Effect of non-Maxwellian Velocity Distributions of EC Heated Plasmas on Electron Temperature Measure...
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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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Ge zhuang 1 2

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

    • Includes

      • X2:[email protected], 6 gyrotrons, 0.45MW, 2seach

        ncutoff= 4.251019 m-3

      • X3:[email protected], 3gyrotrons, 0.45MW, 2seach

        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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    Ge zhuang 1 2

    Thomson Scattering System on TCV

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    Ge zhuang 1 2

    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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    Ge zhuang 1 2

    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

    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%

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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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