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Electron Heat Transport in steady-state discharges on Tore Supra

Electron Heat Transport in steady-state discharges on Tore Supra. J.F. Artaud * , F. Imbeaux, V. Basiuk, G. Giruzzi, G.T Hoang, P. Maget, and Tore Supra Team. Association CEA-Euratom sur la Fusion, CEA/DSM/DRFC, CEA Cadarache, 13108 St Paul-Lez-Durance, FRANCE.

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Electron Heat Transport in steady-state discharges on Tore Supra

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  1. Electron Heat Transport in steady-state discharges on Tore Supra J.F. Artaud*, F. Imbeaux, V. Basiuk, G. Giruzzi, G.T Hoang, P. Maget, and Tore Supra Team Association CEA-Euratom sur la Fusion, CEA/DSM/DRFC, CEA Cadarache, 13108 St Paul-Lez-Durance, FRANCE * E-mail: artaud@drfc.cad.cea.fr

  2. Find a reliable electron heat transport model for scenario prediction (various heating schemes and power) Tore Supra: steady-state plasma with dominant electron heating Dataset from 2002 campaign, with various heating schemes : LHCD, ECRH, ICRH (minority), FWEH (1996 campaign) and Ohmic. Test of mixed Bohm-gyroBohm model New model elaborated and tested: “Force-Free” Motivations

  3. Scenario A: LHCD only • Ip from 0.5 to 0.65 (MA) • nbar from 1.6 to 1.8 (1019 m-3) • PLH from 2.8 to 3.2 (MW ) • Vloop from -50 to 75 (mV) • ILH/Ip from 65% to 90 % • Iboot/Ip from10% to 15 % • Duration up to 265 s, 750 MJ injected • shot example : 30414

  4. Scenario B: LHCD + ICRH • Ip from 0.65 to 0.75 (MA) • nbar from 2.2 to 3.8 (1019 m-3) • PLH from 2.8 to 3.2 (MW ) • PFCI from 1.5 to 2.7 (MW) • Vloop from 100 to 250 (mV) • ILH/Ip from 40% to 50 % • Iboot/Ip from10% to 15 % • Duration up to 124 s, 420 MJ injected • shot example : 30351

  5. Tool for transport studies : CRONOS integrated modeling code • Calculation of heat / CD sources • integrated modules : PION for ICRH and REMA for ECRH • hard X-ray bremsstrahlung tomographic inversion used as “measurement” of LHCD profile, CD efficiency adjusted consistently with inductive flux consumption • neoclassical quantities : NCLASS • Ions temperature estimation • Te > Ti • Ti constrained by : X Bragg spectrometry, neutrons flux, transport consistency • check with predictive simulation with ionic mixed Bohm/gyroBohm • equipartition term always small compare to other electron heat sources • Interpretative simulations of current diffusion • q-profile, bootstrap current, power balance heat diffusivity • Heat transport predictive simulations • test of models against experimental data

  6. Assessment of mixed Bohm-GyroBohm for Tore Supra * M. Erba et al, Nuclear Fusion, Vol. 38, N° 7, pp 1013-1028, 1998

  7. Data base for fit of CB coefficient Plasma parameters • 20 shots:18134,18370,18372,18507,29996,30007,30058,30353,30358,30399,30414,30555,30559,30776,30777,30787,30804,30805,30806,30807. • Several times slices per shot.

  8. Legend Fit of CB coefficient CB=7.85 10-5 + 3.79 10-5 * Pheat Bohm coefficient • CB must be adjusted to fit the data: Linear dependence with Pheat  model has inadequate description of turbulence increase versus Pheat • No dependence found with other 0D parameter Pheat (MW)

  9. Test of stronger dependence on electron pressure gradient fit of CB=1.09 10-6 + 1.53 10-7 * Pheat fit of CB=1.20 10-8 + 1.44 10-10 * Pheat Bohm *(Pe) Bohm *Pe Bohm coefficient Bohm coefficient • Suggests (Pe)2 dependence for the “Bohm” term • still strong dispersion of CB Pheat (MW) Pheat (MW)

  10. Electron temperature prediction for Tore Supra # 30555, time traces Electron temperature (keV) : ECE (blue) / Simulation (red) mixed Bohm-gyroBohm prediction with CB = 2.5 10-4 x = normalized radial position

  11. Elaborating more adequate expression to replace “Bohm” term * J. F. Artaud et al, Physical Review B, Vol. 64, ref 094517, 2001

  12. Linear relation between PB and “Force Free” term Linear relation between PB (power balance) and “Force Free” term with offset of the order of 0.3 m2 s-1. This is greater than the electron neoclassical term, but close to the original gyroBohm term. Therefore, it is consistent to replace the Bohm term by FF. # 30555 PB (m2 s-1) offset FF

  13. Fit of coefficients CFF and CgB for the new model standard deviation = 0.2

  14. Ohmic shot with density ramp down Electron temperature # 30353 force free model prediction Good agreement with all measurements at each selected time slices. Small discrepancy at the center of the plasma

  15. Electron temperature prediction for Tore Supra # 30353, time traces Te (keV) : Thomson scattering (blue) / Simulation (red) Electron temperature (keV) :ECE (blue) / Simulation (red) Good agreement between simulation and measurements. The predict temperature is a little high at center of the plasma.

  16. Ohmic shot with ECRH modulations. Electron temperature # 29029 force free model prediction ECRH deposition ECRH time (s) Good agreement at all time slices. 0 1 x

  17. Electron temperature prediction for Tore Supra # 29029, time traces Te (keV) : Thomson scattering (blue) / Simulation (red) Electron temperature (keV) :ECE (blue) / Simulation (red) Excellent agreement between simulation and measurements. Initial discrepancy due to initialization of the current diffusion.

  18. Ohmic, LH, LH + ECRH, ECRH shot Electron temperature # 30555 force free model prediction Accurate Te prediction for every heating scheme

  19. Electron temperature prediction for Tore Supra # 30555, time traces Electron temperature (keV) : ECE (blue) / Simulation (red) Good agreement the whole pulse. The small difference in LH phase is within the error bars of the equilibrium identification. x = normalized radial position

  20. high power (3 MW) LHCD Electron temperature # 30007 force free model prediction Good agreement with all measurements at each selected time slices. Small discrepancy in the high power, low density phase (60 s).

  21. Electron temperature prediction for Tore Supra # 30007, time traces Electron temperature (keV) : ECE (blue) / Simulation (red) Wee can see a good agreement between simulation and measurements. The discrepancy in phase with 3MW LH additional power is compatible with error in measurements, especially in density profile determination. x = normalized radial position

  22. Ohmic & FWEH pulse. Electron temperature #18370 force free model prediction Good agreement with all measurements at each selected time slices.

  23. Electron temperature prediction for Tore Supra # 18370, time traces Te (keV) : Thomson scattering (blue)/ Simulation (red) Wee can see a good agreement between simulation and measurements except for x> 0.7 (boundary condition ?). x = normalized radial position

  24. Multi phases shot with density and current variations. Electron temperature # 30807 force free model prediction Good agreement with all measurements at each selected time slices. Some discrepancy when ICRH is on and in final phase with Te oscillations (also, uncertainly on minority concentration).

  25. Electron temperature prediction for Tore Supra # 30807, time traces Te (keV) : Thomson scattering (blue) / Simulation (red) Electron temperature (keV) :ECE (blue) / Simulation (red) Correct agreement between simulation and measurements. The predict temperature is a little high at center of the plasma. The Pion program (fully coupled with CRONOS code) compute the electron heat source due to ICRH (uncertainty on minority concentration).

  26. Mixed Bohm/gyroBohm model has a too low Pe dependence. Coefficient of Bohm term must be adjusted linearly as function of Pheat New “Force Free “ model proposed, by analogy with type II superconductor physics: Excellent agreement ohmic and L-mode phases, with various schemes (LHCD,ECRH,FWEH). Discrepancies observed with IC minority heating (uncertainties on minority concentration and ion temperature ?). Conclusions

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