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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 of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, P.R. China

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slide1

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

content
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

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tcv tokamak
TCVTokamak

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tcv tokamak1
TCVTokamak
  • 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

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various plasma shapes
Various Plasma Shapes

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electron cyclotron wave system
Electron Cyclotron Wave System

ncutoff= 4.251019 m-3

ncutoff= 11.51019 m-3

  • X2: Heating and Current drive
    • Tuneable toroidal and poloidal injection angle
    • Non-inductive current: 100-200kA
  • X3: Now heating only
    • Mirror radially moveable

X3

X2

X2

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slide7

Thomson Scattering System on TCV

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slide8

Thomson Scattering System

  • Hardware:
      • Laser:Q-Switch Nd:YAG, =1.064m,20Hz, 10-15ns, 1.8J
      • Spatial revolution: 25 observation volumes along the laser beam
      • Spectral channels: 4(3) interference filters in a polychromator
      • Detector:Si-avalanche photodiode
  • Range of measurement:
      • Te: 50 ev~(20-25) keV
      • ne: >31018 m-3

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scattering form factor
Scattering form factor
  • Principle:
  • Scattered Power Spectrum @ Scattering form factor
  • Distribution function f (v||, v) can take any forms
  • Thermal Equilibrium→Relativistic Maxwellian Distribution

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slide10

Scattering form factor

  • With Te increasing
  • Peaking blue-shifted
  • Spectrum broaden
  • FWHM widen

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tcv ts setting processing
TCV TS setting & processing
  • Collection of scattered light:
    • BT
    • || BT
    • Both
  • Spectral channels:
    • Many Narrow-band
    • A few wide-band
  • Signal processing:
    • Non-linear spectral fitting (Peaking, FWHM, and so on)
    • Least-square method(χ2 fitting)
    • Conversion function and Signal Ratios

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conversion functions
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

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evaluation of t e
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

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uncertainties of t e measurements
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

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non maxwellian velocity distribution during ech eccd
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)

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non inductive current drive
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 modelling
Fokker-Planck Code modelling
  • CQL3D 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)
  • Strong distortion of the distribution function with respect to

a Maxwellian

*R.W. Harvey and M.G. McCoy, TCM/ASMTP, Montreal, 1992

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analysis method
Analysis Method

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ohmic heating and ec heating
Ohmic heating and EC heating
  • Ip = 200 kA
  • Ohmic heating
  • Te 1270 eV, ne 1.7 × 1019 m−3
  • EC heating( 0.9MW, X2, off-axis)
  • Te 2423 eV, ne 1.8 × 1019 m−3

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ec heating eccd
EC heating + ECCD

Ip = 200 kA

0.45MW ECCD+ 0.45MW ECH

[email protected](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%

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pure eccd
Pure ECCD

Non-inductive current drive, Ip = 165kA

co-ECCD: Off-axis(0.9MW) + Central (0.45MW)

 =24°

[email protected]/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%

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conclusion
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

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