J. Nuclear Energy II, 1957, Vol. 4, pp. 203 to 208. Pergamon Press Ltd., London

AN INVESTIGATION OF HIGH-CURRENT PULSED DISCHARGES*

L. A. ARTSIMOVICH, A. M. ANDRIANOV, 0. A. BAZILWSKAYA, Yu. G. PROKHOROV, and N. V. FILIPPOV

Abstract-High-power pulsed discharges with a high rate of current increase have been investigated experimentally. The technique is briefly outlined, and the pulsations of the plasma filament are described.

THE purpose of these experiments was to study the properties of pulsed discharges at very high currents. In such discharges, the electrodynamic forces acting will cause a constriction of the plasma due to the attraction of parallel currents. The work done by electrodynamic forces in compressing the plasma increases the kinetic energy of the charged particles, and in a high-current discharge the pressure and temperature of the plasma may therefore attain very large values. Other papers(ly2) have described the properties of pulsed discharges in rarefied gases with currents from 102-IO4 A. The present paper deals with pulsed discharges in hydrogen, deuterium, helium, argon, and xenon at initial gas pressures of from 0.005 to several millimetres of mercury, and with peak discharge currents in the range 105-IO6 A.

The electrical powe; source was a bank of condensers with capacitance from some tens to 400 microfarads and voltages in the range 20 to 50 kV. The rate (&/dt), of current increase in the initial phase of the discharge varied from 3 . 1O’O amps see-l to 1.5 . loll amps set-l; and the time taken for the current to increase from zero to the maximum value was between 8 and 17 psec. Porcelain discharge tubes 60-100 cm long and 2@40 cm in diameter were employed. The electrodes were plane flanges of copper or dural. Before each discharge pulse the tube was evacuated to a high vacuum and then filled with a fresh charge of gas. An oscillographic method was used to measure the quantities characterizing the state of the plasma during the pulsed discharge. The discharge-current waveform was obtained by means of a Rogowsky coil, sometimes with an integrating RL circuit, and the voltage by means of low-resistance ‘potential dividers connected in parallel with the discharge gap. In addition, to determine the current distribution over the cross-section of the tube, the magnetic field strength was measured at different points in the plasma. Variations of pressure in the plasma were recorded with piezoelectric elements.

Detailed information about the methods and results of the investigations will be published shortly in the Journal of Experimental and Theoretical Physics. The present paper only gives a general description of the properties of the discharges.

Under the conditions of the present experiments, the discharge current was periodic with strong damping. The most interesting phase of the discharge is the first half-cycle. Fig. 1 shows two current and voltage oscillograms for the first half-cycle obtained with a double-beam oscillograph. These are for discharges

* Translated by L. C. RONSON from Atomnaya Energiya 1, No. 3, 76 (1956).

203

204 L. A. ARTSIMOVICH et al.

in deuterium at pressures of 0.03 and O-2 mm Hg with a condenser voltage of 40 kV. In both cases the maximum current was approximately 500 kA. In the initial stage of the discharge after the breakdown of the gap, both current and the voltage at the discharge gap increase with time. Then, at a certain moment, the voltage collapses, and a kink, showing a temporary drop in current, appears simultaneously on the current oscillogram. After the first fall, the voltage increases sharply and then once again rapidly decreases. At the instant corresponding to the second abrupt drop of voltage the current oscillogram shows a second kink. These deviations from steady development of the discharge are a distinctive feature of high-current pulsed discharges and are of a regular character. They are particularly noticeable with discharges in gases of small atomic weight (hydrogen, deuterium, helium) and at low initial pressures.

For an initial rate of current increase of lOi amps se&, the interval T from the breakdown of the gas to the first collapse of the voltage is a few psec. The quantity 7 is a function of the parameters which specify the initial conditions of the discharge. Fig. 2 shows a plot of the relation between T and M, M being the mass of gas per

1 10-6 10-5 j0-4 10-3 10-2

M g.cm-’ FIG. 2.--7 plotted against M, for V, = 30 kV, r0 = 20 cm.

(1) dI/dt = 6. lOlo amps/set-’ (for light gases) (2) dI/dt = 7.5. lOlo amps/set-’ (for heavy gases).

unit length of the discharge tube. The measurements of T were made with discharges in hydrogen, deuterium, helium, argon, and xenon for the same size discharge tube and the same condenser voltage. The graphs indicate the approximate relation 7 N q/M. For a given M the value of T increases with the radius of the discharge tube, but decreases when (dl/dt)O is increased.

In a pulsed discharge with a large rate of current increase, the inductance of the discharge considerably exceeds its resistance. Consequently the time variation of the inductance of the discharge can be determined from current- and voltage- oscillograms. The variation of the radius of the plasma filament can then be cal- culated if the discharge is assumed to be a sharply defined cylinder.

Such an analysis reveals that in the initial phase of the process there is an increase of the inductance, caused by the contraction of the plasma towards the axis of the discharge tube. This contraction is more rapid the greater (dZ/dt), and the smaller

(b) p0 = 0.2 mm Hg.

FIG. I.-Current and voltage oscillograms for discharges in deuterium U, = 40 kV.

facing p.204

An investigation of high-current pulsed discharges 205

the density of the gas. At the moment of the kink on the current oscillogram the inductance begins to decrease. This must therefore be the time of maximum con- striction of the plasma filament. This is followed by a rapid spreading of the plasma, which is in turn followed by a second contraction. The presence of several kinks on the current oscillogram means that a succession of contractions and expansions of the plasma tiament takes place. From the known radius of the filament at different moments in time one can calculate the velocity of contraction of the plasma, which is found to vary with M and (dZ/dt),.

In the present case the velocity of the plasma varied from 1 . lo6 cm se+ for discharges in gases with high initial density, to 1.2 . 10’ cm set-l for discharges in hydrogen and deuterium with initial pressures of the order of 0.01 mm.

During the initial stage of the discharge the degree of ionization of the gas is small. Spectrographic measurements by S. Yu. LUKYANOV and V. I. SINITSIN(~) show that up to the completion of the first phase of contraction not more than 5-10x of the total number of gas atoms are ionized. (This result is for discharges in hydrogen and deuterium with maximum currents of about 200 kA, and initial pressures O*l-1.0 mm Hg.) It seems that after the first contraction the ionization of the gas in the central region of the discharge can be very high. Spectrographic investigations also reveal that in the case of high currents, after repeated contraction of the filament, considerable amounts of impurity appear in the discharge space, produced by the interaction of the plasma with the tube walls. The investigation of the later stages of the discharge is therefore of less interest.

By measuring the magnetic field at different distances from the axis of the dis- charge tube, the distribution of the current density over the discharge cross-section can be determined for every moment in time. The experimental data lead to the following picture of the current distribution in the plasma. After breakdown, due to the skin effect, the region occupied by the current is a thin cylindrical layer close to the walls of the discharge tube. The internal boundary of this layer moves at first slowly and then more rapidly towards the axis. The movement of the boundary continues until there is current flowing in the whole tube. The time at which the current flow reaches the axis coincides in practice with the first kink on the current osdillogram. At this instant the current density near the discharge axis is about twenty-five times the mean current density over the tube cross-section. Nevertheless, the current distribution has no sharply defined boundary, and only less than half of the total current flows in the central region with radius of a few centimetres. During the subsequent expansions and contractions the current density in the central region remains very high, although it undergoes considerable fluctuations.

To illustrate these results, Fig. 3 represents the current distribution over the tube cross-section for a discharge in deuterium with initial pressure 0.05 mm Hg and condenser voltage 40 kV. It corresponds to the phase of the second contraction of the plasma. A characteristic peculiarity of the distribution is that, in some regions of the discharge, the current changes its direction because of the skin effect.

Measurement of the pressure variation in the plasma with a barium titanate piezoelectric element reveals that during the first contraction phase a pressure wave coincides with the internal current boundary as this moves towards the tube axis. Up to the moment of maximum contraction the pressure near the axis is negligibly small, but when the current reaches the axis the pressure in the central region increases

206 L. A. ARTSIMOVICH et al.

rapidly to 25-50 atm (for an initial gas-pressure in the tube in the region of 0.1 mm Hg). The picture of the mechanism of the principal processes emerging from the ex-

perimental observations is this: during the rapid increase of the current in the initial phase, the electrodynamic forces, which are proportional to P, are not compensated

in cm

FIG. 3.-Distribution of current density over the discharge cross-section in deuterium for O0 = 40 kV, p,, = 0.05 mm Hg, during the second contraction phase.

by the internal pressure of the ionized gas. Therefore, under the action of these electrodynamic forces the plasma cylinder, which is initially close to the discharge- tube wall, is accelerated toward the tube axis.

A considerable part of the work done by the electrodynamic forces during this stage of the process goes into the kinetic energy of directional motion of the particles of the contracting plasma layer. Since the charged particles of different polarity move with the same velocity, the ions receive a large kinetic energy while that of the electrons remains almost constant because of their small mass. The process of contraction may be also considered as the formation of a shock wave moving towards the axis. Before the internal ,front of this wave there is at first neutral gas. During the motion of the plasma layer, the gas is partly carried along with the charged plasma particles (due to the large effective cross-section of the ions for charge ex- change) and is ionized. The mass of matter thus set in motion gradually increases, and the total number of electrons and ions in the plasma rises rapidly.

A quantitative theory of the process of contraction of the plasma filament has been developed by M. A. LEONTOVICH and S. M. OSOVETS,(~) which gives the following formula for T, the time between the separation of the plasma layer from the tube walls and the instant of maximum contraction of the filament:

where r,, is the tube radius, and the current I is expressed in e.m. units. This formula

An investigation of high-current pulsed discharges 207

is represented by the continuous line in Fig. 2; agreement between theory and experi- ment is satisfactory over a wide range of values of M.

The last stage of contraction occurs when the plasma, accelerated by the magnetic field, reaches the axis. At this instant a considerable proportion of the energy of the directional motion is transformed into heat, which leads to a rapid increase of pressure and temperature in the plasma. From rough estimates, the temperature of the plasma during the phase of maximum contraction reached a value of the order of IO6 degrees. (This was for discharges in hydrogen and deuterium at initial pressures of the order of 1O-2 to 5 . 1O-2 mm Hg.) This estimate of temperature is based on a consideration of the energy balance for the discharge. Results obtained by this method are in agreement with the measurements of the pressure in the central region of the discharge.

The determination of the plasma temperature will be discussed in detail in later papers. A few remarks, however, are appropriate here to explain the processes involved. To prevent misunderstanding, it should be noted that the temperature of the plasma is considered to mean the temperature of the heavy particles, i.e. of the ions and neutral atoms. It can be assumed that because of the large effective cross-section for charge exchange, the temperature of the ions and atoms in the compressed plasma column will be the same. As was shown above, a considerable proportion of the work done by the electrodynamic forces during the contraction is converted to kinetic energy of directed motion of the heavy particles. At the same time, during the contraction of the hollow plasma cylinder towards the axis the mass set in motion progressively increases, so that a fraction of the work must be spent on inelastic [sic] processes, i.e. on an increase of temperature of the plasma. Energy balance calculations for the discharge indicate that, even before the moment of maximum compression, the temperature of the ions and atoms attains some hundreds of thousands of degrees, corresponding to a mean energy of random motion of the order of several tens of electron volts. By contrast, the temperature of the electron component of the plasma during the first phase remains very low and corre- sponds to a mean energy in the region of a few electron volts. This follows from the data obtained by spectrographic measurements, which reveal a small degree of ionization of the plasma. If the mean energy of the electrons were several tens of eV, the gas would be completely ionized even before the moment of maximum contraction.

The character of the processes taking place after the time of maximum contraction is not, as yet, very clear. It is obvious, however, that following the maximum con- traction an expanding shock wave must occur, which will carry the plasma outwards towards the walls. The expanding wave must be rapidly retarded by the electro- dynamic forces which act inwards, and as a result a new contraction phase will start which will be followed by a second spreading of the filament. At this stage of the process, when the current densities are large, various types of instability of the plasma filament must obviously begin to appear and, as a result, the shape of the filament may change very considerably. Loss of stability of the plasma filament and the strong interaction between the plasma and the tube walls lead to a considerable change in the character of the processes involved. During the later stages of the discharge a large amount of foreign gases appears in the discharge volume and the temperature of the plasma decreases considerably.

208 L. A. ARTSIMOVICH et al.

REFERENCES

1. COUSINS S. and WARE A. A. Proc. Phys. Sot. B64, 159 (1951). 2. WARE A. A. Phil. Trans. Roy. Sot. 243, 197 (1951). 3. LUKYANOV S. U. and SINITSIN V. I. J. Nucl. Energy 4, 216 (1957). 4. LEONTO~ICH M. A. and Osovms S. M. J. Nucl. Energy 4, 209:(1953).