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OBS E RVAT ION O F DENS ITY LIM IT IN A M IC R OWAVE PLASMA
D. J. Holly and J. C. Sprott
September 1975
Plasma Studies
University of Wisconsin
PLP 652
These PLP reports are informal and preliminary and as such may contain errors not yet eliminated. They are for private circulation only and are not to be further transmitted without consent of the authors and major professor.
This report describes experiments done recently in=the small toroidal
octupole in which electron density was measured as a function of microwave
power for an ECRH microwave-produced plasma. It has long been known that at
low values of power the density increases linearly with power.1
The plateau
region where density ceases to increase with increasing microwave power was
observed and the forward and reflected power were measured in order to see
whether the observed density limit was due to an impedance mismatch between
the microwave system and the plasma-filled cavity.
A block diagram of the experimental setup is shown in Fig. 1. A
2450 MHz magnetron capafule of up to about 5 kWCW output power is used to
produce the plasma; earlier experiments with a 1.5 kW magnetron had indicated
that more power was needed to reach maximum density. The magnetron was
isolated from the cavity and plasma by a pre-terminator claimed to
attenuate reflected power by 35 dB; this was intended to eliminate the
coupling of the plasma back to the magnetron seen when using an 8.5 dB
isolator. A variable attenuator was used in conjunction with a variable
current regulator supplying the magnetron to L( vary the rf power to the
plasma. A directional coupler located after the attenuator samples the
forward and refl ected power. The forward and refl ected power <l1l'emmeasofted
using matched 1N21 diode detectors. The microwaves are fed into the octupole
cavity through an E-H stub tuner which allows the impedance of the cavity to
be matched so that reflected power from the empty cavity is only a few per
cent of the forward power. Power is coupled into the cavity through a
window located in the midcylinder in the upper lid.
-2-
The weighted line-average Langmuir probe developed by E. Strait2
was used to monitor the plasma. It was located between the lower outer
hoop and the outer wall.
Fig. 2 shows a typical succession of shots at increasing power levels.
The microwave power waveform is roughly a square wave starting about .5 msec
after the rise of the magnetic field and lasting about 4 msec. Measurements
of the forward power, reflected power, and ion saturation current were made at
the arbitrarily chosen time of 2.5 msec after the start of the magnetic field
rise; this is approximately peak magnetic field. Note that as in b, c, and
d of Fig. 2, the shape of the ion saturation current signal from a to 2.5 msec
is still changing with increasing input R.F. power, while the value at 2.5 msec,
which was used to derive the subsequent plots, and later times is almost
constant as the input power level is increased. The decay in the ion
saturation current as microwave power continues to be pumped in c, d is
perhaps due to some spatial shifting of the plasma; no attempt has been
made to spatially resolve the density profile. The <ne> shown is a volume
averaged density.
Fig. 3 and the center curve in Fig. 4 show the dependence of <n > on e
the input microwave power at t = 2.5 msec. The error bars shown are typical
and represent variations within a few hundred microseconds of the measure-
ments. The electron temperature was measured at several points in the plateau
region on the right of Figs. 3 and 4 by sweeping Strait's probe from - 40 V
to + 60 V in 100 �sec; it was found to be constant to within measurement
accuracy at 8-10 eV. A value of 8 eV was assumed in deriving the densities
shown in Figs. 3, 4 from the ion saturation current with the probe biased
to - 45 V.
-3-
The three density curves in Figs. 3 and 4 were obtained at three
different voltages on the capacitor bank that supplies the magnetic field
energy. In each case the density reaches a plateau beyond which further
increase in microwave power produces no further density increase. One might
expect this plateau to be reached around a density given by
or
-3 3 f = 2450 MHz = fp = 9 n (cm ) x 10
whereas the experimentally determined densities are roughly a factor of
two or three below this in the plateau region. The measured densities are
also somewhat below what other people have measured recently, so the
discrepancy may be partly due to probe contamination or some other effect.
The reflected power measurements for a bank voltage of 2.0 kV are
also plotted in Fig. 4 vs. microwave input power; similar results were
obtained at 1.5 and 2.5 kV bank voltages. The fluctuations in the
reflected power were fairly high (see Fig. 5) but there is no obvious
dependence of Prefl
on the plasma density. The reflected power is in
general small compared to the forward power, and is fairly constant as the
input power is varied.
One reproducible effect observed in the reflected power is the peak
at the end of the microwave forward power pulse, shown in Fig. 5. The fact
that it shifts to later times as the bank voltage is increased suggests it
is connected with a fixed value of magnetic field, e.g. the resonance zone
sweeping by the microwave window might cause a momentarily high reflection.
The magnetic field values corresponding to the time at which the peak in
reflected power occurs for the various bank voltages are within 15% of one
another. Also, at high power levels as in d ), Fig. 5, a peak in the
-4-
reflected power occurs at the beginning of the microwave pulse (about
1.1 msec in Fig. 5d ) at the same magnetic field value as the second peak.
Some dependence of maximum obtainable density on bank voltage
(corresponding to magnetic field strength) can be seen in Figs. 3 and 4.
Fig. 6 shows this dependence explicitly. The microwave input power levels
in this case were presumably high enough so that the density was in the
plateau region: there appears to be a fairly well-marked transition from
low-field, low density plateau region to a region with a higher density
plateau at a bank voltage of about 2.5 kV. This transition occurs
appr0ximately at the point where the resonance zone sweeps by the microwave
window during the initial breakdown, and suggests that the heating at high
densities is better when the microwaves are incident on the resonance from
the high field side. A similar conclusion was reached by wong.3
The observed saturation of density as the input microwave power is
increased, suggests a pronounced drop in heating at high densities. In
fact, Wong3
has measured that the normalized ECRB rate (G) falls sharply in
accordance with the theoretical prediction
2 2 2 G = Go exp (- 41T BOWp
/AlvilBlow ) .
In order to test this prediction, program SIMULT4
was modified to include a
term
G = Go exp (- 0.03 an/f ) ,
where a is the plasma minor radius (cm ) , n is the average plasma density
(cm-3 ), and f is the microwave frequency ( Hz ). The result of the simulation
is shown in Fig. 4 and agrees quite well (factor of 2 ) with the observed
values of density.
-5-
We are therefore inclined to conclude that a density limit exists
for ECRH plasmas at a density the order of the critical density (wp
= w),
but at a value that depends on the magnetic field shape and cavity Q, and that
in sufficiently large cavities, the power not absorbed by the plasma is
absorbed by the cavity walls and is not reflected back to the microwave
source. It would then appear ineffective to attempt to improve the
impedance match between the source and the plasma, but some improvement might
be obtained by a different' location of the microwave input (i.e., in the
bridge region).
FOOTNOTES
1. J. C. Sprott, Phys. Fluids li, 1795 (1971) .
-6-
2. This probe is a modified version of the one designed for the
large octupole, described in PLP 566, averaging probe for the
large octupole. E. Strait (May 1.974).
3. K. L. Wong, Ph.D. thesis, University of Wisconsin (PLP 601) .
4. PLP 556. Numerical Simulation of Multipole Confinement. (Revised).
J. R. Patau and J. C. Sprott (March 1974) .
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