Proceedings of ITC/ISHW2007

ECE and Reflectometry on the Helically Symmetric Experiment
Konstantin M. LIKIN1), Carsten LECHTE2), Huijuan LU1), F. Simon B. ANDERSON1)
1)

The HSX Plasma Laboratory, University of Wisconsin, Madison, WI 53706, USA
2)
University of Stuttgart, Stuttgart, Germany

For plasma heating in the Helically Symmetric Experiment (HSX) with on-axis magnetic field of 0.5 Tesla, theextraordinary wave at the second harmonic is used, while the ordinary wave at the fundamental resonance isefficient in operation at 1 Tesla. A non-Maxwellian distribution function is detected in HSX plasmas by various
diagnostics. The electron cyclotron emission (ECE) spectra are measured with an eight channel radiometer. Byswitching the narrow band filters, measurements have been made across the plasma column within +/- 0.6 of its
effective radius. To model the ECE spectra we use (1) a Bi-Maxwellian distribution function and (2) results fromthe CQL3D Fokker-Planck code. Results of measurements and modeling are reported in this paper. Plasma
fluctuations can be responsible for enhanced heat transport from the plasma. Fourier spectra of ECE signals, as wellthose from the nine-chord interferometer, Langmuir probes, and magnetic coils show the presence of a coherentmode in the plasma core. To study the density fluctuations, a new reflectometer has been installed and tested on
HSX. We present ECE data and the first reflectometer results on density fluctuations in 0.5 Tesla HSX plasmas. As
do the other diagnostics, the reflectometer detects the coherent mode in the 50 – 250 kHz frequency range ofplasma fluctuations. A wavelet technique is applied to get the time evolution and the radial localization of thismode.
Keywords: Stellarator, plasma heating, electron distribution function, electron cyclotron emission, plasma density
fluctuations, reflectometer, wavelet analysis.

1. Inroduction
In plasma heating experiments on fusion machines
the particles may have a non-thermal distribution function
in momentum space, i.e. there are more particles withhigh energy as compared to the thermal equilibrium state.
Even a small number of high energy particles leads toenhanced emission at the cyclotron harmonics and makesa comparison between experiment and theory, which
deals with Maxwellian plasmas, more difficult. Moreover
the presence of a non-thermal component obscures a bulk
plasma response on small perturbations, such as cold
gas injection and/or heating pulse modulation, and as aresult in such cases the perturbation method is impracticalfor measuring the electron thermal conductivity of bulk
plasma from ECE signals. Also an excessive number of
runaway particles may absorb a significant part of theheating power resulting in uncertainty in determining thepower absorbed by the thermal particles based on ECE
and/or the diamagnetic loop data.
On the HSX stellarator we use the extraordinary
wave at the second harmonic to make plasmas at 0.5 T.
HSX also operates at the full designed magnetic field of 1
Tesla, in this case the wave polarization corresponds tothe ordinary wave. Available launched power is up to 100
kW and is focused on the plasma axis into a beam spot of
4 cm in diameter. Based on ray tracing calculations [1]e-mail: kmlikin@.wisc.edu

the absorbed power density in the HSX plasma is highenough (up to 5 W/cm3) to produce a tail of high energy
electrons, in particularly, in 0.5 T operation when theplasma density is low. For instance, an electron can get
up to 10 keV in one pass through the beam at such powerdensity. To make a correct interpretation of measured
ECE spectra, we solve the radiative transport equation (1)in bi-Maxwellian plasma [2,3] and (2) with the electron
distribution function from the Fokker-Planck code [4].
The ECE radiometer can measure plasma density
fluctuations if the plasma isn’t simply a black body. It isour case for the plasma parameters at 0.5 T. The calculated
optical depth is less than 1. We have found a coherentmode in the frequency spectrum of ECE signals in QHS
plasmas. The mode was first detected by the interferometer[5] and then by a set of Mirnov coils. We have estimatedthe relative amplitude of this mode based on ECE
fluctuations.
Recently we installed the reflectometer on HSX. The
reflectometer can operate with an extraordinary polarized
probing beam in 0.5 T operation and/or the ordinary wave
at 1 T. The frequency of the probing beam can (1) be fixedduring the plasma discharge and/or (2) be swept tomeasure a radial profile of fluctuations. We intensively use
the wavelet analysis on reflectometer data and make acomparison with Fourier spectra from the Mirnov coils.
The wavelet method allows us to see the fast time changeProceedings of ITC/ISHW2007(on scale of tens of microseconds) in the plasma
fluctuation spectrum. Numerical modeling helps us toestimate the amplitude of measured fluctuations.
The standard magnetic configuration in our stellarator
is quasi-helical symmetric (QHS) when the symmetric
spectral component dominates along the field line. In theconfiguration with broken symmetry the mirror term isadded to the magnetic field spectrum and we name thisconfiguration Mirror. The gross magnetic properties are thesame in both configurations but they differ in amplitude ofmagnetic field ripples (QHS has less εeff at r/ap = 2/3 by anorder of magnitude). In this paper we present the results.
obtained at 0.5 T with 50 kW of launched power at (1.4 1.6)·10 12 cm-3 of the line averaged plasma density (Fig. 1).

0.1) to get a decent emission. Thus, we configure the ECEchannels between 0.2 and 0.7 of the effective plasma
radius.
The ECE radiometer has been calibrated against theThomson scattering (TS) in plasmas with off-axis heatingwhen the plasma stored energy measured by thediamagnetic loop and integrated from TS profiles is inagreement. For the HF set of IF filters the resonance isshifted outboard at r=+0.3·ap and for the LF set we use
inboard resonance at r=-0.2·ap, in both cases the TS
profiles are identical. Then we took data in on-axisresonance with the two sets of filters. The measured ECE
spectrum is shown in Fig. 2. It is clearly seen that thespectrum is non-symmetric (28 GHz corresponds to theplasma axis) due to the presence of supra-thermalelectrons.
To find the population and the temperature of the highenergy electrons the Bi-Maxwellian plasma model isapplied. We use TS profiles (Te(0) = 0.6 keV, ne(0) =2.6·1012 cm-3) to calculate the optical depth of the bulk
plasma. The results of modeling are shown in Fig. 2. The
higher emission at the HF side compared to the level ofFig.1 Plasma density profile in QHS and 10% Mirror

2. ECE Measurements and Modeling
The HSX radiometer has eight narrow band filters. By
switching the filters we can get the ECE spectrum over theentire plasma. In this paper we report the results obtainedwith two sets of intermediate frequency (IF) filters. One set
allows us to measure the emission from the high magnetic
field (HF) side while the other one from the low magnetic
field (LF). As we use the extraordinary wave at the second
harmonic for heating and ECE measurements the emission
cannot be detected from the heating resonance layer. At theplasma periphery the plasma optical depth is too low (τ <Fig.2 Measured ECE spectrum and the fit basedon Bi-Maxwellian plasma model

Fig.3 Normalized Ne and Te profiles for bulk and tailplasmas
grey plasma is mostly due to the broad population of
supra-thermal electrons, and the tail temperature isresponsible for enhanced signals at the LF side (Fig. 3).
The best fit to the measured spectrum is for Ttail = 4.5 keV,ntail = 0.6·1011 cm-3. The calculations made with theCQL3D Fokker-Planck code support the simple
Bi-Maxwellian model (Figs. 4,5). In Fig. 5 the results at 1
T are also shown. At 50 kW of launched power the plasma
stays thermal at a high density (> 6·1012 cm-3). The central

Fig.4 Black body spectrum from CQL3D codeProceedings of ITC/ISHW2007
electron temperature is 1.2 keV at 50 kW and 2 keV at 100
kW corresponding to the experimental data.

Bi-Maxwellianplasma modelFig.5

Normalized TECE calculated by CQL3D

In the QHS configuration the ECE radiometer is able
to detect the coherent plasma density fluctuations in thenarrow frequency band (38 - 44 kHz). The amplitude of themode is defined as follows.

rms ≡∫ pdf

ADCΔfdouble frequency conversion so that the output signal
frequency band is broad enough to detect plasma density
fluctuations up to 10 MHz. To get reflections from low andhigh density plasmas two overlapping microwave sources
are used. A fast pin switch (switch time ~ 10 nsec) is used
to connect the appropriate source to the output channel. Anextraordinary wave is used in 0.5 T operation. Thepolarization can be easily changed for 1 T plasmas byrotating the horn antenna. The probing beam is focused
inside the vacuum vessel into a small spot (~ 10 cm indiameter). To protect the sources and the mixer diodes
narrow band-stop filters at 28 GHz are used.
In this paper we present the first results on plasma
density fluctuations measured with the new reflectometeron HSX. The frequency spectra are measured in QHS andMirror configurations. In Fig. 7 the spectra at fixed probing
beam frequency (fo = 19 GHz), which corresponds to theplasma density gradient region, are shown. The Mirror
spectrum is much broader than the QHS one. To estimate(1)

Two inboardchannels

Fig.7

Fig.6 Amplitude of plasma density fluctuations
measured by ECE radiometer
The channels (1 – 6) correspond to the LF side andchannels 7 and 8 are on the HF side. For the thermal
plasma channel #1 receives emission at r = 0.2·ap, channel#6 – at r = 0.6·ap, #7 and #8 – at -0.5·ap and -0.6·ap,
respectively (Fig.6). The mode is well pronounced in theplasma core (r < 0.7·ap) in the QHS configuration.
According to Dr. C.Deng, the mode is driven by highenergy electrons. The frequency of the mode is equal to theprecision frequency of trapped particles circulating aroundthe machine.

3. Reflectometer on HSX
Reflectometry is a well known method for measuring
the plasma density [6]. We use a heterodyne detection withFFT of the reflectometer signals in QHS and
10% Mirror

the amplitude of fluctuations we need to apply 2-D
modeling for the wave propagation in the HSX plasma.
In the QHS configuration the reflectometer detects
the coherent mode as well. The frequency of the probing
beam can be swept. We use a step function for a single
sweep in order to localize the mode. The single sweep (Fig.
8) is chosen to be 10 msec so that there are up to 5 fullsweeps in the 50 msec plasma discharge. The X-wave

Fig.8 Probing beam frequency sweep and X-wave
cut-off frequency in HSX plasmaProceedings of ITC/ISHW2007
cut-off frequency is calculated based on TS profile (seeFig.1) and Biot-Savart code (Fig. 8). We use wavelet
analysis to get good temporal resolution. The Mironov coil
is monitoring the presence of the mode in the time windowof this full sweep. Based on time evolution of the wavelet

the probing beam frequency greater than 23 GHz, theharmonics of the main mode (50 kHz) are found (Fig. 10).
At this moment we do not know why the mode has
harmonics. Another feature of the mode is its bursty
character. The fast changes are on the order of theelectron-electron collision time (100 μsec). The FFTtechnique has a better frequency resolution than thewavelet analysis. The Fourier spectrum in a 2 msec time
window shows a very narrow frequency band where themode exists (Fig. 11).

4. Summary

Fig.9 Wavelet coefficients in QHS (one full sweep ofthe reflectometer)
coefficients (Fig. 9) and the calculated cut-off frequency
we easily see that the mode is localized within the plasmacore (r < 0.4·ap).

ECE spectra in HSX plasma have been measured at
0.5 T. The Bi-Maxwellian model and CQL3D
Fokker-Planck code show the presence of 5 keV tail ofelectrons in the distribution function. The ECE radiometer
detects the coherent mode in QHS plasma as do theinterferometer, Mirnov coils and Langmuir probes. Thismode is thought to be driven by high energy trapped
particles circulating around the machine.
First results on plasma density fluctuations havebeen obtained with the new reflectometer. The frequency
spectrum in 10% Mirror configuration is much broader
than in QHS. The reflectometer data show that the coherentmode in QHS plasmas is localized in plasma core and its
amplitude gradually reduces with the mirror percentage (at8% of mirror term the mode vanishes). The wavelet
analysis helps us to see the bursty behavior of the coherentmode and its harmonics. The fast changes are on the orderof electron-electron collision time.

Acknowledgments

Fig.10 Time evolution of the coherent mode (5 msec
time window)

The authors are thankful to Dr. C.Deng for his help in
preparing the experiments on reflectometry and fruitful
discussions of the results. This work could not be done
without the help of the HSX team and the authors thankeveryone.
This work is supported by DOE grant #DE-FG02-93ER54222.

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Fig.11 FFT of reflectometer signal in time intervalof (0.832 – 0.834) sec
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