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MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS – 1963
02м 4-й рrs-L
ROUGH DRAFT
8/6/65
CONF-650806-6
OBSERVATION OF A MIRROR-LIKE INSTABILITY IN A HOT ELECTRON PLASMA=
SEP 21 1965
W. B. Ard and R. A. Dandi
Oak Ridge National Laboratory
Oak Ridge, Tennessee, U. S. A.
and
R. F. Stetson
Florida Atlantic University
Boca Raton, Florida, U. S. A.
Abstract
Iwo types of instabilities have been observed in a hot electron plasma
produced by electron-cyclotron heating in a magnetic mirror. One type results
in radial loss of particles across magnetic field lines and appears to be due
to the growth of flutes. The other results primarily in loss along magnetic
field lines and appears to be due to the mirror instability. Both types are
accompanied by RF oscillations and result in the loss of ~ 10% of the energy
stored in the plasma.
MELLASED FOR ANNOUNCEMENT
AN NUCLEAR SCIENCE ABSTRACTS
Research sponsored by the U. S. Atomic Energy Commission
under contract with the Union Carbide Corporation.
ROUGH DRAFT
8/6/65
p www
:
....
OBSERVATION OF A MIRROR-LIKE INSTABILITY IN A HOT ELECTRON PLASMA=
o sitions
i kommer malinkan perinteine anderemo ..
W. B. Ard and R. A. Dandl
Oak Ridge National Laboratory
Oak Ridge, Tennessee, U. S. A.
and
mode
ing
de residence that wonder
R. F. Stetson
Florida Atlantic University
Boca Raton, Florida, U. S. A.
het mome
Hot electron, plasmas produced in magnetic mirrors by radiation at the
voidaat wordt
electron-cyclotron frequency have been found to be unstable under certain
conditions!' The evidence indicating the presence of instability in this
plasma was the observation of large bursts of x rays accompanied by sudden
vall
decreases in stored plasma energy. Recent investigations of the plasma has
:
shown that these x-ray bursts are due to two different types of electron
here there
losses. In one type of loss the electrons cross the magnetic field lines
RA
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.
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and strike the wall on the midplane of the mirror field. In the other type
of loss the electrons leave the plasma along the magnetic field lines.
A diagram of the apparatus is shown in Fig. 1. The region between the
magnetic mirrors is enclosed by a perforated copper liner. The liner serves
to confine the microwave heating power to the region containing the plasma.
A plasma is produced if the magnetic field intensity is 3750 gauss at same
place in the liner. This is the field that gives an electron-cyclotron
frequency of 10.6 KMC, the frequency of the microwave power source.
Under typical operating conditions, the hot electron component of the
plasma has the following properties. The total energy stored in the plasma
.
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1
Research sponsored by the U. S. Atomic Energy Commission
under contract with the Union Carbide Corporation.
Sa.
is 9 joules. The average electron energy is from 50 to 100 keV. The plasma
volume is about 4 x 103 cc. This gives a density of from 1.5 to 3 x 1044/cc
and a B of 0.06. The plasma is maintained by a continuous l'eed of neutral
gas into the region occupied by the plasma and continuous feed of microwave
energy into the same region. The pressure outside the plasma is typically
about 10") torr. There is therefore a background density of much cooler
electrons always present in the plasma. The density of cooler electrons is
estimated to be about the same as that of the hot electrons.
This estimate
is based on the current collected by probes outside the magnetic mirrors.
Also shown in Fig. 1 is the arrangement of various probes for investi-
gating instabilities. Fast electrons lost along field lines are detected by
silicon solar cells placed outside tne mirrors. The four solar cells are
positioned on field lines that come through holes in the end of the liner at
VT-i
n
0, 1, 2, and 3 inches from the magnetic axis. The cells are shielded from the
plasma by thin aluminum foils. Since signals were observed from the solar
cells only when they were placed along the field lines that came through a
hole in the liner, it was determined that the signals were due to fast elec-
trons and not x rays. The cells were operated short circuited so as to give
a current output proportional to the incident flux. The response time of the
cells operated in this way is less than 1 usec.
A collimated x-ray detector was used to detect x rays from electrons
striking the liner in the mirror region. The response time of the x-ray
detector was 0.02 usec. An rf pickup loop was placed just inside the liner
on the midplane in order to look for oscillations at very high frequency.
Lower frequency oscillations could be detected by the current probe located
just outside the mirror. The stored plasma energy was measured with a diamag-
netic loop /27. Since the loop was wound around the copper liner, its response
time was much too long to follow the change in energy during an instability.
However, the response time was considerably shorter than the plasma build-up
time so that the total energy lost during the instability could be measured
quite accurately. The times involved were as follows: duration of instability -
several microseconds, response time of diamagnetic loop - 10 milliseconds, plasma
During one of the types of instability observed, the solar cells detected
bursts of energetic electrons that lasted for from about 2 to 20 microseconds.
All four of the cells gave signals at the same time; however, variations in siga
.
nal level during the bursts were not well correlated between the detectors 10-
cated on different field lines, although the beginnings and ends of the signal
from the cells were well correlated. During the time that the solar cells indi-
cated a large flux of energetic electrons out the mirror, the current probe
showed a decrease of plasma current out the mirrors. Radiation was detected on
the rf loop during the bursts.
The radiation was in a frequency band about 50-mc
wide, centered near 5.3 KMC. This frequency is half of the frequency of the
microwave power source used to heat the plasma. Figures 2 and 3 show 'typical
responses of the solar cell (upper traces) and the microwave receiver (lower
traces) during an instability. The large variation in output from the receiver
is mostly due to the frequency of the oscillation drifting out of the bandwidth
of the receiver. In order to determine whether or not the 5.3 KMC oscillation
was a plasma resonance driven by the microwave source, the source was turned off
as soon as the electron burst could be detected. The source could be turned off
less than 0.5 ubec after the burst started. The result was that the bursts
continued for several microseconds and the 5.3 KMC radiation also continuea.
There was apparently no change in either the intensity or the spectral char-
acter of the rt with or without the microwave source on. While this shows
that the oscillation is not just a parametric amplification of the applied
microwave radiation, it does not rule out the possibility that the oscillation
is triggered by the presence of the applied microwave power.
The average time interval between the bursts could be made arbitrarily
long. This time was essentially determined by the magnitude of the static
magnetic field intensity. In fact, if the field were set below a critical
value, no bursts were observed.
The fact that the instability is influenced by the magnitude of the mag-
netic field suggests that the important parameter is the location in the mirror
field of the region where the electron-cyclotron frequency is resonant with the
microwave power source. The onset of the instability occurred when the minimum
field in the mirror, B., was 0.8 times the resonant field, Bp. If we assume
that electrons gain energy from the microwave source only when they are in
resonance and that they only gain energy transverse to the magnetic field, then
the ratio 16 determined by the ratio Electrons whose turning points in
the mirror are at a field less than B, do not gain energy until they scatter
enoigh to have their turning points in the resonant region. Electrons whose
turning points lie at fields larger than By gain transverse energy until their
turning point is at B. This assumption seems reasonable if, for those elec-
trons that traverse the resonant region, ( ak from interaction with the micro-
wave field is larger than
· /from scattering.
If most of the energetic
5
electrons turn at B = By, then we have the relation
E/8,- (B/B. - TJ :
· As B. is incre
increases rapidly. The fact that the instability
sets in as Bo is increased suggests that the instability is due to temperature
anisotropy. The finite B of the plasma further suggests the "mirror instabil-
ity":/3/. The condition for this instability in an infinite plasma is given by
2 B (E./E, - 1) >1.
For B = 1.25, is 4. This gives a critical B of 0.17. This is about
3 times the observed B. However, we think that the observations are consistent
with the "mirror instability." The result of this instability would be a magnetic
compression of the plasma towards the midplane of the mirror. While the plasma
is compressed, the cold plasma current out the mirror should be very small. As
the plasma surface moves toward the midplane, the oscillation frequency of the
electrons between their turning points in the mirror field resulting from the
instability would rise rapidly. We propose that when this frequency reaches
the motion of the electrons between the mirror is coupled to the transverse
motion of the electron at the cyclotron frequency. A modulation of the compres-
sion field at the cyclotron frequency would couple in this way. (It is analogous
to the case of a weight supported by a string hanging from a vertically oscillating
rod. The string will oscillate if the natural frequency of the string is hall the
frequency of the rod.) The result of this type of oscillation is to convert trans-
verse elėctron energy to parallel energy. This could account for the observed
enhanced loss of electrons out the mirrors. The compression field collapses
due to the decrease in transverse energy and the increase in the parallel
pressure. However, the total transverse energy lost during the instability is
never more than about 10% of the total transverse energy. This measurement is
made by measuring the total change in the magnetic moment of the plasma. We
have not determined what fraction of this loss is due to actual particle loss
and what fruction is due to increased parallel energy of the remaining plasma.
A second type of instability observed appears to be the same as one ob-
served by Post in a hot electron plasma /47, 15/. This instability is charac-
terized by a loss of energetic electrons to the wall at the midplane of the
field. The electrons that strike the wall are detected by looking at the wall
with a collimated x-ray detector. The drift velocity of the electrons across
the field lines is much smaller than their precessional velocity due to the
gradient in the magnetic field. In fact, a scraper extending about an inch
inward from the liner intercepts all the electrons that are lost radially from
the plasma. Oscillating electric fields are observed when the plasma is subject
to this instability. Oscillations have been observed with frequencies from 3 me
up to about 30 mc. The oscillations last for a few microseconds and may recur
several times within a period of about 50 usec. Frequencies around 10 mc seem
to be most prevalent. Bursts of x rays from the scraper usually accompany these
oscillations. In fact, the x-ray intensity from the scraper can be modulated at
the same frequency as the electric field fluctuations. Figure 4 is a photograph
of the output from the x-ray detector and the signal from an electrostatic probe
just outside one of the magnetic mirrors. The surface of the plasma is apparently
rippled and the variations in x-ray intensity is due to the precession of the
ripples around the magnetic axis. The frequency of precession around the magnetic
axis is I mc for a 100 keV electron. Since frequencies of several megacycles
are prevalent, modes with m > 1 predaninate.
This instability can be suppressed by increasing the neutral gas pressure
in the region of the plasma. This suggests that the instability is suppressed
by increasing the conductivity of the plasma to the copper end walls of the
vacuum liner. This behavior also agrees with Post's observations and we, too,
believe this to be a flute instability.
If the neutral gas pressure is low enough and the rati low enough,
the plasma is subject to both types of instability and both types are observed
to occur more or less at random.
When the plasma is compressed during the "mirror" instability, it is
unstable to the flute. This is probably due to the greatly decreased conduc-
tivity to the end walls. The flutes that occur during this time begin to grow
T.
IV.
a microsecond or so after the electrons start leaving the plasma along the field
lines. The x rays from the wide wall often appear toward the end of the mirror
instability. See Fig. 5. It is likely that the increased electron loss due to
the flute helps to terminate the compression. However, in many instances, the
compression continues after the losses due to the flute have stopped.
1.
Aman
SA
C
.
REFERENCES
1. R. A. Dandl et al., Nuclear Fusion 4, 344 (1964).
2. W. B. Ard et al., Camptes Rendus de la vie Conférence Internationale
sur les phénomènes d'Ionisation dans les Gaz, Paris 1963, Vol. IV, p. 75.
3. H. P. Furth, Phys. Fluids 6, 48 (1963).
4. R. F. Post and W. A. Perkins, Phys. Rev. Letters 6, 85 (1961).
5. W. A, Perkins and R. F. Post, Phys. Fluids 6, 1537 (1963).
-
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FIGURE CAPTIONS
Fig. 1
Heating cavity showing location of detectors. Solid
lines are flux lines; dashed lines are lines of
constant-B.
Fig. 2
Upper trace: Solar cell signal. Lower trace: Micro-
wave receiver output with tuning at 5300 Mc. weep
rate: 2 usec/cm.
Fig. 3
Upper trace: Solar cell signal. Lower trace: Micro-
wave receiver onput with tuning at 5300 M. Sweep
. rate: 2 usec/cm.
Fig. 4
Upper trace: Current probe RF signal. Lower trace:
X-ray detector signal. Sweep rate: 0.2 usec/cm.
· Upper trace: Solar cell signal. Lower trace: X-ray
detector signal. Sweep rate: 2 usec/cm.
X-RAY DETECTOR
FIELD COILY
-LEAD SHIELD
-CURRENT PROBE
SOLAR CELLS

Trauma
Ir.
RF PROBE-
LPLASMA SCRAPER
Fig. 1. Heating cavity showing location of detectors. Solid
lines are flux lines; dashed lines are lines of constant-B.
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Fig. 2. Upper trace: 'Solar cell signal. Lower trace: Microwave
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