Download Propulsion of Plasma by Magnetic Means

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.