy of �20 J at a frequency of 1 00 Hz (Jones, 1 978), and radiate reliably an average power of 1 0 kW and higher. A comprehensive analysis of the energy characteristics of lasers of this type was carried out by McDaniel and Nighan ( 1 982), Smimov ( 1 983), and Mesyats et al. ( 1 995). These lasers operate in the non-self-sustained discharge mode; that is, the voltage applied to the laser cell is lower than the Paschen (de breakdown) voltage. �

(a)

Figure 26. 7. Schematic of the excitation circuit (a) and design of a repetitively pulsed C02 laser (b): case {1), pulse generator (2), electrodes (3), preionization systems (4), fan (5), and heat exchanger (6}

The C02 lasers excited by a self-sustained electrical discharge seem to hold much promise. Such systems appeared later, after the development of methods for initiating self-sustained discharges in large volumes. Let us consider the most interesting high-power pulsed lasers. A plasma-electrode C02 laser (Pavlovsky et al., 1 976) was assembled according to the scheme shown in Fig. 26.3, h. The working volume of the laser was confined between 80-cm long plasma electrodes and measured

HIGH-POWER PULSED GAS LASERS

509

1 5 x l 5 em in cross section. The pulsed power supply was a six-stage Marx generator. The reduced energy input in this laser reached 200 J/(l · atm), and the reduced radiation energy was 30 J/(l·atm) with an efficiency of 1 5%. This device features the use of plasma electrodes formed by a discharge over the surface of a dielectric. A further increase in volume of the active medium was achieved due to its preionization by an auxiliary discharge operating directly in the working zone. The principal units of the device (Fig. 26.3, c) were a gas-discharge chamber and high-voltage power supplies for the main and auxiliary discharges. The trigger electrode, cathode (C), and anode (A) of the main discharge gap were mounted in the chamber (Apollonov et al. , 1 987). The anode was 2.3 m long with a total width of 65 em; the electrodes separation was 3 5 em. The electrode system was placed in a dielectric tube of diameter 1 m and length 3 m. The power supply for the auxiliary discharge was a 24-stage 1 -MV, 300-J Marx generator with a capacitance of 0.59 nF. The main discharge was initiated with the help of two five-stage Marx generators capable of storing 40 kJ and generated a pulse of peak voltage up to 300 kV. A total output energy of 8.4 kJ could be extracted from the entire volume with an efficiency of 2 1 %. C02 lasers with initial electrons transported to the main discharge gap from an auxiliary discharge seem to allow more room for increasing the active volume. Measurements performed for a laser of this type have shown that for d = 40 em and an absorbed energy of 1 50 J/1, the reduced radiation energy was 1 8 J/1, which corresponds to an efficiency of 1 5%. This value matches the results obtained for d = 1 5 and 20 em and an atmospheric-pressure mixture of C02 :N2 :He = 1 : 1 :8. As a rule, electric-discharge C02 lasers operate at near-atmospheric pressure of the working gas mixture. However, in some cases, the pressure may be as high as 1 0 atm and even more. High-pressure electric-discharge lasers are of interest as systems generating short radiation pulses and allowing continuous tuning. The first publication in this field (Hidson et al. , 1 972) described a C02 laser with a gap of 2.5 em between a cathode consisting of 1 20 tungsten points and a solid brass anode. The working pressure ranged from 1 to 5 atm. Subsequently, for electric-discharge lasers with preionization of the working medium at the stage of discharge initiation, the working frequency range was considerably extended and continuous tuning was realized (Alcock et al. , 1 973; Bychkov et al. , 1 977; Karlov et al. , 1 987). A rather wide continuous tuning range (46 cm- 1 ) was attained by Karlov et al. ( 1 987) for a radiation pulse energy of up to 70 mJ. For the C02 :N2 = 1 : 1 working gas mixture at 8-atm pressure, continuous tuning was attained for the P- and R-branches of the 00° 1 - 1 0°0 and 00°1 -02°0 transitions in the frequency ranges 938-95 1 , 970-980, 1 04 1 - 1 054, and 1 073-1 083 cm- 1 , respectively.

510

Chapter 26

Considerable advances in increasing the peak power of C02 lasers were made when an electron-beam-controlled non-self-sustained discharge was used for their pumping and the possibility of volume current passage in gaseous media at a pressure of up to 1 5 atm was demonstrated (Mesyats et al. , 1972). The results of further work on this line (Evdokimov, 1 982; Mesyats, 1 97 5; Mesyats et al. , 1 99 5) formed the basis for the creation of high-power gas lasers. Lasers with the working medium pumped by a non-self-sustained discharge controlled by radiation from an external ionizer are referred to as electron-beam-controlled lasers. Lasers of this type were first built at the Physics Institute of the USSR Academy of Sciences (Basov et al. , 197 1) and later at Los Alamos National Laboratory (Fenstemacher et al. , 1 971). The development ofthese lasers was a breakthrough in quantum electronics. I

3

2

4 6

5

7

8

9

+ Vo

Figure 26.8. Schematic of the design and power supply circuit of the electron-beam­ controlled pulsed C02 laser

A schematic circuit for the initiation of an electron-beam-controlled non­ self-sustained discharge is shown in Fig. 26.8. The working medium fills a gas cell 7 containing a grid cathode 5 and a specially shaped solid anode 8, which form the active zone 5-8 of the laser. The gas cell is adjacent to a vacuum diode 2 in which an electron beam is formed between a bowl-shaped cathode 1 0 and foil 6 (or a special extractor), which also plays the role of a transparent anode. The electrode gap 5-8 is in a constant electric field, which provides the most efficient energy transfer to the upper laser level. As the spark gap SG operates, the capacitor C1 discharges into the explosive­ emission vacuum diode that generates a large-cross-section electron beam. The electron beam entering the cathode-anode gap through the thin metal foil 6 ionizes the working medium and produces plasma with a charge carrier density n . The plasma, which is in an electric field, carries a current of density

HIGH-POWER PULSED GAS LASERS j = evn = ec

( !)

511 (26. 14)

n,

which delivers to the gas the energy required for pumping w=

p J t }E 0

dt

.

(26. 1 5)

Here, fp is the pumping pulse duration, n is the electron concentration, c is a constant characterizing the gas, and E is the electric field strength. The designs of electron-beam-controlled C02 lasers are described in numerous publications. Let us consider some design versions. Figure 26.9 shows schematically the main units of the LAD-2 C02 laser with an active volume of 270 1 (30x30x300 em), developed at IHCE (Bychk.ov et a/. , 1 976). The gas was ionized by an accelerated electron beam. The gas cell 1 of volume 4500 I was made of steel; its inner surface was lined with fiber glass 3 to suppress corona discharges. Anode 2 of the gas cell with a working area of 30x300 ern was made of duralurnin and specially shaped to prevent coronas. The cell was filled with an atmospheric pressure COz:N2 :He = 1 : 1 :3 gas mixture. 2620 mm

Figure 26.9. Schematic of the LAD-2 electroionization C02 laser

An electron accelerator produced an electron beam of cross section 30x300 em with a current density of 0.4 A/crn2 uniform to ±1 5%. The average electron energy in a pulse of duration 1-3 J..LS was 200 keY. In the vacuum diode 4, a multipoint cold cathode 5 operating in the explosive emission mode was used. The beam was extracted through a window

512

Chapter 26

covered with polymer film 7 of thickness 1 50 Jliil resting on a metal grid 6. The discharge current in the laser cell closed on a steel grid 8 that protected the film from the thermal action of the discharge. The total transparency of the window and the grid for 200-keV electrons was no less than 50%. The energy needed to excite the active volume of the gas cell was stored in a capacitor bank of capacitance 1 5 � and voltage 200 kV. High-voltage pulses of amplitude up to 500 kV were fed to the vacuum diode from a Marx generator whose capacitance with the capacitors connected in series was 0.67 �. In this laser, use was made of a resonator with an output mirror 9 of diameter 240 mm, which was made of a plane-parellel K.RS-6 plate with a 1 7% reflectance of an individual face. The totally reflecting mirror was a gold-plated quartz substrate of diameter 300 mm and radius of curvature 1 2 m. The radiation energy extracted in a pulse of 1 .5 JlS FWHM was 5 kJ with an efficiency of 20%. The use of an unstable resonator and the extraction of radiation from the entire volume made it possible to obtain with this laser a radiation energy of 7500 J (Mesyats et a/. , 1 995). This design is quite conventional for pulsed C02 lasers with various volumes and pressures. Its interesting version is a double-beam and, hence, double­ cell C02 laser producing 2.5 kJ of output energy in a pulse (Eninger, 1 976). Further advances in laser technology were made in connection with the development of large-scale oscillator-amplifier systems intended for studying the applicability of C02 lasers to ICF research. Over a short period, the Helios and Antares systems (Perkins, 1 980) were developed which are capable of radiating 1 -40 kJ in a nanosecond pulse. These systems are based on devices similar in design to those described above. The reduction of the overall dimensions of electron-beam-controlled C02 lasers is important in the context of the creation of compact high­ sensitivity gas analyzers, lidars, high-resolution spectrometers, and other instruments in which the properties of overlapped laser amplification spectrum are used. In MIG-4, a compact repetitively pulsed electron-beam-controlled C02 laser (Mesyats et al. , 1 995) (Fig. 26. 1 0), the volume discharge intended to pump the working gas medium was initiated between a solid brass anode and a grid cathode and occupied a volume of 3 x3.5 x72 em. The energy needed to initiate the discharge was stored in a low-inductance capacitor bank 3 of capacitance 0. 1 9 JlF, which was charged from a de voltage source to 50 kV. A volume discharge was initiated in the working zone of the laser by an electron beam with the following parameters: peak current 7.2 kA, cross­ sectional area 72x3 em, duration 4.2 ns, average electron energy 1 55 keV, and pulse repetition rate 1-50 Hz.

HIGH-POWER PULSED GAS LASERS

513

This laser generated 30-J radiation pulses at a repetition rate of up to with up to 25% efficiency. In a quasistable medium, the radiation power at 50 Hz was -1 kW at the early stage and 400-500 W at the quasistationary stage up to the rupture of the foil. The chemical composition of the laser active medium changed in the course of repetitive operation, resulting in a decrease in output energy. This is due to the fact that as the laser turns on, there occur decomposition of C02 and accumulation of CO and electronegative molecules of 02 , NO, N02, and N20, resulting in a decreased discharge duration due to enhanced electron attachment and, hence, in a lower output energy.

50 Hz

Figure 26. 1 0. Block diagram of the MIG-4 C02 laser: distributed-constant energy storage line (1), vacuum diode (2), storage capacitors (3), heat exchanger (4, 5), working wheel of the cross flow fan (6), and internal guide ( 7)

In electroionization C02 lasers with a high gas pressure ( 1 0 atm and higher), a continuous tuning is possible (Bagratashvili et a/., 1 97 1 ). When the working mixture in a C02 laser is at a pressure of 1 0 atm, the vibrational­ rotational lines in the gain spectrum overlap and continuous tuning can be realized with the help of a selective resonator. This effect is described in detail elsewhere (Mesyats et a/., 1 995).

5 14 4.

Chapter 26 DESIGN AND OPERATION OF HIGH-POWER EXCIMER LASERS

For electron-beam pumping of excimer lasers, electron accelerators are used which produce electron beams of energy 0. 1-2 MeV, current density 1 0- 1 03 A/cm2, and duration from 2 J..lS to 5 ns. When combined pumping by an electron beam and an external electric field is used, the beam current density can be several times lower. Figure 26. 1 1 shows schematically a laser in which an electron beam is used for two-sided pumping. For combined pumping, energy storage capacitors are charged by a de or pulsed voltage.

Figure 26. 1 1. Schematic of a laser pumped from two magnetically focused beam accelerators: Marx generators (1), water lines (2), vacuum diodes (3), laser chamber (4), foil (5), and magnets (6)

The principle of operation of such devices is as follows: A Marx generator used as a power supply charges coaxial lines with a vacuum diode as a load. The cathode is a needle or a graphite plate operating in the explosive electron emission mode or specially created plasma. The anode is made of thin metal foil or Dacron film through which electrons are injected into the laser chamber. Since the working pressure in rare-gas-halide lasers ranges between 1 and 5 atm, the foil is supported by a grid on the vacuum side. As mentioned in Section 2 of Chapter 26, in the case of two-sided pumping, the plasma density distribution in the laser cell is spatially nonuniform. To make the plasma more uniform, multisided pumping is used. For example, four electron beams produced by planar-diodes accelerators were simultaneously inj ected in the chamber of the laser described by Edwards et a/. (1 983). With such a design, the total current injected into the laser chamber can be increased without disturbing uniform pumping. Excimer lasers with a radiation energy of 1 03- 1 04 J are described by Rosocha et al. ( 1 986). Much attention is being given to the development of KrF lasers (A. = 249 nm) as the most efficient type of excimer lasers. The maximum radiation energy (� 1 0 kJ) in a pulse of duration �500 ns was attained at LANL on the Aurora system (Rosocha et a/. , 1 986). With KrF molecules, reduced output energies of up to 40 J/1 can be achieved with an

HIGH-POWER PULSED GAS LASERS

515

efficiency of up to 1 2% (Rica et a/. , 1 980). In designing wide-aperture devices capable of radiating over 1 0 kJ of energy, the rated specific energy density is usually taken as � 1 0 mJ/cm3 for an efficiency of 1 0%; in this case, the active volume of the laser must be over 1 03 1. Owadano et al. (1 987) described the design of a high-power laser pumped by a pulsed electron beam of duration � 1 00 ns which is used as the third amplification stage in a laser system. The electron beam is formed by eight cathodes to which voltage is applied from four water strip lines charged from a high-voltage generator. For an active volume of 66 1, radiation of energy � 1 and 0.6 kJ and pulse duration 1 00 and 1 0 ns, respectively, was generated. Earlier, a similar KrF laser system generated radiation of en�rgy �200 J (Edwards et al. , 1 983). Systems of this type show a rather high total efficiency [�2% for the laser described by Sullivan ( 1 987)], but they can form only single radiation pulses in view of the technical difficulties associated with renewal of the active medium. The laser whose design is shown in Fig. 26. 1 1 can be equipped with a working gas renewal system. It should be noted that the highest radiation energies have been achieved with lasers of this type (Cartwright, 1 989; Rosocha et al. , 1 986; Ueda and Takima, 1 988). The laser shown in Fig. 26. 1 1 differs from one described by Owadano et al. (1 987) in that the electron beam is injected into the laser chamber from two sides, and uniform energy input is provided by applying a magnetic field directed in parallel with the electron beam. The total efficiency of this type of laser is rather low since the creation of a magnetic field is power consuming. The electron beam in these two laser systems was formed by the same scheme. The laser design shown in Fig. 26. 1 1 has been accepted as a basis for the development of systems capable of radiating up to 1 00 kJ of energy (Sullivan, 1 987). A XeCl excimer laser (A. = 308 nm) with six-sided electron-beam pumping is described by Mesyats et al. ( 1 992). Twelve accelerators with Marx generators discharged into explosive-emission graphite-cathode diodes were used. Each accelerator generated an electron beam ( 1 JlS) of energy 600 keV, current 60 kA, and beam cross-section 25 x 1 00 em. The accelerators were arranged on two levels and pumped a coaxial laser cell of volume 600 1. The Marx generators and the diodes were mounted in a common vacuum chamber. This resulted in a compact laser operating without coaxial energy storage lines. The Marx generators operated with a small jitter (�1 0 ns). The total electron current was 700 kA. The radiation pulse energy was 2 kJ (Mesyats et a/., 1 995). A schematic diagram of this laser is given in Fig. 26. 12. Electric-discharge excimer lasers are also being extensively developed. The systems initiating a volume discharge in lasers of this type are similar to those shown in Fig. 26.3. For pumping excimer lasers, transverse discharges

516

Chapter 26

exhibit the most promise. With transverse volume discharges, pumping powers of 1-10 MW/cm3 have been attained for working mixtures of R:R':X = 1 000: 10: 1 at a pressure of several atmospheres. When a storage capacitor is discharged into a gap filled with a rare-gas­ halide mixture, the voltage waveform, in the case of formation of a volume discharge, indicates three characteristic stages of the process: a) the prebreakdown stage whose duration usually ranges from 50 to 100 ns; the gap voltage increases and, immediately prior to breakdown, becomes several times greater than the de breakdown voltage; a volume discharge starts developing due to preionization; b) the stage of rapid voltage drop that lasts -10 ns; the current through the gap increases by several orders of magnitude, while the voltage decreases to a value several times smaller than the de breakdown voltage; the formation ofthe volume discharge is completed; c) the quasistationary stage whose duration depends on a large number of parameters and may be over 1 !J.S. (During discharges in rare gases, the voltage at the quasistationary stage is considerably lower than the de breakdown voltage due to the effect of stepwise ionization, while this voltage in nitrogen is approximately equal to the de breakdown voltage.) The pumping of the active medium occurs at the stage of rapid voltage drop and at the quasistationary stage.

Figure 26. 12. Schematic of an excimer laser with a transverse discharge and working mixture renewal: storage capacitor (1), peaking capacitor (2), thyratron (3), nonlinear iron-coil choke (4), screen (5), grid anode (6), cathode (7), fluoroplastic plate (8), gas chamber case (9), turbofan (1 0), auxiliary electrodes (11), and blocking capacitor (12)

HIGH-POWER PULSED GAS LASERS

517

At elevated pressures, only a multielectron-initiated volume discharge is possible (Mesyats et a/. , 1 995). The conditions for the formation of a homogeneous discharge under elevated pressures can be formulated as follows: First, it is necessary that the density of initial electrons produced by an external ionizer be over (rcrt3 (where rcr is the critical radius of the electron avalanche head), the electron density at which a streamer starts developing. Second, in view of the fact that the preionizer usually operates for a short time and the initial electrons leave a layer of width x adjoining the cathode due to drift, the condition x < rcr must be satisfied. In this case, the streamer formation can be avoided due to insufficient overlap of avalanches in the electron-depleted layer near the cathode. Thus, preionization makes it possible to produce initial electrons in the bulk of the gas and/or at the cathode from which electron avalanches develop. Overlapping of individual avalanches (the rate of evolution of avalanches depends on the applied electric field) leads to the formation of an elevated-pressure homogeneous discharge. The duration of the volume stage of a discharge at an elevated pressure is determined by many factors (specific input energy, mixture composition and pressure, electrode shape, material, and surface condition, etc.); however, the most common reason for discharge constriction is cathode instability (Mesyats, 1 975; Mesyats et al., 1 995). To attain lasing in high-pressure rare-gas-halide pulsed lasers, an energy of �0. 1 J/(cm3·atm) must be supplied to the active medium within a short time (usually � 0.1 �s), thus providing for the operation of a volume discharge. Therefore, high-pressure lasers must incorporate both a pumping generator and a preionization system. The choice of the circuit design is dictated by the requirements on the pumping pulse. For capacitive energy storage, use can be made of individual capacitors or distributed-constant lines (e.g., water-insulated lines). It is very important to match the pumping generator to the discharge gap. Here, matching implies not only that the wave impedance of the generator must be equal to that of the gap, but also that the inductance of the discharge gap leads must be as low as possible to minimize the losses in delivering energy from the generator to the load. Figure 26. 1 2 shows schematically a compact excimer laser with a transverse discharge and working medium renewal with the use of a turbofan (Mesyats et al., 1 995). The energy storage capacitor is charged from a pulse generator producing pulses of duration 1 0 �s and peak voltage controllable in the range 10-35 kV. After the operation of the switch, a peaking capacitor is charged. For the switching element, a thyratron is used. This pumping generator operates with a voltage of 25 kV at a pulse repetition rate of up to 500 Hz.

518

Chapter 26

The physical processes occurring in other types of excimer lasers and their designs are described elsewhere (Rhodes, 1 979; McDaniel and Nighan, 1 982; Mesyats et al. , 1 995; Mangano and Jacob, 1 975; Searles and Hart, 1 975; Brau and Ewing, 1 975; Eletsky, 1 978; Evdokimov, 1982; Rosocha et a!. , 1 986; Rica et al. , 1 980; Owadano et al. , 1 987; Ueda and Takima, 1 988; Sullivan, 1 987; Mesyats et al. , 1 992; Baranov et a/. , 1 988; Ischenko et al. , 1 976; Smimov, 1 983).

REFERENCES Alcock, A. J., Leopold, K., and Richardson, M. C., 1 973, Continuously Tunable High­ Pressure C02 Laser with UV Photopreionization, Appl. Phys. Lett. 23:562-564. Apollonov, V. V., Baitsur, G. G., Prokhorov, A. M., Semenov, S. K, and Firsov, K. N., 1 987, Dynamic Profiling of the Electric Field during the Formation of a Self-Sustained Volume Discharge under Intense Ionization of the Electrode Regions, Kvant. Elektron. 14:221 8-2220. Bagratashvili, V. N., Knyazev, I. N., and Letokhov, V. S., 1 97 1 , On the Tunable Infrared Gas Lasers, Opt. Commun. 4: 1 54-1 56. Baranov, V. Yu., Borisov, V. M., and Stepanov, Yu. Yu., 1 988, Electric-Discharge Rare­ Gas-Halide Excimer Lasers (in Russian). Energoatomizdat, Moscow. Basov, N. G., 1 964, Opening Remarks: Fourth International Quantum Electronics Conference, IEEE J Quant. Electron. 2:354-357. Basov, N. G., Belenov, E. M., Danilychev, V. A., and Suchkov, A. F., 1 97 1 , A Pulsed C02 Laser with a High-Pressure Gas Mixture, Kvant. Elektron. 3: 1 2 1 . Berger, M . Y . and Seltzer, S. M., 1 964, Tables ofEnergy Losses and Ranges ofElectrons and Positrons. NASA Spec. Pub!. No. 3012. Brandenberg, W. M., Bailey, M. P., and Texeira, P. D., 1 972, Supersonic Transverse Electrical Discharge Laser, IEEE J Quant. Electron. 8:4 1 4-4 1 8. Brau, C. A. and Ewing, J. J., 1 975, 354-nm Laser Action on XeF, Appl. Phys. Lett. 1 975. 27:435-437. Bychkov, Yu. I ., Karlova, E. K., Karlov, N. V., Koval'chuk, B. M., Kuz'min, G. P., Kurbatov, Yu. A., Manylov, V. 1., Mesyats, G. A., Orlovsky, V. M., Prokhorov, A. M., and Rybalov, A. M., 1 976, A 5-kJ Pulsed C02 Laser, Pis 'ma Zh. Tekh. Fiz. 2:2 1 2-2 16. Bychkov, Yu. 1., Osipov, V. V., and Savin, V. V., 1 977, Electric-Discharge C02 Lasers. In Gas Lasers (in Russian, R. I . Soloukhin and V. P. Chebotaev, eds.). Nauka, Novosibirsk. Cartwright, D. C., 1 989, Inertial Confinement Fusion at Los Alamos. Vol. 1 -2. Progress on Inertial Confinement Fusion Since 1985. Los Alamos. Chang, N. C., and Tavis, M. T., 1 974, Gain of High-Pressure C02 Lasers, IEEE J Quant. Electron. 10:372-375. Edwards, C. B., O'Neill, F., and Shaw, M. J., 1 983, "SPRITE" - a High Power E-Beam Pumped Kr-F Laser. In Proc. Conf Excimer Lasers, American Inst. Phys., New York, pp. 59-65. Eletsky, A. V., 1 978, Excimer Lasers, Usp. Fiz. Nauk. 125:279-3 14. Eninger, J. E., 1 976, Broad Area Beam Technology for Pulsed High Power Gas Lasers. In Proc. I IEEE Intern. Pulsed Power Conf, Lubbock, TX, pp. 499-503. Evdokimov, 0. B., ed., 1 982, Injection Gas Electronics (in Russian). Nauka, Novosibirsk.

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Fenstemacher, C . A., Nutter, M. J., Rink, J. P., and Boyer, K., 1971, Electron Beam Initiation of Large Volume Electrical Discharges in C02 Laser Media, Bull. Amer. Phys. Soc. (Ser. II.) 16:42. Heard, H. G., 1 963, Ultra-Violet Gas Laser at Room Temperature, Nature. 200(4907):667. Hidson, D. J., Makios, V., and Morrison, R. W., 1 972, Transverse C02 Laser Action at Several Atmospheres, Phys. Rev. Lett. 40A:41 3-4 14. Hoffman, J. M., Hays, A. K., and Tisone, G. C., 1976, High-Power UV Noble-Gas-Halide Lasers, Appl. Phys. Lett. 28:538-539. Ischenko, V. N., Lisitsyn, V. N., and Razhev, A. M., 1 976, High-Power Superluminosity of ArF, KrF, and XeF Excimers in Electrical Discharges, Pis 'rna Zh. Tekh. Fiz. 2:839-842. Javan, A., 1 959, Possibility of Production of Negative Temperature in Gas Discharges, Phys. Rev. Lett. 3:87-89. Jones, C. R., 1 978, Optically Pumped Mid IR Lasers, Laser Focus. 4:68-72. Karlov, N. V., 1 983, Lectures on Quantum Electronics (in Russian). Nauka, Moscow. Karlov, N. V., Kisletsov, A. V., Kovalev, I. 0., Kuz'min, G. P., Nesterenko, A. A., and Khokhlov, E. M., 1987, Continuously Tunable High-Pressure C02 Laser with a Plasma Cathode, Kvant.Eelektron. 14: 2 1 6-2 1 8. Kast, S. J. and Cason, Ch., 1 973, Performance Comparison of Pulsed Discharge and E-Beam Controlled C02 Lasers, J. Appl. Phys. 44: 1 63 1 - 163 7. Laflame, A. K., 1 970, Double Discharge Excitation for Atmospheric Pressure C02 Lasers, Rev. Sci. Instrum. 41 : 1 578. Leonard, D. A., 1 965, Saturation of the Molecular Nitrogen Second Positive Laser Transition, Appl. Phys. Lett. 7:4-6. Mangano, J. A. and Jacob, J. H., 1 975, Electron-Beam-Controlled Discharge Pumping of the KrF Laser, Ibid. 27:495-498. Mathias, L. E. S. and Parker, J. T., 1 963, Stimulated Emission in the Band Spectrum of Nitrogen, Ibid. 3: 16. McDaniel, E. W. and Nighan, W. L., eds., 1 982, Gas Lasers. Acad. Press, New York. McFarlane, R. A., 1 965, Observation of a n-J:r,- Transition in the N2 Molecule, Phys. Rev. 140 (4A): l 070- 1 07 1 . Mesyats, G . A., 1 975, Electric Field Instablilities i n a Volume Gas Discharge, Pis 'rna Zh. Tekh. Fiz. 1 :660-663. Mesyats, G. A., Osipov, V. V., and Tarasenko, V. F., 1 995, Pulsed Gas Lasers. SPIE Optical Engineering Press, Bellingham. Mesyats, G. A., Bychkov, Yu. 1., and Koval'chuk, B. M., 1 992, High-Power XeCl Excimer Lasers. In Proc. SPIE. Intense Laser Beams, SPIE Press, Los Angeles, Vol. 1 628, pp. 70-80. Mesyats, G.A., Koval'chuk, B.M., and Potalitsyn, Yu.F., 1 972, USSR Inventor's Certificate No. 356 824; 1 970, Dokl. Akad. Nauk. 191: 76-78. Owadano, Y., Okuda, 1., Tanimoto, M., Matsumoto, Y., Kasai, T., and Yano, M., 1 987, Development of a 1 -kJ KrF Laser System for Laser Fusion Research, Fusion Techno!. 1 1:486-491 . Patel, C . K. N., 1 964, Selective Excitation through Vibrational Energy Transfer and Optical Maser Action in Ne--C02, Phys. Rev. Lett. 13:61 7-6 1 9 . Patel, C. K . N. and Kerl, R . J., 1 964, Laser Oscillation o n X 1 L.+ Vibrational-Rotational Transitions of CO, Appl. Phys. Lett. 5:8 1-83. Pavlovsky, A. I., Bosamykin, V. S., and Karelin, V. I., 1 976, Electric-Discharge Laser with Active Volume Initiation, Kvant. Elektron. 3:60 1 -604.

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Perkins, R. B., 1 980, Progress in Inertial Research at Los Alamos Sci. Lab. In VIII Intern. Conf on Plasma Phys. and Control. Nucl. Fusion Res. , Brussels, IAEA-CN-3 8/B-2. Prokhorov, A. M., 1 958, On a Molecular Amplifier and Submillimeter Wave Generator, Zh. Eksp. Teor. Fiz. 34: 1 658- 1 659. Rhodes, Ch. K., ed., 1 979, Excimer Lasers, Springer, Berlin. Rica, J. K., Tisone, G. C., and Patterson, E. L., 1 980, Oscillator Performance and Energy Extraction from a KrF Laser Pumped by a High Intensity Relativistic Electron Beam, IEEE J. Quant. Electron. 16: 1 3 1 5- 1 325. Rosocha, L. A., Bowling, P. S., Burrows, M. D., Kang, M., Hanlon, J., McLeod, J., and York, G. W., Jr., 1 986, An Overview of Aurora: a Multi-Kilojoule KrF Laser System for Inertial Confinement Fusion. In Laser and Particle Beams [Selected papers from CLE0'85 - 13m Int. Conf. on Quantum Electronics (Laser and Electro-Optics), May 1 985], Baltimore, Vol. 4, Pt 1 , pp. 55-70. Searles, S. K. and Hart, G. A., 1 975, Stimulated Emission at 28 1 .8 nm from XeBr, Appl. Phys. Lett. 27:243.247. Shipman, J. D., Jr., 1 967, Traveling Wave Excitation of High Power Gas Lasers, Ibid. 10:3. Smimov, B. M., 1 983, Excimer Molecules, Usp.Fiz. Nauk 139:53-8 1 . Smimov, B . M., ed., 1 983, Pulsed C02 Lasers and Their Application in Isotope Separation (in Russian). Nauka, Moscow. Sullivan, J. A., 1 987, Design of a 1 00-kJ KrF Power Amplifier Module, Fusion Techno/. 1 1 :684-704. Ueda, K. I. and Takima, H., 1 988, Scaling of High Pump Rate 500-J KrF Laser. In Proc. Conf Lasers and Electro-Optics, Annaheim, CA., Vol. 7, pp. 2-4. Vorob'ev, A. A. and Kononov, B. A., 1 966, Passage of Electrons Through Matter (in Russian). Tomsk State University Publishers, Tomsk.

Chapter 27 GENERATION OF HIGH-POWER PULSED MICROWAVES

1.

GENERAL INFORMATION

The progress in many fields of science and technology is closely connected with advances in creating new pulsed oscillators capable of producing coherent electromagnetic radiation in various wavelength ranges. A great deal of effort was directed for mastering the microwave range, especially the range 1 0-3-1 m. Microwave devices must meet a large number of requirements set by their specific application (efficiency, overall dimensions, bandwidth, coherence, pulse duration, etc.). In many fields of use, such as radio detection and ranging, plasma physics, and accelerator technology, the maximum output power level is of major importance. High radiation powers are usually generated within short times, i.e., in the pulsed mode. The use of high-power electron beams produced due to explosive electron emission has made it possible to increase the microwave power by many orders of magnitude and bring it to 101 0 W and higher in pulses of duration of the order of 1 o-9-1 o-7 s. This caused a revolution in the views of the potentialities of pulsed microwave elecironics which became possible owing to comprehensive investigations of the interaction of high­ power charged particle flows with electromagnetic waves. One line of investigation has been the study of stimulated emission of electron flows and its applications for the creation of high-power sources of coherent electromagnetic radiation in a wide range of wavelengths and pulse durations. In this respect, high-current pulsed electron accelerators considered in previous chapters possess unique potentialities. In electron accelerators intended for microwave electronics applications, magnetically

522

Chapter 27

insulated coaxial diodes (see Chapter 23) or, more seldom, e.g., in vircators, planar diodes without a magnetic field are used. The first attempt to generate high-power pulsed microwaves was made by Nation ( 1 970). At that time, the systems for beam formation and electron energy extraction were far from perfect. This was the reason for the low efficiency of the microwave oscillator (much lower than 1 %). First important results w�re obtained researchers of the Institute of Applied Physics (Nizhni Novgorod) and Institute of General Physics (Moscow) (Kovalev et al. , 1 973). Microwave pulses of power 3 · 108 W and duration 1 0-8 s with efficiency over 1 0% were generated at a wavelength of 3 em. The next important step on this line was the creation of microwave oscillators operating at high pulse repetition rates at IHCE (El'chaninov et a/. , 1 979). To induce oscillations, stimulated emission of various types of radiation (Cherenkov radiation, cyclotron radiation, transient radiation, etc.) is used. The most common microwave devices using high-current electron beams are the relativistic backward-wave oscillator (BWO or carcinotron) (Kovalev et a/. , 1 973; Carmel et a/. , 1974; El'chaninov et a/. , 1 979; Levush et a/., 1 992; Moreland et a/. , 1 994), multiwave Cherenkov oscillator (MWCO) (Bugaev et a/. , 1 99 1 ) , relativistic klystron (El 'chaninov et a/. , 1 982; Friedman et al. , 1 990), reltron (Miller et al. , 1 992), plasma-assisted Cherenkov oscillator (Kuzelev et a/. , 1982), plasma-assisted slow-wave oscillator (PASOTRON) (Goebel et a/. , 1 998), relativistic gyrotron (Ginzburg et al. , 1 979), relativistic magnetron (Didenko and Yushkov, 1 984), magnetically insulated line oscillator (MILO) (Clark et a/. , 1 988), and virtual cathode oscillators (vircators) (Didenko and Yushkov, 1 984; Jiang et a/. , 1 999; Kitsanov et a/. , 2002). Mechanisms of the stimulated emission of radiation by high-current electron beams and the results of investigations of high-power microwave oscillators and accelerators used for their power supply are described in collection of papers (Gaponov-Grekhov, 1 979-1992; Mesyats, 1983) and in monographs (Bugaev et a/., 199 1 ; Didenko and Yushkov, 1 984; Benford and Swegle, 1 992; Granatstein and Alexeff, 1 987; Barker and Schamiloglu, 2001 ). Among the above microwave oscillators, carcinotron using Cherenkov radiation is most generally employed. For this reason, we will mainly consider in this chapter the microwave oscillators based on carcinotrons. From the viewpoint of the generation of coherent electromagnetic radiation, a free electron has the following obvious advantages over bound (in quantum-mechanical sense) particles (electrons and atoms): a) in going from one state of its continuous energy spectrum to another, a free electron emits a photon whose energy (frequency) can be varied over a wide range by properly choosing the static field and the slow-wave structure;

GENERATION OF HIGH-POWER PULSED MICROWA VES

523

b) it can give up a large number of identical (or almost identical) quanta to the radiation field. The first circumstance allows devices based on classical principles to cover continuously a wide frequency range, while the second one makes them capable to efficiently generate high-power radiation. The stimulated emission process in microwave devices includes an rf current appearing in the electron beam due to electron grouping induced by the rf field and the reverse action of this current on the radiation field. Steady progress in classical microwave electronics made it possible to predict that the performance of microwave devices could be essentially improved by using relativistic electron beams. However, it was obvious that the currents of electron beams produced by "ordinary" accelerators were too low for stimulated emission could be realized. Hopes for the production of electron beams in which relativistic energy of particles would be combined with a high density became reasonable only in the late 1 950s owing to the progress in pulsed power technology. First high-current electron accelerators were developed in the 1 960s.

2.

EFFECTS UNDERLYING RELATIVISTIC MICROWAVE ELECTRONICS

We start our analysis from the conditions that must be realized for at least one electron to emit photons. The main prerequisite to efficient emission is the so-called phase synchronism under which the velocity of a particle is close to the phase velocity of the wave. Therefore, a particle (or group of particles) "immersed" in the decelerating phase of the field may reside in this phase for a long time and give up a considerable portion of its energy to the wave. To realize the mode of synchronism, one of the methods illustrated in Fig. 27. 1 can be used (Gaponov-Grekhov and Petelin, 1 979). First, this may be slowing down a wave or its spatial harmonic. In the case of a homogeneous or spatially periodic medium (Fig. 27. 1 , a, b), Cherenkov radiation is generated, while in the case of an inhomogeneous medium (Fig. 27. 1 , c), this is transient radiation. Second, an electron can be set into motion with a varying transverse velocity (Fig. 27. 1 , d). From the viewpoint of rf electronics, of particular interest are the cases where an electron emits photons as an oscillator during its periodic motion in a static field such as a uniform magnetic field (cyclotron or magnetic bremsstrahlung, Fig. 27. 1 , e) or a spatially periodic field (undulator radiation, Fig. 27. 1 , g). A combination of the above methods can also be used. Such a combination leads to an essentially new effect, viz., anomalous Doppler

524

Chapter 27

effect, such that the oscillatory velocity of an electron increases during the emission of bremsstrahlung, and the oscillator energy and radiation energy are taken from the translational motion of the electron. In addition to single photon (in reference to one electron) emission processes, multiphoton (combination) scattering processes may also take place where a wave incident on a moving electron is re-emitted as another wave (Fig. 27. 1 , h). / / / / // / / / // // // // / // / / / / i. / (. / / /8 � // // 7/ // 7/ / / /'// // // / / / / / / � � � f23 e (b) � � f7l f7l (a) Cherenkov and transient radiation

(c)

(d)

Bremsstrahlung

(e) (f)

(g) Wave scattering

(h)

e

•

f23 f7l

I

�

eooo

l,./- / / /. / / '/ / / '/ / / /'// /j /) / / L±J

/ // / / / / /// //

v;��T �

~

Figure 27. 1. Mechanisms ofthe emission of radiation by an electron

For the conditions of distributed interaction of an electromagnetic wave with an electron beam guide by a static (uniform or spatially periodic) magnetic field, the criterion for synchronism can be written as

ro = k 11v1 1 + n0 (n = O, ± l, ... )

(27.1)

where ro and k 11 are the wave frequency and constant of its propagation through the waveguide and n and v 1 are the oscillation frequency and translational velocity of the electrons. In going from nonrelativistic to relativistic velocities, the emission of electrons changes qualitatively. Let us

GENERA TION OF HIGH-POWER PULSED MICROWA VES

525

consider this phenomenon for Cherenkov radiation (see Fig. 27. 1 , c). In this case, n = 0 in formula (27 . 1 ) . Radiation of this type is used, e.g., in a traveling,wave tube. Let an electromagnetic wave with constant amplitude and phase velocity interact with an electron flow, steady-state and monoenergetic at the entrance, on a bounded segment. If the wave and the flow are in strict synchronism, the integrated energy balance of their interaction is obviously equal to zero since electrons are displaced "symmetrically" toward the nodes of the varying field and therefore the energy absorbed by accelerated electrons and the energy radiated by decelerated electrons are mutually compensated. If the phase velocity of the wave is slightly higher than the initial velocity of the electrons, the latter are grouped in the acceleration phase of the ac field. Charged particle accelerators employed in nuclear physics operate in such a mode. If, on the contrary, the wave "lags behind" the electrons, the latter, in the course of grouping, are shifted into the deceleration phase and give up their energy to the wave; this is the mode of operation for generators of electromagnetic radiation. For a microwave oscillator to operate with high efficiency and high output power, the following four conditions must be satisfied (Gaponov­ Grekhov and Petelin, 1 979): 1 . The electron beam must transfer a high power, i.e., the beam current and particle density must be high. 2. The beam electrons must be grouped to form compact clusters. To this end, their dynamic displacement relative to one another due to the action of the wave on a segment of length L must be of the order of the "retarded" wavelength "-r = A.j3:

=

(27.2)

where <>v is the change in electron velocity under the action of the wave, T = Ll vo, 13 Vole, and A. = 21tC/w . 3 . Each cluster must go to the middle of the deceleration phase of the wave. For this to occur, the kinematic displacement of electrons associated with an excess 8v = v0 - vph of their initial velocity v0 over the phase velocity Vph of the wave should be comparable to the "retarded" wavelength: (27 .3) 4. Finally, the energy <>e � eEL taken away by the electric field E of the wave from the electrons must be comparable to the initial energy of the electrons, e:
or, which is the same,

(27.4)

Chapter 2 7

526 EL � V ,

(27.5)

where V is the accelerating voltage of the electron injector. The difference between the slightly relativistic ( � « 1 ) and ultrarelativistic ( � � 1 ) cases stem from the difference in the corresponding relations between the velocities of electrons and their energy: os ov � - ( � « 1 ); s

(27.6)

v0

Here, y = (1 - � 2 t 1 12 = 1 + e V/m0 c 2 is the relativistic mass factor. In view of relations (27 .6) for optimal values of the length of the interaction space, loss of synchronism, and the wave amplitude associated with the so-called "acceleration" parameter a = eEA./m0 c2 , Eqs. (27 .2)-(27 .4) yield the following estimates:

L �� A. and

'

�v

Vo

�1

'

a��

�v 1 1 L 2 �2, a ��y ' A. y y Vo

for � « 1

for � � 1

(27.7)

.

(27.8)

Thus, the laws governing the optimal parameters of slightly relativistic and ultrarelativistic devices are different. In the former case, the device length is proportional to the square root and in the latter case, to the square of voltage. Moreover, the laws describing the variation of the wave amplitude E (to be more precise, the working longitudinal electric field component) in the slightly relativistic and ultrarelativistic energy ranges are even opposite: E is proportional to the square root of voltage in the former case and is inversely proportional to voltage in the latter case. An important consequence of the above analysis is that high efficiencies are in principle attainable for arbitrarily large energies of electrons. The above relations can be used for estimating the optimal range of parameters for Cherenkov-type microwave devices. However, calculations using the equations of the rigorous nonlinear theory give, of course, more realistic predictions. If we substitute n = 1 , Q = 2rtv11 1d , where d is the period of magnetostatic field, into resonance condition (27. 1) (see Fig. 27. 1 , g), we obtain a device with stimulated undulator radiation, which is called an ubitron. The other name for this device is a free elec