A Degeling, Y Martin, J Lister, X Llobet and P Bak Effect of non-Maxwellian Velocity Distributions of EC Heated Plasmas on Electron Temperature Measurements by Thomson Scattering Ge Zhuang 1,2 1. College of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, P.R. China 2. Centre de Recherches en Physique des Plasmas, Ecole Polytechnique Fédérale de Lausanne Lausanne, Switzerland
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Effect of non-Maxwellian Velocity Distributions of EC Heated Plasmas on Electron Temperature Measurements by Thomson Scattering Ge Zhuang 1,2 1. College.
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A Degeling, Y Martin, J Lister, X Llobet and P Bak
Effect of non-Maxwellian Velocity Distributions of EC Heated Plasmas on Electron Temperature
Measurements by Thomson Scattering
Ge Zhuang1,2
1. College of Electrical and Electronic Engineering, Huazhong
University of Science and Technology, Wuhan, P.R. China
2. Centre de Recherches en Physique des Plasmas,
Ecole Polytechnique Fédérale de Lausanne
Lausanne, Switzerland
May 2006 HUST, China & CRPP, EPFL, Swiss 2
Content
Introduction TCV tokamak Electron Cyclotron Wave (ECW) system Thomson scattering system
Te Measurement by Thomson scattering Non-Maxwellian distributions during ECH/ECCD
Experimental measurements Code modelling
Influence of Non-Maxwellian distributions on Te measurement
volumes along the laser beamSpectral channels: 4(3) interference
filters in a polychromatorDetector : Si-avalanche photodiode
Range of measurement:Te: 50 ev~(20-25) keV
ne: > 31018 m-3
May 2006 HUST, China & CRPP, EPFL, Swiss 9
• Principle:
• Scattered Power Spectrum @ Scattering form factor
• Distribution function f (v||, v) can take any forms
• Thermal Equilibrium→Relativistic Maxwellian Distribution
d
ckkcf
NSrdd
PdS
siiisk
Esi
s
eie
s
SCs
33
2
22
5
2
22
1
1111
1
cos
cos),(
22
121
2
212252
KfM
expeTcm 22
0
Scattering form factor
12sin2
D
i
si
si
kkk
May 2006 HUST, China & CRPP, EPFL, Swiss 10
Scattering form factor
iis
With Te increasing
Peaking blue-shifted
Spectrum broaden
FWHM widen
May 2006 HUST, China & CRPP, EPFL, Swiss 11
TCV TS setting & processing
• Collection of scattered light: BBTT
|| BT
Both
• Spectral channels :Many Narrow-band A few wide-bandA few wide-band
• Signal processing:Non-linear spectral fitting
(Peaking, FWHM, and so on) Least-square method(χ2 fitting) Conversion function and Signal Conversion function and Signal
RatiosRatios
May 2006 HUST, China & CRPP, EPFL, Swiss 12
Conversion functions Conversion Function build-up
• S(ωs) @ Maxwellian
approximation and TCV TS configuration
• Simulated signals @
• Signal ratios only depend on Te and monotonic
increasing Directly get the Te values
using the conversion function Fast and simple
sessd dTSP ,,
May 2006 HUST, China & CRPP, EPFL, Swiss 13
Evaluation of Te
For Te measurement at each observation volume: Six combinations of signal ratios, S2/S1, S3/S2, S3/S1, S4/S1, S4/S2, S4/S3 Noise sources (Attribution to an uncertainty interval of the signal ratio) :
the statistical fluctuations in the number of photoelectrons
detector and amplifier noise
fluctuations in the plasma radiation
Each signal ratio together with its uncertainty interval determine a Te,i value
and its error Te,i.
Final result:
Ideally, for a Maxwellian distribution, the Te,i values should be identical
Noise in the signals or systematic errors leads to variations and discrepancies
n
iie
n
iieieM TTTT
1
2
1
2 1 ,,,
May 2006 HUST, China & CRPP, EPFL, Swiss 14
Uncertainties of Te measurements
Ip=200kA, Ohmic heating, stationary phase Variation of Te values obtained from different signal ratios can be attributed to
statistical fluctuations The typical statistical error ~ 5% serve as a reference for comparison with the
systematic errors discussed later
MMie TTT ,
May 2006 HUST, China & CRPP, EPFL, Swiss 15
Non-Maxwellian velocity distribution during ECH/ECCD
• On TCV tokamak, absorption of EC wave power of high temperature plasmas → Electron population reaches a velocity distribution no longer be described by a Maxwellian
• ECE measurements [Blanchard et al]
• Hard x-ray detection [Coda, et al]
• CQL3D Modelling [Nikkola, et al]
• Apart from the high energy tail, the low energy part of the veloctity distribution may become affected and deviate from the original Maxwellian shape
• ? How about Te Measurement by Thomson scattering
P. Blanchard, et al, Plasma Phys. Contr. Fusion, 44, 2231(2002)S. Coda, et al, Nucl. Fusion 43, 1361(2003)P. Nikkola, et al, Nucl. Fusion 43, 1343 (2003)
May 2006 HUST, China & CRPP, EPFL, Swiss 16
Non-inductive current drive
Pure ECCD, Non-inductive current drive:
• CO-ECCD: Off-axis(0.9MW X2) +
Central (0.45MW X2); =24°
• Ip = 165kA
• Te(0): 5 keV, ne(0): 1.2∙1019 m-3
May 2006 HUST, China & CRPP, EPFL, Swiss 17
Fokker-Planck Code modellingCQL3D Code:
• Bounce average Fokker-Planck*: 2D ; 1D
• Ray-Tracing: TORAY-GA Code
• Agreement between modelling reults & experimental results (ECE and Hard X-ray detection, etc)
||,vv
RTQLEC t
f
t
f
t
f
t
f
t
vvf
,, ||
• Strong distortion of the distribution function with respect to a Maxwellian *R.W. Harvey and M.G. McCoy, TCM/ASMTP, Montreal, 1992