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Electron Density Distribution in HSX
C. Deng, D.L. BrowerElectrical Engineering Department
University of California, Los Angeles
J. Canik, S.P. Gerhardt, D.T. Anderson,
P. Probert, F.S.B. Anderson
•The HSX Plasma Laboratory
•University of Wisconsin-Madison
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Abstract A multichannel interferometer system is now routinely
operating on the new quasi-helically symmetric stellarator, HSX, to measure the equilibrium profile and electron density dynamics. The interferometer system has 9 viewing chords with 1.5 cm spacing. The density spatial distribution is reconstructed from the measured line-integrated density. At high density [ ], an m=1 density oscillation with frequency of (1-2) kHz is observed. Perturbative particle transport studies will be carried out using modulated gas puffing. The particle source will be measured by a multi-channel H system. By using the continuity equation, the total
radial particle flux r can then be estimated. The diffusion
coefficient D and convection velocity V will also be modeled.
*Supported by USDOE under grant DE-FG03-01ER-54615, Task II and DE-FG02-93ER54222.
312102_
cmne
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Interferometer CapabilitiesInterferometer Capabilities
• Spatial resolution: 9 chords, 1.5cm spacing and width.
• Fast time response: analog: 100-200 sec, real time digital: <10 sec
maximum bandwidth 250 kHz [with 2 MHz sampling]
• Low phase noise: 24 mrad (1.6o) (nedl)min = 9 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
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Solid State SourceSolid 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 Transmission 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– Cut-off frequency: ~220 GHz– ~ 10% loss– attenuation ranging from 92db at 28 GHz to 68 db at 150 GHz.
• Edge Filters: – mounted inside port windows to reduce diffraction of the window
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Interferometer SchematicInterferometer Schematic
Plasma
Phase Comparator
Sawtooth Modulator
Filter
Gunn 96 GHz Tripler 288 GHz
Filter Amp. Mixer Lens
Detection System
9 channels Probe
Reference
∆Ø=∫nedl
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HSX Interferometer LayoutHSX Interferometer Layout
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HSX Interferometer SystemHSX Interferometer System
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Probe
Reference
Plasma
Parabolic Beam
Optics
Receiver
Polyethylene Lens Array
Corner CubeMixer Array
Local OscillatorBeam
Local Oscillator Beam
Probe Beam
(see inlet)
Beam Expansion Optics and Receiver Array
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Flux Surfaces and Interferometer Chords
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Density Profile InversionDensity Profile Inversion
• Method: Abel inversion; Singular Value Decomposition - 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 twenty vacuum flux surfaces,
• SOL plasma contribution: One viewing chord is outside the
separatrix. This provides information on the SOL
contribution.
• Refraction correction: necessary for chord length and position
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HSX Density Profile (QHS)
Measured Line-Integrated Density Profile and fitting Inverted Density Profile
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HSX Density Profile (Mirror)
Measured Line-Integrated Density Profile and fitting Inverted Density Profile
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HSX Density Profile (Anti-Mirror)
Measured Line-Integrated Density Profile and fitting Inverted Density Profile
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Perturbative Particle Transport Study
Density perturbation obtained by gas puffing modulation provide a good tool for particle transport study. Previous successful experiments on TEXT, ASDEX, W7-AS
Diffusive and convective effects can be obtained by analyzing profile time evolution:
Sinusoidal wave is ideal for this analysis, which give higher accuracy of the analysis. And a few cycles will be needed to obtain certain accuracy. The amplitude will be around less than 10% to reduce the effects of plasma parameters dependency.
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),(),(),(),(
),(1
trStrntrVr
trntrDr
rrtn
The electron density can be constant on magnetic flux surfaces. We use cylindrical geometry transport Equation:
Parameters n and S can be separated into two part: (1) stationary part n0 and S0, and (2) perturbed part and .
where is the frequency of the density perturbation generated by modulating the gas feed. Also assume D and V areindependent of time. Linearizing equation (1) leads to:
~n ~S
tiennn ~0 tieSSS ~
0
Continuity Equation
(2)
(1)
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~~
~~~
),())()(
(
),()
)()((
),()(),(
2
2
SrnrrV
rrV
rrn
VrrD
rrD
rrn
rDrni
The boundary conditions are:
at r=0 ;
at r=a. 0;10~~ 39
imre ncmn
Linearized Equations
(5)
(6)
(7)
0~~ rnrn imre
imre ninn~~~
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modulated gas feed
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Fourier coefficientsThe Fourier coefficients of the line-integrated
density were obtained by fitting the following function
to the measured data:
)()2sin()2cos()sin()cos(
22102,
2,~
1,1,~
~~~
tataatNtNtNtNI
im
reimre
Here and are the real and imaginary parts of the
Fourier coefficients at the ith Harmonic of the modulation
frequency. The a0,a1 and a2 correspond to constant, linear and
quadratic time dependence and take into account a possible
slow time evolution.
ireN ,~
iimN ,~
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Density Perturbation Amplitude and Phase
• Amplitude and phase of the first harmonic of the modulation frequency for the line-integrated densities
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Estimated Source
• At this moment, electron source profile unknown.
• Assume source profile has exponential fall-off.
• Amplitude and position of the Source were chosen (roughly) according to the H measurement.
1 2 3 4 5 6 7 8 90.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Line
Inte
grat
ed E
mm
issi
on (
10-5
W/s
r*cm
3 )
1 2 3 4 5 6 7 8 90.5
1
1.5
2
2.5
3
3.5
4
n edl (
1013
cm
-3)
Chord number (1 is outboard)
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Results for D=const. and V=0
A rough estimate of D from measured particle confinement time,
gives ~ 3ms, Dest=a2/(6 p )~ 1.0m2/s
S
nep
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Results for stepped D, with V=0
The modeling is not sensitive to the detailed structure of D
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Sensitivity of Modeling to D
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Sensitivity of Modeling to V
ar
Vrr
VV
v
2
1
)/)(exp(1
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Sensitivity of Modeling to Source Profileif x<xc
S=no*exp(-abs(x-xc)/xl1);if x>xc S=no*exp(-abs(x-xc)/xl2);xl2=5cmPeak position: xc=3.4cm
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Density Perturbation at different frequencies
The Particle transportis unchanged with the frequency of gas feed modulations
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Density Perturbation with different Densities
The Particle transportchanges a little with density, which would give smaller D at higher density.
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Modeling of the recent experiment
D=2.0m2/secV=0m/sec
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Better fit with outward convection
D=2.0m2/secV=300m/secSource same as last slide
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Summary
• Equilibrium Density Distributions for QHS, Mirror, Anti-mirror modes were obtained.
• The preliminary measurement and analysis shows the
possibility of perturbative particle transport study on HSX,the modeling shows the D around 1-2m2/s.
• Improved Electron source measurement (or modeling) required to determine D and V which provide best fit to interferometer data.