Measurement of Electron Density
Profile and Fluctuations on HSX
C. Deng, D.L. Brower, W.X. Ding
Electrical Engineering Department
University of California, Los Angeles
A.F. Almagri, D.T. Anderson, F.S.B. Anderson,
S.P. Gerhardt, P. Probert, J. Radder, J.N. Talmadge
The HSX Plasma Laboratory, University of Wisconsin-Madison
Measurements of Electron Density Profile and Fluctuations
on HSX
The 288 GHz interferometer system on the quasi-helical
stellarator HSX views the plasma cross section along 9 adjacent chords
with 1.5 cm spacing. At this frequency refraction is manageable but
requires correction when doing inversions. The interferometer has
11
-2
sensitivity nedl = 8 10 cm and frequency response of up to 1 MHz.
Improved time response permits measurement of high-frequency
density fluctuations as well as fast changes to the equilibrium profile.
nd
First results from HSX with 2 harmonic ECH at 28 GHz, using a 5
chord version of the interferometer, indicate that the density profile is
quite peaked for both quasi-helically symmetric (QHS) plasmas and
those where the quasisymmetry is broken (mirror mode) for ne ~ 1
12
-3
11
-3
10 cm . However, for densities ne = 3 10 cm , the profile for the
QHS plasma (high stored energy) is narrower when compared to the
mirror mode (low stored energy). Density profile variation with plasma
configuration and resonant heating location using the 9 channel
interferometer will be described. For high density HSX plasmas, ne =
12
-3
3 10 cm , coherent oscillations are observed in the line-integrated
density traces which are out of phase across the magnetic axis. These
m=1 oscillations are observed at frequencies of 1-2 kHz and result in a
periodic displacement of the density profile.
*Supported by USDOE under grant DE-FG03-01ER-54615,
Task III and DE-FG02-93ER54222.
Interferometer Capabilities
• Spatial resolution: 9 chords, 1.5cm spacing and width.
• Fast time response: analog: 100-200 msec, real time
digital: <10 msec
maximum bandwidth 250 kHz [with 2 MHz sampling]
• Low phase noise: 24 mrad (1.6o)
(Dnedl)min = 8 x 1011 cm-2
0.4% level density fluctuations can be measured
• Density fluctuations: wavenumber resolution
(i) k^< 2.1 cm-1, (ii) k|| < 0.07 cm-1
Solid State Source
• Solid State Source:
– bias-tuned Gunn diode at 96 GHz with passive solid-state Tripler
providing output at 288 GHz (8 mW)
• Support of Optical System:
– 2.5 meter tall, 1 ton reaction mass, mounted on structure independent of
HSX device. Reduces structure vibration and minimizes phase noise.
• Dichroic Filters:
– mounted on port windows to shield interferometer from 28 GHz gyrotron
radiation plus,
– cutoff frequency: 220 GHz
– approximately 10% loss
– attenuation ranging from 92db at 28 GHz to 68 db at 150 GHz.
Interferometer Schematic
Gunn
96 GHz
Tripler 288 GHz
Reference
Sawtooth Modulator
Filter
Detection System
9 channels
Phase Comparator
Filter Amp. Mixer Lens
∆Ø=∫nedl
Plasma
Probe
Beam Expansion Optics and Receiver Array
Probe
Parabolic Beam
Optics
Reference
Plasma
Polyethylene Lens Array
Receiver
(see inlet)
Corner Cube
Mixer Array
Probe
Beam
Local Oscillator
Beam
Local Oscillator Beam
HSX Interferometer Layout
HSX Interferometer System
FFT Spectra Analysis
Reference
0.5
Power
0.4
Variable Bandpass Filter
0.3
0.2
0.1
0.0
0
100
400
500
IF = 232 kHz
0.30
Power
200
300
Frequency (kHz)
Probe Signal
0.20
2nd harmonic (464 kHz)
4th harmonic (72 kHz)
3rd harmonic (304 kHz)
0.10
0.00
0
100
200
300
Frequency (kHz)
400
500
• 768 kHz IF sampled at 1
MHz, aliased to 232 kHz
• Sawtooth frequency
modulation of source
produces harmonics
• Unable to remove harmonic
components completely
with existing electronic
filters (70 kHz < passband <
2 MHz at 3 db points).
DPC Phase Noise
Phase (rad.)
0.4
Bandwidth=1 00kHz, rms noise=0 .2 24 rad
0.2
0.0
-0.2
-0.4
0.0
0.2
0.4
0.6
Time (ms)
0.8
1.0
0.4
Phase (rad.)
Bandwidth=7 0KHz, rms noise=0.02 4 rad
0.2
0.0
-0.2
-0.4
RMS Phase Noise (Deg.)
0.0
0.2
0.4
0.6
Time (ms)
0.8
1.0
12
8
4
50
100
150
Bandwidth (KHz)
200
• Including harmonic content
in bandwidth of DPC
causes phase oscillation
• Excluding harmonics from
DPC bandwidth reduces
rms phase noise to 24 mrad
(same as analog PC with
<10 kHz bw)
• 100 kHz max. bandwidth
with 1 MHz sampling
• 250 kHz max. bandwidth
with 2 MHz sampling
Chord Lengths
Magnetic Flux Surfaces and Chord Positions
30
Last Closed
Flux Surface
Vacuum Vessel
20
Z (cm)
10
0
-10
-20
-30
-20
-10
0
10
R-Ro (cm)
20
Density Profile Inversion
• Method: H. K. Park technique; asymmetric Abel inversion
- flexible boundary conditions
- non-circular geometry
- plasma scrape-off-layer SOL estimate
• Model: spline fit to 9 channel line-density profile
- no Shafranov Shift
• Path lengths: calculated for ten vacuum flux surfaces,
• SOL plasma contribution: One viewing chord is outside
the separatrix. This will provide information on the SOL
contributions to other chords.
• Refraction correction: necessary for chord length and
position
HSX Density Profile
13
4
x 10
11
12
no refraction
correction
t=820ms
t=850ms
10
3
n (cm -3)
-2
NL (cm )
x 10
6
e
2
8
1
0
-10
after refraction
correction
-5
0
X (cm)
4
2
5
10
0
0
2
4
6
R-R (cm)
o
8
10
Density Profile Time Evolution
Line-Integrated Data for QHS Plasma
8
Shot 35: 10-16-2001
ECRH off
8.5 cm
7
5.5
4
2.5
1
-0.5
-2
-3.5
nedl (1013 cm-2)
6
4
2
0
800
810
820
830
time (ms)
840
850
860
Line-Integrated Data for Mirror Mode
8
Shot 48: 10-16-2001
-2
nedl (1013 cm )
ECRH off
8.5
7
5.5
4
2.5
1
-0.5
-2
-3.5
6
4
2
0
800
810
820
830
time (ms)
840
850
860
QHS and Mirror Mode
Comparison
13
13
x 10
x 10
Spline fit
measured data
added data
calculated line
density
3
2
3
2
1
1
0
-10
0
-10
-5
0
X (cm)
QHS
5
10
Spline fit
measured data
added data
calculated line
density
4
NL (cm -2)
-2
NL (cm )
4
-5
0
X (cm)
5
Mirror Mode
10
Inverted Density Profiles
11
15
x 10
10
QHS mode,
outboard heating
e
n (cm -3)
Mirror mode,
outboard heating
5
0
0
2
4
6
R-R (cm)
o
8
10
-2
nedl (1013 cm )
QHS and Mirror Mode Density Profiles
4
4
3
3
2
2
QHS_s35
MM_s48
1
1
0
0
-4
-2
0
2
4
R-Ro (cm)
6
8
10
mirror mode plasmas have inboard higher density
Profile Changes with ECRH Location
4
4
3
-2
nedl (1013 cm )
nedl (1013 cm-2)
Mirror Mode
2
QHS plasmas
central
inboard
outboard
1
3
central_s40
inboard_s43
outboard_s48
2
1
0
-4
-2
0
2
4
R-Ro (cm)
6
8
10
-4
-2
0
2
4
R-Ro (cm)
profile shape does not vary with heating location
6
8
10
Profile Changes with Density
8
1.4
1.0
0.8
4
QHS plasmas
0.6
2.0 x1012
0.3 x1012
2
-2
1.0
6
0.8
4
0.6
Mirror Mode
2
0
2
4
R - R0 (cm)
6
8
10
0.4
2.0 x1012_s54
0.3 x1012_s64
0.4
0.2
-4
-2
1.2
6
1.2
nedl (1013 cm )
nedl (1013 cm-2)
8
0.2
0.0
0
-4
-2
0
2
4
6
R-Ro (cm)
profile shape varies little with density
8
10
m=1 Density Fluctuations
13
-2
nedl (10 cm )
10
8
m=1 ac tivity
6
8.5
7.0
5.5
4.0
2.5
1.0
- 0.5
- 2.0
- 3.5
4
2
0
800
805
810
815
820
time (ms)
825
830
cm
cm
cm
cm
cm
cm
cm
cm
cm
835
13
-2
nedl (10 cm )
10
8
m=1 ac tivity
6
8.5
7.0
5.5
4.0
2.5
1.0
- 0.5
- 2.0
- 3.5
4
2
0
812
813
814
815
time (ms)
816
cm
cm
cm
cm
cm
cm
cm
cm
cm
817
m=1 Density Fluctuations
Frequency Spectra
frequency (kHz)
Chord at x = 1 cm
12
9
6
3
813
814
815
time (ms)
0
2
4
6
8
HSX105__WL_805_82_x
816
10
Inverted Density Profiles
11
15
x 10
10
QHS mode,
outboard heating
e
n (cm -3)
Mirror mode,
outboard heating
5
0
0
2
4
6
R-R (cm)
o
8
10
Coherence and Phase
1.0
Coherence
0.8
Cohe rence
Nois e
0.6
C hords at x = 2.5 and -3.5 cm
0.4
0.2
0
2
4
6
Frequency (kHz)
8
10
150
Phase (deg.)
100
50
0
-50
-100
-150
0
2
4
6
Frequency (kHz)
8
10
Summary
• Multichannel 288 GHz interferometer system has been installed and is now
operating on the HSX stellarator
• Refraction correction to line-integrated data is required
• Initial inversions show a peaked density profile, inversion development still
in progress
• Differences between QHS and Mirror Mode plasmas are being evaluated
• Little profile variation found with changing density or ECRH location
• For high density plasmas, large-amplitude m=1 oscillations (3 kHz) are
often observed
HSX Stellarator
• Helically Symmetric EXperiment, HSX
quasi-helically symmetric [QHS] stellarator
major radius: R=1.2 m,
average minor radius: <a> = 15 cm,
BT= 0.5 - 1 T , Te = 1 keV, and ne < 1 x1013 cm-3
Heating and breakdown: 28 GHz ECRH, 200 kW
• Unique toroidal magnetic configuration: no toroidal curvature and
a helical axis of symmetry.
Physics goals:
• Greatly reduced neoclassical transport with respect to other
stellarators and comparable tokamaks.
• Reduced anomalous transport by low parallel viscous damping in the
direction of symmetry.
Data Acquisition System
• Analog phase comparator: PCI-MIO-16E-1, 12 bits resolution,
maximum sampling rate 75 kHz for 9 channels
• Digital phase comparator: PCI-6110 E, 12 bits resolution, max
sampling rate 5 MHz for 10 channels
• Control and manage: PC and LabVIEW.
Comparison of Analog and Digital
Phase Comparator Output
809.0
809.5
810.0
810.5
811.0
811.5
812.0
12
160x10
16
ECRH off
-2
line-integrated density [cm ]
140
14
Analog
120
12
Digital
100
10
80
8
60
6
40
4
20
2
0
0
809.0
809.5
810.0
810.5
811.0
time [ms]
811.5
812.0