1. 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

2. May 2006 HUST, China & CRPP, EPFL, Swiss 2 Content  Introduction  TCV tokamak  Electron Cyclotron Wave (ECW) system  Thomson scattering system  T e 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

3. May 2006 HUST, China & CRPP, EPFL, Swiss 3 TCV Tokamak

4. 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 B T ： 1.5T Max I p ： 1.2MA Limiter or divertor configuration

5. May 2006 HUST, China & CRPP, EPFL, Swiss 5 Various Plasma Shapes

6. May 2006 HUST, China & CRPP, EPFL, Swiss 6 Electron Cyclotron Wave System Includes  X2 ： 82.7GHz@1.45T, 6 gyrotrons, 0.45MW, 2s each n cutoff = 4.25  10 19 m -3  X3 ： 118GHz@1.45T, 3 gyrotrons, 0.45MW, 2s each n cutoff = 11.5  10 19 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

7. May 2006 HUST, China & CRPP, EPFL, Swiss 7 Thomson Scattering System on TCV

8. May 2006 HUST, China & CRPP, EPFL, Swiss 8 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:  T e : 50 ev~(20-25) keV  n e : > 3  10 18 m -3

9. 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 Scattering form factor

10. May 2006 HUST, China & CRPP, EPFL, Swiss 10 Scattering form factor With T e increasing Peaking blue-shifted Spectrum broaden FWHM widen

11. May 2006 HUST, China & CRPP, EPFL, Swiss 11 TCV TS setting & processing Collection of scattered light:   B T  || B T  Both Spectral channels ：  Many Narrow-band  A few wide-band Signal processing:  Non-linear spectral fitting (Peaking, FWHM, and so on)  Least-square method(χ 2 fitting)  Conversion function and Signal Ratios

12. May 2006 HUST, China & CRPP, EPFL, Swiss 12 Conversion functions  Conversion Function build-up S(ω s ) @ Maxwellian approximation and TCV TS configuration Simulated signals @ Signal ratios only depend on T e and monotonic increasing  Directly get the T e values using the conversion function  Fast and simple

13. May 2006 HUST, China & CRPP, EPFL, Swiss 13 Evaluation of T e For T e 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 T e,i value and its error  T e,i.  Final result:  Ideally, for a Maxwellian distribution, the T e,i values should be identical  Noise in the signals or systematic errors leads to variations and discrepancies

14. May 2006 HUST, China & CRPP, EPFL, Swiss 14 Uncertainties of T e measurements Ip=200kA, Ohmic heating, stationary phase Variation of T e 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

15. 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)

16. 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° I p = 165kA T e (0): 5 keV, n e (0): 1.2∙10 19 m -3

17. May 2006 HUST, China & CRPP, EPFL, Swiss 17 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

18. May 2006 HUST, China & CRPP, EPFL, Swiss 18 Analysis Method

19. May 2006 HUST, China & CRPP, EPFL, Swiss 19 Ohmic heating and EC heating Ip = 200 kA Ohmic heating T e 1270 eV, n e 1.7 × 10 19 m −3 EC heating （ 0.9MW, X2, off-axis ） T e 2423 eV, n e 1.8 × 10 19 m −3

20. May 2006 HUST, China & CRPP, EPFL, Swiss 20 EC heating + ECCD I p = 200 kA 0.45MW ECCD + 0.45MW ECH Thomson@(r/a)~0.12: T e 2.46keV; n e 2.6×10 19 m −3 ECE ： T b 2.3 keV;T s 21 keV;η10% Bi-Maxwellian model ： S(ω S ), signals based on f c and f b deviates from that based on f M f c and f b give a better description of the measurement than f M systematic error is up to ~20%

21. May 2006 HUST, China & CRPP, EPFL, Swiss 21 Pure ECCD Non-inductive current drive, I p = 165kA co-ECCD: Off-axis(0.9MW) + Central (0.45MW)  =24° Thomson@r/a =0.15: T e 3.18 keV;n e 1 ×10 19 m -3 S(ω S ), signals based on f c and f b clearly deviates from that based on f M. Systematic error reaches ~30% > 5%

22. 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 T e 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