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The effect of ECRH on the electron velocity distribution function

The effect of ECRH on the electron velocity distribution function. with I. Klimanov, S. Alberti, G. Arnoux, P. Blanchard, A. Fasoli and the TCV team. Centre de Recherches en Physique des Plasmas. EPFL, Association Euratom-F é d é ration Suisse, Lausanne, Switzerland. S. Coda. v . v ||.

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The effect of ECRH on the electron velocity distribution function

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  1. The effect of ECRHon the electron velocitydistribution function with I. Klimanov, S. Alberti, G. Arnoux,P. Blanchard, A. Fasoli and the TCV team Centre de Recherches en Physique des Plasmas EPFL, Association Euratom-Fédération Suisse, Lausanne,Switzerland S. Coda S. Coda, MHD workshop, PPPL, 22 Nov. 2004

  2. v v|| vth Strong ECRH  non-Maxwellian e.d.f. CQL3D Fokker-Planck modelling S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  3. ECRH resonance Strong ECRH  non-Maxwellian e.d.f. v v|| vth S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  4. further afield… S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  5. Non-Maxwellian e.d.f.  strong ECRH  AuroralKilometricRadiation (Maser instability) + MHzemissionfrommagnetizedplanets Ergun et al, Ap.J. 538 (2000) 456 S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  6. Why use ECRH? • highest resonant frequency in plasma shortest wavelength in vacuum good localization and directionality • no edge evanescence  easy to launch S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  7. e.g. the X2 system in TCV Why use ECRH? S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  8. Significant gyrotron development The 9 gyrotrons of TCV S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  9. Tools Diagnostics • hard X-rays • electron cyclotron emission • high-field side • vertical • toroidally oblique • Thomson scattering • Langmuir probes • spectroscopy S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  10. Tools Simulation codes • Fokker-Planck quasilinear • Monte Carlo nonlinear S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  11. From heating to profile tailoring • e.g. • sawtooth control • neoclassical tearing mode stabilization S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  12. Driven system  population inversion? df/dv>0  unstable  Maser amplifier (AKR) From profile tailoringto distribution function engineering S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  13. Distribution function engineering ECRH in fusion experiments: partial population inversion • to drive current (Fisch-Boozer + Ohkawa ECCD) • to enhance absorption (synergistic effects) S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  14. Off-axis power deposition hollow current profile: non-inductive, steady-stateinternal transport barrier  co-ECCD r + e.d.f. tailoring (Fisch-Boozer) Putting it all together… S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  15. …population inversion to enhance absorption (synergy) X3 X3 suprathermalsabsorb X3 suprathermals only partiallyabsorbed X2 ECCD X2-X3 synergy S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  16. X2 (100%) X2 X3 100%measured X3 (16%) TORAY ray tracing X2-X3 synergy S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  17. bi-Maxwellian two-slope (better) X2-X3 synergy Model e.d.f. to match: absorption high-field-side ECE hard X-ray profile hard X-ray spectrum S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  18. only free parameter X2-X3 synergy Thomson slope(2 keV) hard X-ray slope(10 keV) S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  19. Temperature (keV) Modelledsuprathermal density ECE Trad (simulatedvs. measured) Measured hard X-ray emission Thomson X2-X3 synergy 100% absorption reproduced S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  20. high power density  higher energy electrons:quasilinear effects when pabs/n2 > 0.5 (MW/m3, 1019 m-3) Harvey et al, PRL 62 (1989) 426 Plasma self-regulation S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  21. Plasma self-regulation • high power density  higher energy electrons:quasilinear effects when pabs/n2 > 0.5 (MW/m3, 1019 m-3) •  enhanced ECCD efficiencyif electrons remain in the interaction zone S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  22. Plasma self-regulation • high power density  higher energy electrons:quasilinear effects when pabs/n2 > 0.5 (MW/m3, 1019 m-3) •  enhanced ECCD efficiencyif electrons remain in the interaction zone • lifetime  v3 even with equal diffusion,faster electrons travel fartherDr  D1/2 v3/2 S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  23. Plasma self-regulation • high power density  higher energy electrons:quasilinear effects when pabs/n2 > 0.5 (MW/m3, 1019 m-3) •  enhanced ECCD efficiencyif electrons remain in the interaction zone • lifetime  v3 even with equal diffusion,faster electrons travel fartherDr  D1/2 v3/2 • D could also increase (power degradation) S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  24. 40-50 keV HXR emissivity (a.u.) EC power (MW/m3) (TORAY) TCV, 2.5 MW ECCD Suprathermal electron broadeningin quasilinear regime S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  25. Below QL power threshold ( ITER)transport has little effect on driven current At QL power levels, transport sets a limitto QL current-drive enhancement CQL3D Fokker-Planck modelling for TCV r r r r CQL3D Fokker-Planck modelling for DIII-D [Harvey et al, PRL 88 (2002) 205001] Attenuation of quasilinear effects S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  26. ECE ECCD TCV ECCD to probe e.d.f. dynamics average power 20 kW no QL saturation S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  27. ECE ECCD Reconstruct dynamics by coherent averaging of ECE signal (typ. 200 pulses) Average power 20 kW ECCD to probe e.d.f. dynamics S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  28. ECE ECCD Visualization of e.d.f. dynamics S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  29. bi-Maxwellian approximation • suprathermal temperature from relativistic shift S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  30. bi-Maxwellian approximation • suprathermal temperature from relativistic shift • optically thin suprathermal population • derive suprathermal density S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  31. bi-Maxwellian approximation • suprathermal temperature from relativistic shift • optically thin suprathermal population • derive suprathermal density • model with spatial diffusivity D + slowing-down time t S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  32. bi-Maxwellian approximation • suprathermal temperature from relativistic shift • optically thin suprathermal population • derive suprathermal density • spatial diffusivity D + slowing-down time t • time-to-peak  r2(small r) r2/(4D)  r(large r) ½ (tr2/D)1/2 S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  33. bi-Maxwellian approximation • suprathermal temperature from relativistic shift • optically thin suprathermal population • derive suprathermal density • spatial diffusivity D + slowing-down time t • time-to-peak • decay time  r2(small r) r2/(4D)  r(large r) ½ (tr2/D)1/2 t S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  34. Suprathermal relaxation dynamics and radial transport on-axis heating assumed suprathermal temperature ~ 11 keV S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  35. Profile evolution after shut-off on-axis heating assumed suprathermal temperature ~ 11 keV S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  36. D = 12.6 m2/s t = 1.5 ms Simple diffusion/slowing-down modelsuggests large energies and large diffusivities r = 0.14 r = 0.28  E > 50 keV r = 0.47 S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  37. Profile evolution after shut-off on-axis heating assumed suprathermal temperature ~ 11 keV S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  38. More rapid transport in heated plasma 2nd harm. absorption 3rd harm. absorption with 0.5 MW heating S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  39. More rapid transport in heated plasma with 0.5 MW heating assumed suprathermal temperature ~ 20 keV S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  40. Profile evolution after shut-off off-axis heating assumed suprathermal temperature ~ 11 keV S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  41. Conclusions • ECRH is a mature technology that has moved from simple heating to profile and e.d.f. tailoring • Array of complementary diagnostics and codes are increasingly constraining quantitative understanding of e.d.f. dynamics in physical and velocity space S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

  42. To-do list • more concerted use of complementary diagnostics to fully constrain distribution function • especially HFS, vertical and oblique ECE • high-resolution hard-X-ray tomography • Fokker-Planck modelling at short time scales, including Faraday law • self-consistent theory of ECCD including Ohkawa particle drifts • orbit code? • advanced e.d.f. engineering: Ohkawa current drive, … S. Coda, 33rd EPS Conf. on Plasma Physics, Roma, 22 June 2006

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