P/368
USA
Collapse—The Shock Heating of a Plasma
By S. A. Colgate and R. E. Wright*
There have been numerous independent suggestions
to use high speed shocks to heat deuterium gas to
thermonuclear temperature (E. Teller, R. R. Wilson,
H. Grad, W. Marshall1), and extensive experimental
work in this field is being carried on by, e.g., Kolb,2
and Janes.3 Our own work in this field has been
directed towards a fundamental understanding of the
strong shock process, in the limit of no particle collision, to find out if, within this limit, the ion heating
following the passage of the shock is large enough to
give rise to a thermonuclear reaction.
The reason for the emphasis on the limit of no
particle collision (within the dimensions of the system)
is that for practical magnetic field strengths sufficient
to contain plasma at a thermonuclear temperature of
say 10 kev, the density of plasma is so low that the
collision mean free path becomes many times greater
than the dimensions of the system. Under these conditions it is generally agreed1» 4~6 that the dominant
length in the shock transition process is determined by
the cyclotron radius of the ions or electrons in the
magneticfield,and that the forces of charge separation
dominate the process of momentum change of ions.
The more exact theories treat the case where the
magneticfieldenergy density Я2/8тг behind the shock
dominates the partial pressure of plasma oscillatory
or thermal motion. In the case where magnetic field
pressure is dominant, the oscillatory or thermal energy
density behind the shock resides primarily in the ions.
One of us e has discussed the probable consequences
of extremely strong shocks (in the limit of no particle
collision), for the case where the magnetic pressure
behind the shock does not dominate plasma energy
density. It is tentatively concluded that in this limit
the energy density will reside in electron plasma
oscillations which relax into an electron temperature
before the ions are heated. It is hoped that the
experimental program will eventually test these
theories.
In shock-heating a body of plasma, the basic procedure is to apply a large pressure that rises in a time
short compared to the transit time of sound across a
plasma dimension. A large fraction of the energy input
into a shock will produce irreversible heating, and
this large and sudden heating is the objective. In the
experiment to be described, the geometry used is
* University of California Radiation Laboratory, Livermore,
California.
mirror—or axialfield—andthe shock is created by the
sudden rise of an axial magnetic field. If the plasma
acts as a perfect conductor during the time scale of
dynamic phenomena, then the magnetic pressure outside, Я2/8тг, becomes the magnetic piston that radially
shocks the plasma inward. In the initial experiments,
conducted two years ago, this sudden rise of the
magnetic field was applied to the cold, neutral gas
with the hope that the induced electric field would
electrically break down and ionize the gas to a plasma
in a time short enough to form a shock. These experiments were done in two sizes; in a 4-in.-diameter
system in which the shock magnetic field rose to
3000 gauss in 2 /usec, and in a very small coil (tiny
collapse) 2-cm diameter with a magneticfieldrisingto
10,000 gauss in 0.05 /¿sec. In general, for both experiments, the process of ionization did not occur fast
enough to give a clearly defined shock in a perfectly
conducting plasma. Consequently, an experiment was
started in which the three processes (1) ionization,
(2) current boundary layer formation, and (3) shock
were to be separately accomplished in an optimum
time sequence.
It is desirable to use the minimum gas or plasma
density possible so that the magnetic field strength
needed to form a strong shock is minimum. A P.I.G.|
discharge achieves of the order of a few percent
ionization at an initial pressure of 10 microns deuterium. Then the process of "slow collapse" is designed
to increase the ionization to approximately 100%,
push the plasma slightly away from the outside glass
wall, and at the same time form a current boundary
layer thin compared to the radius.
EXPERIMENT
Slow collapse is produced by an alternating magnetic field created by the discharge of four 7.5 mf
capacitors at 10 kv by ignitrons through the single
turn coils (Fig. 1). The magnitude of the field is such
that Я2/8тг (Я х 2000 gauss) is larger than the plasma
pressure at 20-ev temperature and the frequency is
such that \ cycle time (3 /¿sec) corresponds to roughly
a 20-ev ion transit time across the system. Before
ionization is complete, the induced electricfieldof the
changing magnetic flux induces large currents in the
partially ionized plasma, thereby further heating and
% Phillips Ionization Gauge.
14S
146
SESSION A-9
P/368
S. A. COLGATE and R. E. WRIGHT
INTERNAL FIELD (MAGNETIC
PROBE) INSIDE PLASMA
AT 1/2 RADIUS
\
P.I.G. CATHODE
I 2 3 4 5 6
IMAGE CONVERTER
SHUTTER OPENINGS
RI.G. ANODE
LANGMUIR PROBE
%cm SEPARATION
l/isec PER DIVISION
PROSE ROTATED
ABOUT AXIS
H FIELD
FAST COLLAPSE COI
AXIAL
.010" DIA. TUNGSTEN
PROBE WIRES
EXTERNAL APPLIED
'MAGNETIC FIELD
2 0 0 0 GAUSS PER
DIVISION
MEASUREMENTS
INTERNAL
•GLASS PROBE TUBE
MOVED
AXIS
Figure 1 . Geometry of axial field collapse experiments
ionizing it. When the electrical conductivity becomes
large enough, or the fraction ionized becomes large
enough, the plasma is more strongly coupled to the
oscillating field and a 10- to 20-ev weak shock will be
formed. Externally this appears as an alternating
expansion and compression of the plasma at a velocity
corresponding to a 20-ev ion. This temperature shock
is optimum for ionization because the collision cross
section and ionization cross section are large. In addition, the temperature of the plasma is still low enough
so that the heat flux to the glass wall does not vaporize
the wall surface. The plasma rapidly becomes sufficiently conducting so that there is a major phase lag
between the magnetic fields inside and outside. This,
coupled with the information that the plasma is
moving away from the glass walls, is the appropriate
condition for the application of the fast shock. Internal
magnetic and electric field probe signals and image
convertor pictures verify this concept of the condition
immediately before the application of the strong shock.
Figure 1 shows the geometry of the experiment. The
vacuum envelope is 4-in. pyrex pipe. The bias field
coils and slow collapse coils give an axial mirror-type
field. The single-turn fast collapse coil is mounted in
the center in order to maximize the shock strength for
the limited magnetic field energy available. Consequently, it is not in mirror geometry and there is no
containment after the shock is applied; the plasma is
merely squirted out at the ends. This geometry is
adequate to study the first passage of the shock itself,
but later experiments are envisaged with subsequent
shock containment.
The slow collapse heats and ionizes the gas sufficiently rapidly so that by the beginning of the fourth
current maximum of the slow collapse cycle the plasma
is sufficiently ionized and heated to be a ''perfect"
conductor, and a current boundary layer is formed
away from the glass wall. The fast collapse shock is
applied shortly after this.
The bias magnetic field is small (~ 200 gauss) applied
300 /¿sec before slow collapse. It permits the P.I.G.
ionization to start 20 /¿sec before slow collapse and
serves also to vary the amount of field trapped inside
the plasma during slow collapse.
FAST COLLAPSE
FIELD
APPLIED SLOW
COLLAPSE
+ 2000 GAUSS-
I
-2000 GAUSS-
ENTIRE
TIME OF
UPPER TRACES
CYCLE
5/1 sec PER DIVISION
Figure 2. Oscillograms of slow and fast collapse magnetic fields
RESULTS
Figure 2 shows the traces for the field and rate of
change of field inside and outside of the plasma in the
region of the fourth current maximum of slow collapse.
It is evident that the field inside the plasma is shifted
in phase relative to the applied field. This phase shift
indicates (1) that the plasma is behaving essentially
as a perfect conductor, and (2) that the mass of the
plasma is coupled to the magnetic field.
Figure 3 shows image convertor pictures of the slow
collapse plasma taken at the exposure openings and
times of Fig. 2. In picture 1 the vertical limit is the
glass envelope diameter. The lateral length is the
distance between the slow collapse coils. The fast
collapse coil is removed. By the time of the third
picture the plasma is just leaving the glass walls and
by the fifth picture the plasma is compressed to
minimum radius, approximately one-half, determined
CENTER
L I N E , AXIS
Figure 3. Image converter pictures of slow collapse
147
SHOCK HEATING OF A PLASMA
by the value of the trappedfieldand plasma pressure.
The fast shock is applied at approximately the time
of the second picture when the plasma is just beginning
to leave the glass wall.
Figure 4 shows the oscilloscope traces that describe
the effect of the applied shock created by the spark
gap firing of a single 0.25-mf, 50-kv condenser (shorted
ringing frequency of 2.5 megacycles). Frame (A)
shows an overlay of two traces taken with the magnetic probe inside the glass envelope, axially centered
under the fast collapse coil and at one-half radius
position. The upper trace, V, was taken with no
plasma (vacuum) and shows a typical crowbarred
magneticfieldrisingfrom a negative value of 800 gauss
to a positive value of 1500 gauss in 0.3 /osee. The lower,
P, trace in Frame (A) is the same signal except that a
plasma has been added, with all the necessary preconditioning. The first feature that is evident is that
no signal occurs until after a delay of approximately
0.2/isec. The shock has to travel something like
2.5 cm before reaching the probe and so this is
interpreted as a minimum speed of approximately
107 cm/sec. The next feature is that the initial probe
signal is negative rather than in the positive direction
of the applied fast field. The negative signal is what is
expected in the case of a shock, because the compression behind the shock of a negativefieldis independent
of the properties of the appliedfield,and depends only
upon the piston pressure #а/8тг. The shock compression of a negative initial trapped magneticfieldshould
show an increase of the negative field—exactly as
observed. Following the passage of shock, it is
expected that the subsequent radialflowof the plasma
will uncover the probe and expose it to the positive
applied shock field. The probe indicates the positive
field after 0.4 /xsec. The bottom two traces, Frames (C)
and (D), show the same phenomena of the shock on the
internal magnetic probe (plasma and vacuum) at a
much slower sweep speed in order to illustrate the
combined effects of the slow and fast shocks. The
relative time of the shock and shock arrival cannot be
compared exactly because of the jitter in shock initiation. In the previous upper left trace this jitter was
observed to be small, and was negated by triggering
the oscilloscope from the applied shock field.
DISCUSSION
If the plasma surface acts like a perfect conductor
and moves like a piston, then it should react back on
the initial circuit; that is, it should behave as a
variable inductance that is changing within the time
of the primary frequency. Most of the inductance of
the fast collapse circuit is located in the single-turn
coil around the glass envelope. If a shorted turn of
copper were placed just inside this coil, the inductance
would be reduced and the current (for a given voltage
on the condenser) would rise faster and higher than
without the shorted turn. If now the shorted turn of
copper moved radially inward just after thefieldhad
been applied, the inductance would be increased,
•work would be done on the shorted turn equal to the
magnetic pressure times change in volume, and the
current would decrease by an amount corresponding
to the conversion of magnetic energy to mechanical
energy of the work done on the changing inductance.
Exactly this behavior of the plasma is documented in
Frame (B) of Fig. 4. The external magnetic field, or
current to the fast collapse coil is shown with and
without plasma. The slower rising curve (thefieldsare
measured negative) that ends up at a larger magnitude
corresponds to the vacuum applied shock. When now
the plasma is introduced so that it is at maximum
radius at the time of the shock, then the current rises
more rapidly at first, indicating that the plasma behaves like a shorted turn inside the coil, but then, at
0.2 [isec, the current crosses over the vacuumfieldcase
and ends up at a lower magnitude. This implies that
the current-carrying plasma has moved radially inwards away from the glass walls, and that this motion
has been reflected back on the primary circuit as a
changing inductance. The work done is the thermal
and kinetic energy given to the plasma. To calibrate
the effective radius at which the initial current was
flowing in the plasma, actual copper rings of various
sizes were placed inside the glass and then the reactive
effect observed by the different rates of rise of initial
current. Of course, in the case of a static copper shorting ring the current rose to and remained at a higher
value than in the vacuumfieldcase. In this fashion it
was found empirically that the initial effective plasma
current flowed within | c m of the glass walls. The
inductive interpretation of the circuit assumes that the
resistive penetration is small, as indeed it must be to
explain the observed large phase shifts at the very
much lower frequency of the slow collapse.
We have, in addition, attempted to verify the charge
separation structure of the shock front by the use of
dual Langmuir probes. We have succeeded in applying
the technique, so far, solely to the case of the weak
shock of the slow collapse cycle.
The shock front should be dominated by charge
separation provided the collision mean free path is
very long compared to the electron Larmor radius.
For the slow collapse cycle:
Я > 1000 gauss
Electron energy = 10 ev
+ 2200 GAUSS
О
-2200GAUSS
+2200GAUSS
0
-2200GAUSS
O2iisec/ DIVISION
INTERNAL H FIELD
VACUUM a PLASMA
+ 2200 GAUSS h
-2200GAUSSp
2.0/isec/DIVISION
INTERNAL FIELD
2200 GAUSS/
DIVISION PLASMA
0 2/i/DIVISION
EXT/iRNAL H FIELD
VACUUM a PLASMA
+ 2200GAUSS
0
-2200GAUSS
20/1 sec/DIVISION
INTERNAL FIELD
2200 GAUSS /
DIVISION VACUUM
Figure 4. Magnetic probe measurements of fast collapse shock,
P denotes with plasma, V (vacuum) without plasma
148
SESSION A-9
P/368
S. A. COLGATE and R. E. WRIGHT
LANGMUIR PROBE SLOW COLLAPSE
TRANSVERSE MEASUREMENTS
LANGMUIR PROBE SLOW COLLAPSE
AXIAL MEASUREMENTS
l/i sec/DIVISION
20V/DIVISI0N
+ CHORD SIGNAL
___
3 SHOT OVERLAY
H—I—I—H ±Ф_
dt
- 2 0 VOLTS
+ 2200 GAUSS
- 2200 GAUSS F
FOURTH CURRENT
MAXIMUM
-0.95 cm
Figure 5. Dual Langmulr probe measurements of the shock electric field
Electron Larmor radius = 0.006 cm
Collision mean free path = 0.15 cm (D2 at 10 ц Hg;
temp. 10 ev)
Since the energy the ions receive in falling through
the integral of the space charge separation field is
about equal to the kinetic energy of their fluid flow
behind the shock, we should expect a voltage signal
normal to the shock equal to the ion kinetic energy in
electron volts in the case of a shock that is thin compared to the probe spacing. This signal is observed.
At arradial distance two-thirds of the tube radius,
all three orthogonal components of the electric field
are present. These components were measured by a
dual-wire probe (see Fig. 1) oriented variously in the
three directions, radial, axial, and chord. The oscillating magnetic field of the slow collapse generates
successive shock waves that travel radially toward the
axis and reflect. There is also an axial component due
to the mirror effect of two separate collapse coils. After
a few successive current oscillations, the shock builds
up in strength because the resultant heating and
ionization of the gas make it a better conductor and
consequently more strongly coupled to the magnetic
field. These shocks reach a maximum at the fourth
current maximum (second condenser cycle), and so
all probe signals were studied at this period.
The electric signal from the probes is always
measured in parallel with a circuit impedance which
must be large compared to the plasma impedance, or
else a time-varying correction must be applied. It was
determined experimentally that the signals were
essentially the same whether they were measured
across a 100-ohm or 100,000-ohm impedance, so that
in practice they were fed through two 50-ohm cables
to opposite oscilloscope plates.
Figure 5 shows a set of chord and radial signals,
each with an overlay of the same signal with the probe
rotated through 180 degrees. The self-consistency
of the signal, even under inversion of the probe,
indicates a reproducible phenomenon solely associated
with probe orientation within the plasma.
The electric field inside the plasma should be the
sum of the velocity inducedfieldv x H and the charge
separation field e¡(ne—nj)dx. If the fluid flow is
strictly radial in the region of the dual probe, then the
chord signal should measure the v x H field and the
radial signal the charge separation field. A magnetic
probe coil measurement of d$\dt is also taken at the
position of the Langmuir dual probe. To a first
approximation the d<f>¡dt signal and the chord dual
probe signal should be the same since the plasma
velocity is a measure of the rate of change of magnetic
flux. It can be seen in Fig. 5 that these signals are
approximately the same, thus verifying the interpretation qualitatively. The chord signals give a velocity
of 2 x 10e cm/sec, in agreement with measurements of
the progress of the interface. The radial signal is
SHOCK HEATING OF A PLASMA
displaced somewhat toward earlier times, which is in
agreement with the concept that the charge separation
gives rise to the forces that cause the plasma motion.
The polarity of the radial signal is independent of
magnetic field direction and is predominantly of one
sign (whereas the chord signal reverses sign). The
polarity of the radial signal on the first peak of each
cycle is in agreement with a radially inward acceleration, i.e., the negative electron charge is ahead of the
positive ion charge. Subsequent reflected shocks cause
a reversal of this potential, but since the outgoing
shock is never as strong as the ingoing one, the negative reversals are weaker. The magnitude of the radial
signal is in good agreement with an expected 20-ev ion
kinetic energy.
Figure 5 also shows a polar plot of the chord-radius
signal as a function of angle, taken at a given time.
The sine curve result is an indication of the reproducibility and true plasma origin of the signals.
On the right, Fig. 5 shows the axial electric field
149
measurements. Because of the mirror configuration
of the collapse coils, there is an axial component to the
shock, but at the midpoint between the mirrors, this
component should vanish, giving zero electric field. A
sequence of measurements as a function of position
between the mirror coils shows that the axial electric
field does go through a null and reversal.
The electric field and magnetic field measurements
are in good agreement with present shock theory, and
it is anticipated that future experiments will tend
toward much higher shock strengths in a containment
geometry—either mirror or stabilized pinch.
ACKNOWLEDGEMENTS
The development of the switch gear of the fast collapse system has been the work of D. R. Lasher and
R. H. Munger. The fast condenser has been designed
by E. G. Hartwig of the Electrical Engineering group
in conjunction with the Hudson Falls Capacitor
Division of General Electric.
REFERENCES
1. W. Marshall, Proc. Roy. Soc. (London), 233A, 367 (1955).
2. A. C. Kolb, Production of High Energy Plasmas by Magnetically Driven Shock Waves, Phys. Rev., 107, No. 2,345 (1957).
3. G. S. Janes, Magnetically Driven Electrodeless Shock Tube
for Production of High Energy Plasmas, Bull. Am. Phys.
Soc, 85 D6 (January, 1958).
4. M. N. Rosenbluth and Longmire, to be published.
5. Alfred Bafios, to be published.
6. S. A. Colgate, A Description of a Shock Wave in Free
Particle Hydrodynamics with Internal Magnetic Fields,
UCRL-4829 (February 19, 1957).