Electron Cyclotron Heating in Various Magnetic Configurations of HSX
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THE 14th
INTERNATIONAL STELLARATOR WORKSHOP
Electron Cyclotron Heating in Various Magnetic Configurations of HSX*
J.N. Talmadge, K.M. Likin, A. Abdou, A. Almagri, D.T. Anderson, F.S.B. Anderson ,
J. Canik, C. Deng, S.P. Gerhardt, K. Zhai
The HSX Plasma Laboratory
University of Wisconsin-Madison, USA
AbstractThomson scattering and diamagnetic loop measurements indicate that the central electron
temperature and stored energy increase linearly with power. Experimentally it is found that the central
electron temperature is roughly independent of density. These findings are consistent with a thermalconductivity that scales inversely with the density. Typically in good confinement configurations, the
stored energy shows a peak at low density and is constant at the higher densities, in contradiction tothe model. On the other hand, in configurations that poorly confine trapped particles, the stored
energy increases linearly with density, as expected. From measurements of X-ray emission and
absorbed power, as well as calculations of the absorption efficiency from ray tracing, it is concludedthat at low densities a nonthermal electron population accounts for a significant fraction of the stored
energy for the good confinement configurations.
IntroductionPlasma heating in HSX is done at a magnetic field of 0.5 T using the extraordinary
wave at the second harmonic of the electron cyclotron frequency. In order to investigate the
improved confinement properties of the quasihelically symmetric configuration, a 28 GHz
gyrotron is used to heat electrons to the low collisionality regime. So far, up to 100 kW has
been launched from the low field side of the device in the form of a Gaussian beam with a
spot size of 4 cm. In HSX, neoclassical transport can be greatly increased with a set of
auxiliary coils that adds a toroidal mirror term to the magnetic field spectrum. In the Mirror
configuration, the field is increased at the location of the ECH antenna, while in the anti-Mirror configuration the field is decreased. Trapped particles are well confined for the QHS
configuration, while they are lost from the outboard side of the torus at the location of the
antenna in the Mirror configuration. However, trapped particles launched near the antenna for
the anti-Mirror configuration are lost from both the inboard and outboard sides of the torus.
Neoclassical TransportTransport in HSX is analyzed using the ASTRA code.
1The particle and heat fluxes in
ASTRA, including the off-diagonal terms, are calculated by taking moments of the
monoenergetic diffusion coefficient. These diffusion coefficients are obtained for a broad
range of test particle energies, densities and electric fields using a Monte Carlo code and then
fit to a six-parameter analytic expression originally developed by Shaing2
and later modified
by Painter and Gardner3. The expression can be written in the following manner:
2
26
2 ω
ν ε
π
d t V C D = ν ω ω ω ω ν ω ~)(~
42
32
22
12
BBBE C C C C ++++=
(1)
d B V C 5−=ω ,eBr
K V d = ,
6
~
C
ν ν = ,
rB
E E =ω
, Rr t / =ε
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This simple form of the monoenergetic
diffusion coefficient fits the numerical
data over a broad range of electric fields,
magnetic fields, collisionality, particle
energy and particle mass. One particular
advantage of using this expression is thatit is a fast way of calculating the
ambipolar radial electric field by setting
the ion and electron fluxes equal to each
other, Γ i(r,Er) = Γ e(r,Er), where r is a flux
surface label.
In the ASTRA code, the power
deposition profile is determined from a
ray tracing calculation.4
Typically the
single pass absorption coefficient is
about 0.4 and rises with density. The
deposition profile tends to be verypeaked with central resonance.
Electron Temperature Scaling
Since electron transport in
stellarators is typically not solely
neoclassical, the electron thermal
conductivity is specified as the sum of a
neoclassical term plus an anomalous
component. Previously we used an
anomalous thermal conductivity given by
ASDEX L-mode scaling5
that is
proportional to Te3/2. This yields a
dependence of the temperature on the
density and power, T ~ (P/n)0.4
and a
stored energy that goes as W ~ n0.6
P0.4
.
Recently the central channel of a 10-
channel Thomson system with a
Nd:YAG laser has been made operational. As seen in Figure 1, the central temperature is
roughly independent of density, except perhaps at the lowest densities for the QHS
configuration. This data is with a constant input power of 40 kW. Figure 2 shows the central
electron temperature for a fixed average density of 1.5 × 1018
m-3
, as the gyrotron power is
varied from 20 kW to 100 kW. The absorbed power is estimated from the difference in the
slopes of the stored energy after the gyrotron turn-off. From the figure, it can be seen that forthe QHS configuration, the central Te appears to scale linearly with power. The two scaling
results indicate that the ASDEX L-mode model for the anomalous thermal conductivity does
not follow the experimental scaling.
Instead we find better agreement with the experimental data for an anomalous thermal
conductivity that scales as χe,an = 10.35/ne where the conductivity is in units of m2/s and the
density is in units of 1018
m-3
. This gives a temperature dependence that is independent of
density and linear with the power. Modeling of the particle diffusion coefficient based on
ASTRA:QHS
ASTRA: Mirror
Fig. 1: Central electron temperature as a
unction of line average density. Also shown
are the ASTRA calculations for the QHS and
Mirror configurations (Er = 0, dashed line;ambipolar Er, solid line).
ASTRA: QHS
ASTRA: Mirror
Fig. 2: Central T e versus absorbed power.
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calibrated Hα measurements and
DEGAS calculations gives a similar
dependence on the plasma density.6
This sort of Alcator-like dependence
for the thermal conductivity was found
to be a good fit to the data for the early
Heliotron-E ECH results with a 28GHz gyrotron.
7In Figures 1 and 2 are
also plotted the ASTRA calculation of
the central electron temperature for the
QHS and Mirror configurations. For
the QHS configuration, the transport is
solely determined by the anomalous
transport since the neoclassical fluxes
are so low. For the mirror
configuration however two curves are
plotted, corresponding to the case
when the radial electric field is set to
zero, as well as when the ambipolarelectric field is determined. For these
calculations, the radial electric field is
solely given by the electron root when
the ion flux is set equal to the electron
flux. Such a high positive electric field
lowers the electron fluxes considerably
for the Mirror and makes the transport
properties of this configuration similar
to the QHS mode of operation.
However, there is sufficient reason to
believe that the prediction of an
electron root plasma may be too
optimistic.8
Thus we expect the
experimental data for the Mirror
configuration to fall between the two
limits of the ASTRA calculation. At
this time, there is insufficient data to distinguish which of the two predictions for the Mirror
configuration might best approximate the experimental results.
Stored Energy Scaling
Figure 3 shows that the stored energy increases linearly as a function of the absorbed
power for the QHS and Mirror configurations at a fixed density of 1.5 × 1018
m-3
. This is inagreement with the Alcator-like model for anomalous transport, rather than the ASDEX L-
mode model. The difference between the QHS and Mirror stored energy reflects the 15%
lower plasma volume for the Mirror case. From the figure, it can be seen that only at the
higher powers does the stored energy agree with ISS95 scaling, although the functional
dependence on the power is very different. We would expect from the model that the stored
energy should increase linearly with the density. Figure 4 shows, however that for a constant
input power of 40 kW, this is not so for the QHS configuration and for central resonance in
the Mirror mode. In contrast, Figure 5 shows that for Mirror outboard resonance where
ISS95
ASTRA: QHS
ASTRA: Mirror:
Fig. 3: Stored Energy versus absorbed power
Fig. 4: Stored Energy versus line average
density
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confinement of trapped electrons is poor,
the dependence of the stored energy on
the density does agree with the model.
To understand why the
dependence of the stored energy on the
density does not agree with the model,
we measured the hard X-ray emission
from the plasma using a collimated
CdZnTl detector. Figure 6 shows that the
emission increases with density to a
maximum at 0.5 × 1018
m-3
and then falls
off sharply at higher densities. Similarly
the stored energy also shows a peak at
0.5 × 1018 m-3, but remains roughlyconstant at higher densities. The
conclusion from this comparison of the
X-ray emission to the stored energy is that a nonthermal component in the plasma makes a
significant contribution to the stored energy at the lower densities.
Ray Tracing and Absorbed Power This conclusion is further supported by a comparison of the heating efficiency from a
ray tracing code compared to measurements of the absorbed power.4
Figure 7 shows the
results of the ray tracing calculation. The single-pass absorption is calculated assuming a
parabolic density profile and and exponential electron temperature profile. With a central
temperature assumed to be 0.4 keV, the single-pass absorption coefficient is 0.4 at a line
average density of 1.5 × 1018
m-3
. Using the Thomson scattering data for the central
temperature there is slightly more absorption at the lower densities, but both calculations
show that the absorption efficiency should increase with density up to the cut-off at a line
average density of 3 × 1018
m-3
. Calculations of multi-pass absorption indicate that the total
absorption efficiency can be as high as 70% for two passes.
Figure 8 shows the measured absorption efficiency versus plasma density for the QHS
and Mirror configurations. The absorption efficiency is measured using a set of microwave
Fig. 6: Hard X-ray emission and stored
energy as a function of density forMirror central resonance.
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4
Te = 0.4 keV
T from ex .
Line Average Density, 1018
m-3
Absor
tion
Fig. 7: Ray tracing calculation of absorption
efficiency assuming constant peak temperatureof 0.4 keV. Also shown is calculation based on
experimental measurements.
Fig. 5: Stored energy versus density for
Mirror outboard resonance.
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antennas, four of which are plotted in the figure. For both configurations the efficiency is in
the range of 0.8-0.98. It can be seen that for the Mirror configuration the efficiency drops at
densities less than 0.5 × 1018
m-3
, while for the QHS configuration it remains high.Interestingly, for the anti-Mirror configuration in which the confinement of trapped particles
near the ECH antenna is the worst of the three configurations, the measured absorption
efficiency is never higher than 0.6, while the stored energy remains low at only 5-7 J. For this
configuration, there are no hard X-rays even at the low densities. Hence, the discrepancy
between the ray tracing calculations and measured absorption efficiency at low density is
most likely due to additional absorption on a nonthermal electron population. Furthermore,
the differences in absorption measured for the QHS, Mirror and anti-Mirror configurations
can be explained by differences in trapped particle confinement.
ConclusionIn summary, anomalous transport in HSX is best described by an Alcator-like thermal
conductivity in which the thermal conductivity is inversely proportional to the density.Departures of the experimental results from this model, as with the experimental stored
energy as a function of plasma density, can best be explained by a nonthermal component of
the electron distribution that is accounting for a significant fraction of the stored energy.
*This work is supported by DOE Grant DE-FG02-93ER54222
References:
1 N. Karulin, “Transport Modeling of Stellarators with ASTRA”, IPP 2/328, Dec. 1994.
2K.C. Shaing, Phys. Fluids 27 (1984) 1567.
3
S.L. Painter and H.J. Gardner, Nucl. Fusion 33 (1993) 1107.4K. Likin et al., 30
thEPS Conference on Controlled Fusion and Plasma Physics, to be
published.5
N. Karulin, “Transport Modeling of Stellarators with ASTRA”, IPP 2/328, Dec., 19946
J. Canik et al., “Particle Neutral Density Modeling and Measurements in HSX”, this
conference.7
H. Zushi et al., Nucl. Fusion 24 (1984) 305.8
H. Maassberg et al., Phys. Fluids B 5 (1993) 3627.
QHS
Line Avera e Densit 1018 m-3
Absorption
Mirror
Line Avera e Densit 1018 m-3
Abs
orption
0
0.20.4
0.6
0.8
1
0 1 2 3 4
MD #1
MD #2
MD #3
MD #4
0
0.20.4
0.6
0.8
1
0 1 2 3 4
MD #1
MD #2
MD #3
MD #4
Fig. 8: Multi-pass absorption coefficients for QHS and Mirror configurations,
measured by microwave antennas.