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



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.



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



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.



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.

electron cyclotron heating in various magnetic configurations of hsx

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