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P/367 USA Propulsion of Plasma by Magnetic Means By W . H. Bostick* BUTTON-TYPE PLASMA GUN 1 3 It has been demonstrated " that a small button gun (Fig. 1) can project plasma consisting of metallic ions, deuterium ions, and electrons at speeds up to 2 x 107 cm/sec. These speeds are measured in a vacuum chamber by time-of-flight methods, using a probe and an oscilloscope. The first arriving plasma signal corresponds to this high speed of 2 x 107 cm/sec. There are later signals corresponding to other portions of the plasma which are traveling more slowly. However, from the predominantly positive sign of these slower signals, it can be inferred that some of this slower plasma encountered the walls of the cylindrical vacuum chamber and thereby was slowed down. Since it is thus difficult to measure, by means of a probe and oscilloscope, the velocity profile of the plasma from such a plasma gun, a ballistic pendulum method has been devised to measure the momentum of the plasma coming from a pulsed gun. The pendulum bob is a cup made from thin plastic or aluminium foil, with its opening oriented to receive the plasma. In principle, if the plasma is composed entirely of metallic ions, the mass of the plasma can also be measured by determining the loss of weight of the gun or the gain of weight of the collecting cup after the gun has been fired a specified number of times. Such measurements are in progress. From the point of view of projecting high speed plasma in a given direction these button guns suffer from the following weaknesses. (a) The back emf (the gun is essentially a linear motor, whose armature delivers a back emf) delivered by the guns is, in general, small compared with the voltages which are suitable for capacitors. Consequently, the discharges of the capacitor are not anywhere near critically damped, and the capacitors ring for many cycles, thus dissipating much of their energy in circulating currents rather than storing that energy as kinetic energy of the plasma. The use of pulse transformer coupling between the capacitor and the plasma gun can improve the matching of impedances and bring about a critically damped discharge, but then the discharge time of the capacitor is correspondingly lengthened. (b) The region where the magnetic forces are concentrated and hence effective is within only a few millimeters of the gun. The time taken for a fast moving plasma (~10 7 cm/sec) to travel this short distance is a small fraction of a microsecond. It is impractical to try to have capacitors which store reasonable amounts of energy (~10 3 joules) discharge in this short time. Slower capacitors cannot discharge their energy efficiently into the kinetic energy of the plasma with these guns. (c) Crude measurements indicate and theory predicts that the button source, at least, is not at all unidirectional in its plasma pattern, but fires over a fairly wide angle. RAIL-TYPE PLASMA GUN A more efficient arrangement is to accelerate a sample of plasma by passing a current through the plasma as it rides on rails, as indicated in Fig. 2. This scheme for accelerating plasma by the current in the rails is essentially the electromagnetic gun,f except that the bullet in our case is a mass of plasma or ionized gas. The analysis of acceleration of a bullet by a rail system has been dealt with elsewhere.4 Russian investigators 5 have made a theoretical analysis of the acceleration of plasma on a rail system where an externally-excited magnetic field is applied to the plasma. However, they have not considered the effect of the magnetic field due to the current in the rails. Russian investigators6 have also conducted rail propulsion experiments, involving the acceleration of a plasma produced by evaporation of a metallic wire, and have achieved speeds of 107 cm/sec. A similar type of experimental arrangement has been used at Temple University.7 A simple analysis that assumes an effective current / gives a relatively easy way of assessing the effect of various parameters in a rail-type plasma motor (or gun) without the laborious task of numerical integration of the equations of motion. The Series Plasma Motor If, as is indicated in Fig. 2, m is the mass of the plasma sample which is placed between two rails of \ The development of experimental equipment for accelerating pellets has been carried on very successfully by Mr. Morton Levine at the Air Force Cambridge Research Center. * Stevens Institute of Technology, Hoboken, New Jersey. 427 SESSION A-10 428 P/367 The integration of the equations of motion is somewhat tedious and the results are unwieldy when the inductances of i the condenser, switch and leads are included. Let us assume, for purposes of simplicity, that the capacitor with its internal inductance can be replaced by a battery of voltage F o and internal impedance ZQ = (Lo/Со)* as in Fig. 3. Under these circumstances an approximate load impedance, Zi03iu> representing the plasma and the rails can be assigned: Ceramic 4.24 x 10-i°(72*/m)(log b/a)*. .040" wires of deuterium-loaded Ti Figure 1. Button plasma gun Figure 2. Rail-type plasma motor, or gun A Combination Series-shunt Plasma Motor An obvious step is to add an externally-excited magnetic field H, as indicated in Fig. 2, in order to obtain the analogue of a series-shunt wound motor. The effect of such an additional shunt field H is to increase the field in which the current I in the sample is flowing. The velocity is given by -load 367.3 Figure 3. An approximate equivalent circuit radius a and spacing b, and if an effective current / flows down one rail, through the sample, and back the other rail, the velocity of the sample at the end of a time t is given by (1) the back emf by Vx=o « 4.24 x 10-10(/3¿/w)(log Ъ\а)ъ volts, (2) 4 = 10 amp, v* » 10-2[271og {bla) + ÍOHd\It/m cm/sec. (3) Zioad « IO-1O[O.92I log (b/a)+Hd] x [4.67 log (b/a) + 10Hd]t/m ohms Zo Zi03i)a, CQ and Lo for t h e same values as for the series plasma motor with the value of H equal to 104 gauss. Table 1. Characteristics of Plasma Motors = 6 x 1 0 l 6 x 1 . 6 x 1 0 ~ 2 4 = Ю - 7 g , c/ = 1cm f 4.6 x 107 cm/sec 23 cm 4.24 x 103 v 22 joules 2.4/if 0.42 x 10-6 h 0.42 п 0.42 a (6) from which we obtain the back emf, F#=o = 7Zioad, and the energy input, Е\п = %I4Zi0Blú. In Table 1 we have tabulated the appropriate values H = 0 (senes motor) Co, from Ein = J Lo, from LoCo = (5) The approximate load impedance is given by for v, I, VX=OJ Em, and the energy input to the sample b y 6 2.12 x 10-10(/4/2/w)(log Ъ\а)* joules. (4) Fairly efficient transfer (about 50%) of energy to the load occurs when Zi o a d = ^o- This energy is shared between the kinetic energy of plasma and the inductive energy stored in the two-wire transmission line. Almost complete transfer of energy to the plasma occurs when Zi o a d ^> ZQ. Under these circumstances the back emf due to the plasma traveling in HAY is sufficient to reduce the current almost to zero, and there is then very little magnetic energy left in the transmission line. In Table 1 we have inserted some practical numbers. It can be seen that with a pair of rails 50 cm long, b/a = 1 0 and a current 7 of 10 4 amp, a 10~7 g sample can be given a speed of 4 x 107 cm/sec. The effective plasma impedance, Zi o a d = 0.42 ohm, is fairly high—it is easy to obtain a capacitor with Co = 2.4 /xf, and LQ low enough so that Z o < 0.42 ohm. 367.1 v » 4.6 x 10-2{I4lm) log(b/a) cm/sec, W . H. BOSTICK t = 10-6 sec) H — 10* (senes shunt motor) 1.46 xlO 8 cm/sec 73 cm 4 2.8 x 10 v 140 joules 0.36 ¡d 2.76 x 10-6 h 2.8 H 2.8 п 429 MAGNETIC PROPULSION OF PLASMA 367.4 Figure 4. An equivalent circuit for a pure shunt plasma motor If the magnetic field due to the current in the rails is negligible compared with the externally applied magnetic field, Я, it is possible to use the equivalent circuit of Fig. 4 where Co is the storage capacitor and where the plasma is effectively the capacitance Cj/ into which a certain fraction of the energy of Co will be discharged, depending upon the ratio CL'/CO- If Ci/ = Co, or is made so by the insertion of a pulse transformer, all of the energy of Co can be transferred through the inductance to Ci/. The physical analogue is the complete transformation of electrostatic energy in the capacitance Co to kinetic energy of motion of the plasma in one-half cycle. If Ci/ = Co, then Ci/ = 2E i n /F 2 = \<PmlH4* farad. Presumably the most efficient way to operate the motor is to adjust the parameters so that the back emf reduces the current to zero (and hence leaves no energy stored in the transmission line) just as the plasma leaves the end of the rails. Under these circumstances all of the energy stored in the capacitor is transformed to kinetic energy of motion of the plasma during the first half-cycle of current. Moreover, no arc will be drawn at the end of the rails as the plasma leaves because no current will be flowing. The series and series-shunt motors diagrammed in Fig. 2 put their energy predominantly in the forward direction. They also are capable of developing adequate back emf's. It can thus be seen that they do not suffer from the same difficulties as the button sources. Initial Experiments with Rail-Type Motors Initial experiments on the operation of a rail-type, series-shunt plasma motor have been performed with the experimental arrangement shown in Fig. 5. The cup-shaped rails have proved more suitable than either wire rails or thin strip (3 mm wide) rails in confining the plasma in the Z direction and preventing the plasma from "jumping" the rails in the^y direction (see Fig. 5). The plasma is produced by an arc across the insulator between the two copper wires (just as the plasma is produced in a button gun). The wires are electrically attached to the rails. With a storage capacitance of 0.12 ¡d charged to 14 kv, a resistance of about 3 ohms for critical damping of the current pulse, and a current pulse duration of about 0.6 /¿see, the average plasma speed for the distance from x = 0 (at the breech of the gun) to x = 10 cm (5 cm beyond the muzzle of the gun) is 107 cm/sec. Although this speed is not so spectacular, the encouraging feature is that all of the plasma seems to have this speed, since probe measurements indicate the plasma to be fairly tightly bunched in the x direction. The externally excited magnetic field, Я = 3000 gauss, pervades the entire trajectory of the plasma (both in and beyond the gun). When the plasma leaves the muzzle it is observed to remain much more tightly bunched in the Z direction than the plasma from a button gun when fired across a magnetic field. It is hoped that with longer rails and higher values of H the plasma speed can be substantially increased. Equipment is nearing completion for the operation of a plasma motor which employs gaseous ions instead of metallic ions. Figure 6 shows an arrangement where water vapor or carbon dioxide can be frozen on a chilled insulating column. The capacitor discharge can be expected to vaporize and ionize these substances and then propell them down the rails. It is hoped eventually to try the scheme with frozen deuterium. Figure 5. Experimental arrangement for accelerating plasma generated by a high current arc between metal electrodes Liquid nitrogen Electrically insulating tube 367 6 Figure 6. Experimental arrangement to be used for accelerating plasma from H2O or CO2 Metal (brass or copper) Coils for producing pulsed magnetic field H -Pulsed plasma gun for producing plasma in the annulai space at the appropriate time Pulsed radial electric current 367 7 Figure 7. Arrangement for a rotary shunt plasma motor where the rotational velocity of the plasma ring becomes transformed to linear velocity v as the ring is ejected from the motor 430 SESSION A-10 P/367 ROTARY SHUNT PLASMA MOTOR A variation on the shunt plasma motor is to arrange the magneticfieldas shown in Fig. 7. Here the plasma will pick up rotational kinetic energy and the duration of the application of the current can be chosen to be as long as one pleases. Hence, the plasma can be accelerated in principle to speeds which are limited only by the mechanical strength of the materials used in the apparatus. The rotational kinetic energy will be transformed to translational kinetic energy as the plasma ring is propelled to the right by the gradient in the magnetic field. The copper parts serve asfluxconcentrators, as well as electrodes, so that the magnetic field can be made as high as 105 gauss without any great difficulty. BARRAGE OF BUTTON GUNS The matching of the impedance of the power source can be accomplished by making an array of button sources and connecting them all in series. Although such an arrangement would seem a priori to be inferior to the rail-type plasma motors described in Fig. 2, it nevertheless presents some interesting phenomena involving the manner in which the individual pieces W . H. BOSTICK of plasma ejected from the individual guns interact with one another. Furthermore, such an array when suitable shaped and operated in a gas at a pressure of about 10 mm, is capable of generating shock waves of various shapes. REFERENCES 1. W. H. Bostick, Phys. Rev. 104, 292 (1956); 106,104 (1957). 2. W. H. Bostick and O. A. Twite, Nature 179, 214 (1957). 3. E. Harris, R. Theus and W. H. Bostick, Phys. Rev. 105, 46 (1957). A%. K. Millsaps, The Linear Acceleration of Large Masses by Electrical Means, Hollman Air Development Center, Operations Research. Office, Technical Memorandum No. 3. 5. A. I. Morozov, Soviet JETP 5, 215 (1957). 6. L. Artsimovich, S. Chuvatin, S. Lukjanov and I. Podogorny, Electrodynamical Acceleration of Plasma Bunches, Soviet JETP 33, 3 (1957). 7. T. Kornefí and J. L. Bohm, Experiments in Plasma Acceleration, Conference on Extremely High Temperatures, Sponsored by Air Force Cambridge Research Center, Bedford, Mass., March 1958. % The development of experimental equipment for accelerating pellets has been carried on very successfully by Morton Levine at the Air Force Cambridge Research Center.