Magnetic Compression of Shock Preheated Deuterium

Transcription

1 P/345 USA Magnetic Compression of Shock Preheated Deuterium By Alan C. Kolb * In order to use externally generated magnetic fields to compress a high-density deuterium plasma ( ions/cm 3 ) with a ratio of the external magnetic pressure to the gas pressure near unity (p~l), preheating is necessary to establish a high conductivity initially. The utilization of magnetically driven axial shock waves for preheating has been under investigation in one phase of the controlled fusion research at the Naval Research Laboratory and is discussed in the first part of this paper. The magnetic compression of the preheated plasma is accomplished by discharging a large condenser bank into a coil system surrounding the shock tube. With this general arrangement, axial magnetic fields of the order kilogauss can be generated with currents of X 10 6 amp. The high magnetic pressure raises the gas to high temperatures and highenergy radiation has been observed with a scintillation counter for time intervals of the order 10 isec. The second part of this paper is concerned with the study of the magnetic compression and stability of high-[3 plasmas without the complications introduced by the generation of axial shock waves with an auxiliary capacitor discharge. In order to carry out experiments of this type, in which a pulsed electrodeless discharge is used to compress a plasma with (3 ~ 1, the final high-temperature plasma is actually produced in four steps: (a) Partial ionization, by means of a 27 Me, 1 kw rf electrodeless discharge. (b) Preionization, by means of a high-power, highfrequency capacitor discharge through a single-turn coil with magnetic mirrors surrounding the discharge tube. (c) Shock pre-heating (Г~100 ev), by axial and radial shock waves set up in the ionized gas when the main bank begins to discharge into the coil with magnetic mirrors. (d) Adiabatic compression, by means of the continued increase of the magnetic fieldafter the transient shock phenomena have terminated. With this latter technique it has been possible to establish, in a reproducible way, a fully ionized, spectroscopically pure plasma with a compression ratio greater than 100. * U.S. Naval Research Laboratory, Washington D.C. PROPAGATION OF STRONG SHOCK WAVES CONFINED BY MAGNETIC FIELDS A deuterium plasma can be accelerated along a quartz tube by striking a high current discharge ( kamp in pisec) between a pair of electrodes at one or both ends of a quartz tube. A magnetic field perpendicular to both the current path and the axis of the tube causes the acceleration and resultant shock wave. 1 To prevent cooling by heat conduction to the tube walls an axial magnetic field along the tube is used to drive the plasma radially away from the walls. 2 A shock tube with field coils is shown in Fig. 1. The tube is 30 cm long with an inside diameter of 3 cm. Two shocks are produced at both ends of the tube which collide at the center. This collision brings the plasma to rest and raises the thermal energy to ~ 100 ev/particle as deduced from the measured shock velocities. Streak camera photographs (see Fig. 2) show that the high injection velocities can be maintained by the external field as a result of the compression. Image rotators are used to observe the compression at two points along the tube. The shock velocity decreases after the time of maximum compression and peak current. The radius of the plasma column at the shock front is very nearly that of the tube radius. The radius of the plasma column behind the front decreases with increasing distance from the front. 328 HIGH COMPRESSION EXPERIMENTS In order to generate strong magnetic fields in a long single-turn coil or in a tube surrounded by several single-turn coils connected in parallel, very high currents are required. For a tube 20 cm long and a current of 8 x 10 6 amp the field is ~ 500,000 gauss. Furthermore, the inductance of such coils is low (of the order ~.01 [xh for a radius of ~ 4 cm) so that a very low inductance external circuit is required for efficient energy transfer to the electro-magnetic shock tube. To meet these requirements, a capacitor bank with a short circuit current capability of 15 X 10 6 amp has been constructed. The other electrical parameters are tabulated in Table 1. The capacitors are connected by parallel copper plates with eleven switches. Each switch consists

2 MAGNETIC COMPRESSION OF SHOCK PREHEATED DEUTERIUM 329 simply of a gap in the transmission line acioss which the current flows when triggered from an external spark. The parallel plate geometry is therefore maintained and the switch inductance is small (' ih for eleven switches). The external inductance is somewhat variable depending on the number of switches that are fired. The magnetic field of the plate for the return current drives the ionized gas generated by the switch discharge away from the dielectric insulation. This " magnetic insulation " is very effective and will be described more fully in a separate publication. The effective operation of this capacitor bank and switches has shown that discharges with tens of millions of amperes and magnetic fields in the megagauss range are entirely feasible for large systems by scaling up the present apparatus. One of the magnets used for the highfieldwork is shown in Fig. 3. The coils are designed to withstand magnetic pressures up to 2 x dynes/cm 2. They are connected to a transmission line 2.5 m wide which passes through the floor and is connected to the capacitor bank in the room below. The width and separation of the coils are one centimeter. The inside diameter here is 3.6 cm. A shock wave can be initiated at one or both ends of the tube. Notice also in Fig. 3 that there is no center turn. As a result there is a magnetic mirror geometry 3) 4 with a mirror ratio of 2.5:1. The usefulness of such mirror geometries for high p experiments at high densities for plasma trapping is one of the major problems now under study. Table 1. Characteristics of Entire Bank Figure 1. Shock tube and field coils Voltage 20 kv Number of capacitors 99 Total energy 285,000 joules Total capacitance 1430 [xf External inductance /^ ( h /short = V (СЩ Vt ~ 15 x 10 6 amp (dl)dt) short = VjL ~8 x amp/sec Rise time, short» > 2.8 [ sec Load inductance (typical coils)... ~ jxh Number of switches 11 /load up to 8 X 10 6 amps Яшах ~ 500,000 gauss Rise time with load /-^ 5-10 ( sec Equations for the Compression Cycle In certain experiments, shock waves are sent into both ends of the coil. After the initial acceleration, the collision of the two shocks at the center of the tube will bring the plasma to rest in a rising magnetic field. Calculations of the compression cycle after a high-temperature plasma has been formed in the tube by shock heating have been carried out. In this analysis it is assumed that the compression is adiabatic since the velocity of radial compression is slow compared to the speed of sound in the hot plasma. Exact solutions of the equations of motion for the plasma boundary can be found for а у = 2 gas initially at a uniform temperature, T o, and density N o E и With field T Image rotators E и T No field Figure 2. Streak camera photograph with and without confining field. H = 15,000 gauss; P = 400 microns deuterium. Time scale is in microseconds

3 330 SESSION A-6 P/345 ALAN С KOLB (ions and electrons)/cm 3. The effective y of the plasma could be greater than 5 / 3 at high temperatures due to non-equilibrium velocity distributions so that taking y = 2 is not too unrealistic for the present purpose. In any event, the qualitative results are not very sensitive to the value of y, and assist in the selection of experimental parameters. After the collision of the two primary shocks the current in the coil continues to rise until at a time / 0 the magnetic pressure at the surface of the plasma exceeds the gas pressure, N Q kt 0 (the subscript zero refers to values of the various variables at the time / 0 ). At this time the plasma begins to contract. The voltage FL across the coils (load) is given by d Ht [7 (1 - (1) where L G is the inductance of the coil with no plasma inside the tube, R v is the plasma radius and R c is the coil radius. The appropriate circuit equation is F L = F ft - С Idt = L o dt [(1-Д Р а/дс 2 )/]. In addition we have the relation for the pressure balance Я 2 /8тг = NkT, (3) the expression for the field in a solenoid with n turns/cm Я = 4nnl/cl, (4) the adiabatic relation (2) T/T o = (N/N o ) У-\ (5) and the density ratio after radial compression N N 0 = (До/Яр)*, (6) where R o = R v (0) is the plasma radius at t 0. Equations (3), (4), (5), (6) yield I = I 0 (RJR v )y, (7) where / 0 is the current required to start the compression and is given by Substituting (7) into (2) yields a differential equation for the plasma radius R v. With у = 2, the solution of this equation in terms of appropriate dimensionless variables is / = F(C/L 0 y/ 2 sin [(r + t o l(l c C)V>)(L c /L o ')y*] (9) for 0 < t < t 0 ; and I// o - T/T o = N N 0 = (Д 0 /Д р ) а = Л" 1 sin т + cos т for >/ 0, (10) Figure 3. Coils system for high field experiments where V, C, are the voltage and capacitance of the capacitor bank, respectively, and T =(LcC)-K (t~t 0 ) <p т/т ^ 0 1 ol 1 m L o = L C (R<? - R 0 *)/R c * L o L e = L o -\- LQ = external inductance I m = 7(C/Le)%(l - I*L,;iV*C)* t 0 = (VQK sin-i (I 0 *L 0 'IV*C)*. The compression ratio, final density and temperature can be expressed in terms of the quantity J> 0 : = 4*- = \v С \У* T 2 T \У 21-1 lc n V 2 C \ v ^ / J Using the expression L c = Aiz^R^jcH, for a single turn coil (и = 1), gives i To V 0 C/2 R o where iv 0 = N 0 nr is the total number of atoms in the tube initially. Now for high compression ratios the energy stored in the capacitor bank is large compared to the magnetic energy in the load at the time the plasma first pulls away from the walls. This implies that V 2 C > / 2 0 L o, so that 0 ~^? i?. / Energy stored initially \% R G \Plasma energy at t = tj R o (14) i?n

4 MAGNETIC COMPRESSION OF SHOCK PREHEATED DEUTERIUM 331 With this result, one finds that at the peak of the compression cycle sin т ~ 1, T max -* о and the detachment time is to = W/V (16) Re (15) for initial conditions iv 0 = ст- 3 ;Г 0 = 10 6 K\ I o = 1.5 X 10 4 I amp, t 0 == 1.5 X 10 4 V-4L 0 ' ( sec and s 0 = 0A4nR joule for L o ' in microhenries and V in volts. / In the coil shown in Fig. 1 the axial magnetic field has ripples near the wall of the tube due to the finite coil spacing. With this field configuration, the plasma formed behind the advancing shock front is compressed by the first half-cycle of rising magnetic field and it has been observed in streak camera photographs that the confined plasma appears to be radially stable (see Fig. 2). It is seen that the radius follows the field in an adiabatic fashion for the first half-cycle of the axial field. The compression generates a radially imploding shock wave on the next half-cycle after the shock pre-heated plasma has cooled by wall contact. A more detailed account of these particular experiments, using the apparatus of Fig. 1, can be found in Ref. 2. In the coil shown in Fig. 3 the axial magnetic field is more uniform because of the large coil dimensions. It has been observed that there is a tendency for the plasma behind the advancing front to develop radial oscillations with an amplitude ranging from a few millimeters to a centimeter, so that the plasma may or may not be carried to the wall. Oscillations of a similar type are observed in the center section of the coil, between the magnetic mirrors, after the collision of two shock waves generated at opposite ends of the tube. Here again the amplitude of the radial oscillation is small (see Fig. 5B, 5C) or is large enough to carry the plasma to the walls as in Fig. 5A. The qualitative difference between the experimental results pertaining to the propagation of shock waves in axial magnetic fields obtained with the coil of Fig. 1 and the coil of Fig. 5, may be associated with ripples in the magnetic field near the wall, the field being quite uniform along the magnetic axis in both cases. If there is no confining field the plasma fills the tube as seen in 5D. The time between compressions (half cycle) in Fig. 5A, В, С is six microseconds. (The expanded time axis in Fig. 5A resulted from operating the streak camera at a higher writing speed.) Because of the curvature of the field between the mirrors one would expect some instabilities to arise. However, these experimental observations suggest that for sufficiently large tube diameters such instabilities are not necessarily fatal in high compres- i / // jtt I// /S <> у ^ r^ ' >, ~ ^ - ^ 4 N. \ N \ I ie \ V \ Of)" 25 PLASMAS PREHEATED WITH EXTERNALLY GENERATED SHOCK WAVES Stability of the Compressed Plasma Figure 4. Adiabatic compression of a y = 2 plasma sion experiments of the type described. A final answer to these questions must await further studies under a variety of conditions. Observations with a Plastic Scintillator In Fig. 6 an oscillograph trace of signals from a plastic scintillator shielded by 2 cm of lead is compared with the background transient noise from the discharge. The neutron sensitivity is one scintillation per 4 X 10 3 neutrons. The bursts at 4 and 12 ( sec correspond to two current maxima. These maxima arise from a programmed discharge in which part of the bank was fired just as the shock entered the coil and part was fired 8 ( sec later. The current at the second maximum was 2 x 10 6 amp and 1.5 X 10 8 amp at the first. The peak field was 100,000 gauss and the ambient pressure was 100 microns. The pulse height to be expected for an individual neutron scintillation is about 1/10 of a division as checked by observing 0.66 Mev y-ray signals from a cesium source which has about the same average pulse height. Streak camera photographs showed that the plasma column did not touch the tube walls in this experiment. In no case have we observed signals if there were severe oscillations of the plasma which carried the plasma to the walls. Scintillations have also been observed when dl/dt is zero. In one event pulses were observed for ~ 30 fxsec over three halfcycles of the axial field. If the signals are due to neutrons, then a yield of the order 5 X 10 4 neutrons in the second and third oscillations is indicated and if they are due to neutrons of thermonuclear origin, then it appears that the impurities picked up at the wall when H c^.0 do not seriously contaminate the discharge for some time. Experiments to distinguish between neutrons and y rays have not been completed. With the magnet shown in Fig. 3, the scintillator output is sporadic from shot to shot, presumably due to the unpredictable plasma oscillations which appear in the streak camera photographs. Since these oscillations did not occur with the coil configurations shown in Fig. 1, it is hoped that these difficulties can be overcome in a properly designed coil.

5 332 SESSION A-6 P/345 ALAN С KOLB HIGH-COMPRESSION EXPERIMENTS WITHOUT EXTERNAL AXIAL SHOCKS Experimental Apparatus The experimental arrangement is shown in Fig. 7. The magnetic fields are now generated in single turn steel coils with magnetic mirrors. The coils are split and bolted together to facilitate the insertion of quartz tubes in close proximity to the coil. This method of construction has been found to be suitable for generating magnetic fields up to approximately 300,000 gauss. At higher field strengths arcing in the area of the split causes difficulties. The use of inductively coupled mirrors offers one possibility for circumventing this trouble in future high field experiments; a schematic drawing is shown in Fig. 8. The mirrors are steel discs with a hole and slot, insulated from the main body of the coil by mica and plastic. The parallel plate transmission line leading to the coil is clamped together by large bonded fiber glass blocks so as not to distort the symmetry of the magnetic field unnecessarily (see Fig. 7). The circuit diagram is shown in Fig. 9. The operation of the system is as follows: a 70 kv,.01 juî, 1 Me capacitor is discharged to generate a high voltage pulse leading to 23 trigger electrodes in a magnetically insulated switch of the type described earlier. The 23 cables and preheater bank can be seen to the right of Fig. 7. The preheater bank is connected by copper plates directly to the main collector plate. This switch closes the preheater circuit and a voltage is applied across the coil. About 0.5 ^sec after the preheater is switched, a high-voltage pulse arrives through a delay line to trigger a second 70 kv capacitor which, in turn, sends a high-voltage pulse through the 55 coaxial cables leading to trigger electrodes in the switches on the main capacitor bank. These multiple triggers fire the switches in several places as can be seen in Fig. 10. The large collector plate on the top of the main bank has an area of 7.5 m 2 and has a capacitance C p = 0.15 [xf. The collector plate inductance is small compared to the load inductance so that the collector plate and coil constitute a resonant circuit with a frequency / = (L C C V ) VÍ /2TZ, in the 10 Me range. The preheater bank is used to drive this resonant circuit at high power levels in order to preheat and ionize the molecular deuterium. Typical current and voltage characteristics, calculated on an analogue computer, for different load and preheater inductances, L c and L^, are shown in Fig. 11. With the preheater charged to 40 kv, the circuit on discharge rings at approximately 1 Me and is modulated by an rf signal of approximately 10 Me having an amplitude of approximately 20 kv. The average rf power from this discharge is approximately 4000 Mw. The maximum currents are several hundred kiloamperes. This discharge is damped in about 2 microseconds. The calculated and observed characteristics of the circuit are, during the early phases of the preheater discharge, in good agreement. The preheater bank consists of 9 specially designed low-inductance capacitors each with an inductance somewhat less than 10~ 8 h. The total capacitance, Ch, is one microfarad. Because of the low-inductance properties of the capacitors and switch, a high voltage appears across the coil. This combination of a high-frequency voltage pulse and high current (200 kiloamperes) very effectively pre-ionizes the plasma, so that the surface currents flow in times in the order of 0.5 microseconds and the plasma is closely coupled to the primary coil. In these experiments a 27 Me, 1 kw rf signal is used to partially ionize the gas initially. 200 Microns deuterium Figure 5. Streak photographs of the radial compression (A, B, C). In D there is no confining field. Preheating by externally produced axial shock waves

6 MAGNETIC COMPRESSION OF SHOCK PREHEATED DEUTERIUM 333 Magnetic Compression without the Preheater Discharge Figure 6. Observations with a plastic scintillator. Time scale 2 [xsec per division. A) Output of plastic scintillator, B) Background noise If the deuterium is weakly ionized with the rf excitation without the preheater discharge, the magnetic field penetrates into the plasma and is trapped in the ionized gas at later times. A weak imploding shock wave is generated on the first halfcycle and the plasma is finally compressed at low (3 to about one third of its original diameter. On the next half-cycle the plasma which was preheated on the first half-cycle implodes with high velocities (' y'10 7 cm/sec). In addition, strong shock waves with about the same velocity are generated by the magnetic pressures in the magnetic mirrors. These shock waves move along the axis of the tube and collide at the center. This behavior is similar to the phenomena observed using an auxiliary capacitor for the axial shock generation. The shock propagation is also shown schematically in Fig. 8. Streak camera photographs of this behavior with an f/3 camera (writing speed here was 2.2 mm/(jisec) are presented in Fig. 12 for two different experiments under the same conditions. The behavior of the plasma is reproducible and the oscillations of the type previously discussed (see Fig. 5) are not present. Figure 7. Experimental apparatus

7 334 SESSION A-6 P/345 ALAN C. KOLB Figure 8. MAGNETIC MIRRORS ^CONDENSER BANK DIS CHARGE TUBE "DEUTERIUM PLASMA IH SU L AT ЮН AXIAL SHOCKWAVE IMPLO 01H G SHOCKWAVE Electromagnetic shock tube with magnetic mirrors showing direction of shock propagation the luminosity on the first half is due to deuteriumline radiation. During the second half-cycle, after the imploding shock waves preheat the plasma, the Balmer lines disappear and only a continuum can be seen when the axial shock waves hit at the center of the tube. These observations are consistent with low temperatures on the first-cycle because of the poor inductive coupling of the capacitor discharge to the rf excited plasma. For comparison, a spectrum obtained when the plasma touches the wall of the tube due to oscillations of the type discussed in the preceding section of this paper is presented. In that case the impurity spectrum dominates. The next question is: What is the nature of the radial oscillations that occur near peak compression? A streak camera photograph showing the compression at several position along the tube (Fig. 15) shows that these oscillations occur uniformly along the confined column of plasma. As remarked eailier, a complete understanding of the origin of these oscillations must await further investigation. The plasma radius as a function of time is given in Fig. 13. At t = 0 the plasma begins to contract and a shock wave labeled (A) is formed. The boundary between the plasma and the magnetic field is labeled (B). The shock wave is reflected from the axis and moves outward until at (C) the reflected shock meets the magnetic field-plasmainterface and is brought to rest at (D) by the pressure of the rising axial magnetic field. The shock bouncing is then repeated as in the ordinary dynamic pinch until at (G) the axial shock waves collide at the center of the tube. The collision of the axial shocks raises the internal energy of the plasma so that it expands to about one-half the original radius. The rising magnetic field then compresses the plasma to about one-tenth its original diameter. Then at (I) the plasma begins to undergo large amplitude collective radial oscillations. The mechanism responsible for these oscillations is not yet understood completely. A series of experiments are in progress to determine their origin. These radial oscillations are not observed on the first halfcycle of the discharge even though the peak current is twice as great as on the second half-cycle. Spectroscopic observations with an f/2 spectrograph with a time resolution of 10~ 7 sec (Fig. 14) show that MASTER TRIGGER SWITCH TRIGGER ELECTRODE U TRANSMISSION LINE SWITCHES Figure 9. Schematic diagram of magnetic compression system Figure ,000 joule condenser bank with switches firing at 13 points. Trigger capacitor and cables in foreground The voltage, dl/dt, and current are shown in Fig. 16. The spikes on the second half-cycle are caused by the rapid contraction and expansion of the plasma column. These spikes are not observed without the rf pre-excitation as shown in Fig. 17. With a streak camera one also observes that no radial shocks waves are produced. To summarize these experiments without a preheat er discharge, we observe that high velocity radial and axial shock waves can be generated on the second half-cycle of a high power capacitor discharge by passing the high current through a single turn coil with magnetic mirrors. In addition, the plasma is spectroscopically pure and in a high state of ionization as can be seen from the broadening of the Balmer lines during the first half-cycle and by observing the continuum during the second half-cycle.

8 MAGNETIC COMPRESSION OF SHOCK PREHEATED DEUTERIUM 335 Voltage = V c 40 kv/ctn 0.1 /is/era Current = l c 200 ka/cm 0.1 /is/cm 12 x 10-9 h. 6 x W 9 h. 3 x 10" 9 h x 10-9 h 3 x lu' 9 h Figure 11. Preheater voltage and current for various values of the inductance of the external circuit, Lh, and coil, L c. Analogue computation

9 336 SESSION A-6 P/345 ALAN С KOLB Time in microseconds Figure 12. Smear-camera photograph of radial compression without the preheater for two experiments under the same conditions: p = 0.3 mm deuterium; V = 15 kv; С == 392 [ií; R =.003 1; I = 20 cm; mirror ratio 2/1 ; / x = 1580 ka; / 2 = 790 ka, where 1 г and / 2 are the current maxima on the first and second half-cycles Magnetic Compression with Preheater Because the main discharge is damped, only onehalf the maximum current can be utilized for magnetic compression on the second half-cycle after 75% of the energy in the bank has been dissipated. If the preheater bank is fired before the main bank is discharged, one observes the shock bounces, the burst of continuous radiation when the axial shocks collide and the radial oscillations at high compression on the first half-cycle of the discharge. Streak camera photographs snowing this behavior are shown in Fig. 18. The coil here was 10 cm long with a mirror ratio of 3/1. The first flash of light is due to the discharge of the preheater bank. At t = 0, the main bank is switched and the preheated plasma implodes with a high velocity (again of the order 10~ 7 cm/sec) depending on the circuit parameters and ambient gas pressure. At times the radial oscillations do not appear (Fig. 18). The behavior on the first half-cycle is similar to that observed previously without the preheater on the second halfcycle mm 'La ^TTTTT^rTTiii^i^ S TIME IN MICROSECONDS Figure 13. Radial motion of the compressed plasma on the second half-cycle without the preheater. Same conditions as in Fig. 12 We have made a theoretical analysis of the shock implosion (Fig. 19) using a model in which the plasma is carried toward the axis on a thin shell and the magnetic forces balance the inertial forces. The calculation is similar to the calculation by Rosen - bluth 5 for the pinch effect. The solid curve is the plasma radius and the dashed curve is the velocity, both in dimensionless units, as a function of an appropriate dimensionless time. The velocity and compression are given by the relations dt T = R v /R 0 = y 25 \L о { -f-y 25 I L o } \ I 2 1 p I 7' P t, (17) where the symbols have the meaning as in the previous calculation: with V in volts, L o in henries, p in gm/cm 3, R Q, R v and / in centimeters and / in seconds. The curves are for various ratios (L o + L e )/[L C (R O /R e )*] of the external to internal inductance. This parameter is essentially the ratio of the magnetic energy stored outside the electromagnetic shock tube to that stored inside. The theoretical time for the implosion phase in our present experiments is of the order 0.2 isec, which agrees closely with the observed times. Therefore, it is possible to predict with some accuracy the shock velocity and plasma energy during the initia] dynamic stages of the compression. For a discharge with V = 15 kv, using 1/8 the energy of the large bank and for an ambient deuterium pressure of 0.1 mm, the shock heating raises the plasma temperature to about ev. This is also consistent with a pressure balance calculation just after the axial shock collision. The

10 MAGNETIC COMPRESSION OF SHOCK PREHEATED DEUTERIUM 337 Radial compression Time î H, H H, H Figure 14. Spectrograms of the radiation with (top) and without (bottom) instabilities that throw the plasma to the walls. The radial compression is shown on the same time-scale as the time resolved spectrogram at the top Quartz tube Coil 8 10 Time in microseconds Figure 15. Smear camera photographs of the radial motion at three points along the tube. mirror ratio 3/1 V = 15 kv; С = 392 pif; I 10 cm;

11 338 SESSION A-6 P/345 ALAN С KOLB R F Pre- lomzation Figure 16. Typical electrical characteristics of the main discharge Same conditions as in Fig. 12 adiabatic compression constricts the plasma by additional factor of 5, so that for y = 5/3 a temperature of 7.3 x 10 6 K is indicated for a final volume of about 0.7 cm 3. The field in the central region is about 75,000 gauss and the calculated final density is ions/cm 3. At full bank power with a central field of the order 200,000 gauss, temperatures of several kev are energetically possible. Observations with a plastic neutron counter m our early experiments at higher power levels (Fig. 6) are consistent with a plasma energy of about one kev because the final fieldstrength and initial temperature from the shock preheating are higher than in the previous example. The relatively quiescent behavior of the plasma for several microseconds and the correlation of the scintillations with maximum current Figure 17. Voltage across the coil with (top) and without (bottom) RF pre-excitation support this view. Independent measurements of the temperature and electron densities from X ray and optical continuous radiation have not yet been com Time in microseconds Figure 18. Radial motion of the plasma with preheating. V = 1 5 kv; С = 392 voltage 25 kv. vs. time. i; p = 0.1 mm deuterium, preheater

12 MAGNETIC COMPRESSION OF SHOCK PREHEATED DEUTERIUM 339 collective nature. Further study will undoubtedly disclose their origin and it may be possible to eliminate them or at least to determine their effect on the state of the plasma. They may in fact provide a heating mechanism. Experiments in a toroidal geometry should help to clarify the situation (Fig. 20). This will show whether the radial oscillations are due to the presence of the magnetic mirrors. The torus consists of large steel plates connected to the transmission line. A photograph of one plate with a circular groove to contain the discharge tube is shown in Fig. 21. The major diameter here is 30 cm and the bore is 6 cm. With full power of the 285,000 joule capacitor bank, a field of 100,000 gauss can be generated in this device. The experiment should also give some basic Figure 19. Radius and velocity of the imploding plasma vs. time as discussed in the text pleted but it is hoped that they will yield an independent estimate of densities and temperatures. However, because there may be large accelerating voltages resulting from the radial oscillations, there is a good possibility that hard radiations are caused by this mechanism. Situations of this kind have been encountered in many other plasma experiments and it would be no surprise if this were the case here. One is encouraged, however, by the fact that the plasma can be kept away from the tube walls for many microseconds in a high state of compression and that the radial oscillations show a certain degree of symmetry, reproducibility and appear to be of a INSULATION Figure 20. HIGH FREQUENCY PRE HEATER CONOENSER BANK Schematic drawing of the torus WIN CONOENSER BANK Figure 21. One-half of the steel torus information on the magnitude of the drift velocity of a plasma in a known field gradient. ACKNOWLEDGEMENTS The author would like to thank the many persons who gave assistance during the course of these investigations. The assistance and encouragement of Drs. W. R. Faust and H. Griem have been of particular value. Their critical comments and suggestions helped to clarify many of the points discussed in this paper. Most of the experimental apparatus was constructed by T. H. DeRieux and L. J. Melhart. A number of electrical engineering problems were solved in collaboration with С. В. Dobbie, particularly problems associated with the pre-heater circuit. The forming of complex quartz chambers is due to the inspired work of L. B. Clark. J. M. Frame and С. С Martin designed the coils and worked out the mechanical design of the capacitor banks. The numerical integrations of the equations for the radial motion of an accelerated plasma were performed by A. D. Anderson. Finally, the assistance of С. Е. Thompson on photographic techniques is gratefully acknowledged.

13 340 SESSION A-6 P/345 ALAN С KOLB REFERENCES A. C. Kolb, Production of Strong One-Dimensional Shock Waves with Magnetic Fields, American Nuclear Soc, Washington, D.C. (December 1956), unpublished; Bull. Am. Phys. Soc, Ser. II, 2, 47 (1957); Phys. Rev., 107, 345 (1957); Magnetohydrodynamics, edited by Rolf К. М. Landshoff, pp , Stanford University Press (1957). A. C. Kolb, Phys. Rev., 707, 1197 (1957); Magnetically Confined Plasmas, Phys. Rev. (15 October 1958). R. F. Post, Summary oj UCRL Pyrotron (Mirror Machine) Program, P/377, Vol. 32, these Proceedings; Bull. Am. Phys. Soc, Ser. 11, 3, 196 (1958). L. Spitzer Jr., Physics oj Fully Ionized Gases, Interscience Publishers, Inc., New York (Í956). M. Rosenbluth, Infinite Conductivity Theory of the Pinch, Los Alamos Scientific Laboratory, LA-1850 (14 September 1954).