ge zhuang 1,2

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


TCV Tokamak


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


Various Plasma Shapes


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


Thomson Scattering System on TCV


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


• 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


Scattering form factor

iis

With Te increasing

Peaking blue-shifted

Spectrum broaden

FWHM widen


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


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 ,,


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 ,,,


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 ,


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)


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


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


Analysis Method


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


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%


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%


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

ge zhuang 1,2

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