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
Ohmic heating, EC Heating ECH + ECCD Pure ECCD
Conclusion
May 2006 HUST, China & CRPP, EPFL, Swiss 4
TCV Tokamak
Tokamak à Configuration Variable (TCV)
• Major radius : 0.88m
• Minor radius: 0.25m
• Cross-section: Height 1.54m, width
0.56m
• Elongation κ : 2.8
• Triangularity : -0.77~ 0.86
• Max BT : 1.5T
• Max Ip : 1.2MA
• Limiter or divertor configuration
May 2006 HUST, China & CRPP, EPFL, Swiss 6
Electron Cyclotron Wave System
• IncludesX2 : [email protected], 6
gyrotrons, 0.45MW, 2s eachncutoff = 4.251019 m-3
X3 : [email protected], 3 gyrotrons, 0.45MW, 2s eachncutoff = 11.51019 m-3
• X2: Heating and Current driveTuneable toroidal and poloidal
injection angleNon-inductive current: 100-
200kA
• X3: Now heating onlyMirror radially moveable
X3
X2
X2
May 2006 HUST, China & CRPP, EPFL, Swiss 8
Thomson Scattering System
Hardware :Laser : Q-Switch Nd:YAG, =1.06
4m, 20Hz, 10-15ns, 1.8J Spatial revolution: 25 observation
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
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Scattering form factor
iis
With Te increasing
Peaking blue-shifted
Spectrum broaden
FWHM widen
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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 ,,,
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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
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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
May 2006 HUST, China & CRPP, EPFL, Swiss 19
Ohmic heating and EC heating
Ip = 200 kA
Ohmic heatingTe 1270 eV, ne 1.7 × 1019 m−3
EC heating ( 0.9MW , X2, off-axis )Te 2423 eV, ne 1.8 × 1019 m−3
May 2006 HUST, China & CRPP, EPFL, Swiss 20
EC heating + ECCDIp = 200 kA
0.45MW ECCD + 0.45MW ECH Thomson@(r/a)~0.12: Te 2.46keV; ne 2.6×1019m−3
ECE : Tb 2.3 keV;Ts 21 keV;η10%
Bi-Maxwellian model :
• S(ωS), signals based on fc and fb deviates from that based on fM
• fc and fb give a better description of the measurement than fM
• systematic error is up to ~20%
May 2006 HUST, China & CRPP, EPFL, Swiss 21
Pure ECCD
Non-inductive current drive, Ip = 165kA
co-ECCD: Off-axis(0.9MW) + Central (0.45MW) =24°Thomson@r/a =0.15: Te 3.18 keV;ne 1 ×1019 m-3
• S(ωS), signals based on fc and fb clearly deviates from that based on fM.
• Systematic error reaches ~30% > 5%
May 2006 HUST, China & CRPP, EPFL, Swiss 22
Conclusion
• Interpretation of TCV TS data based on Maxwellian distribution function• Signal Processing relies on the signal ratios and tabulated conversion
function• Non-Maxwellian velocity distribution can appear in the presence of ECH and
ECCD, and may affect the Te measurements by Thomson scattering • Experimental results, compared with the simulated data obtained either from
the results of CQL3D modelling, or in the form of bi-Maxwellian distribution function, showed the deviations from an ideal Maxwellian were significant
• Simulations of Thomson scattering data based on CQL3D modelling distribution showed much better agreement with experimental observations
• Bi-Maxwellian could be used for a interpretation of Thomson scattering measurement if the ideal Maxwellian distribution is inappropriate
• Systematic errors in Te measurement by TS can be identified, in a special case, the discrepancies in Te measurements found to be 25-30%
• The energy content is underestimated by Thomson scattering measurement