Observation of Strong Inward Heat Transport with Off-axis ECRH in Tore Supra

1. Observation of Strong Inward Heat Transport with Off-axis ECRH in Tore Supra S.D. Song1, X.L. Zou2, G. Giruzzi2, W.W. Xiao1, X.T. Ding1, B.J. Ding3, J.L. Ségui2, D. Elbeze2, F. Clairet2, T. Aniel2, P. Moreau2, J. Bucalossi2, F. Bouquey2, R. Magne2, E. Corbel2and Tore Supra Team 1) Southwestern Institute of Physics, P.O. Box 432, Chengdu, China 2) CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France 3) Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, China • Heat pinch experiments with MECH in Tore Supra • Simulation with Linear Pinch Model • Simulation with Critical Gradient Model

2. Motivation diffusive convective • Electron heat transport: one of the key issues in plasma controlled fusion. • Empirically divided into two parts: • Diffusion: proportional to temperature gradient. • Convection: proportional to temperature. Pinch: inward convection. • General form of transport equation • Methods • Steady-state analysis • Assumes flux  conjugate gradient • Perturbative analysis • Allows separation of: Responses to different gradients Diffusion and convection • Single pulse, modulation, step ……

3. Phenomenon • Previous experiments • DIII-D, RTP, FTU, ASDEX-U • Signature of heat pinch • Negative effective heat diffusivity • Inward shift of the maximum of the Te amplitude compared to rdep • Interpretation • Large error bars in heat diffusivity • This Inward shift can be explained by pure-diffusive model due to non-linear dependence on temperature and its gradient T.C. Luce (DIII-D) 1992PRL P. Mantica (RTP) 2000PRL P. Mantica (ASDEX-U) 2006PPCF

4. Experimental Setup in Tore Supra • Heating: • Ohmic: ~ 0.5 MW • ECRH: 118GHz, 2×300kW Gyrotrons, deposition width 3~5 cm, O-mode, off-axis, rdep ~ 0.5, low frequency modulation (1 Hz) • Diagnostics: • ECE: for for Te measurement, 32 channels, spatial resolution ~ 2.5 cm, time resolution 1 ms, • Reflectometry: for ne measurement, frequency sweeping time 20 ms; spatial uncertainty 1 cm • CX spectroscopy for Ti measurement. • Basic parameters • Ip ~ 0.7MA, Bt~ 3.7T • Two regimes: • High density casene0 3~5×1019m-3 • Low density casene0 1~3×1019m-3 Ray tracing of EC waves Power deposition profile

5. Experimental Results • ne0 = 1.5 ~ 1.8×1019 m−3 • Both Te and ne modulated • ne0 = 4 ~ 5.4×1019 m−3 • Te modulated ne less influenced

6. Te perturbation during EC Pulse High Density Case Low Density Case • Time-space evolution of Te perturbation • Sawteeth do not affect this transport process • ECRH driven heat propagates from ECRH position to center in low density case

7. Simulation

8. Power Balance Analysis • Power balance analysis with CRONOS • ECRH deposition profile by ray-tracing • Effective diffusivity at Ohmic and ECRH phase • Marked change around EC heating position High Density Case Low Density Case

9. Linear Pinch Model • Linear Pinch Model • Analytical solution to the simplified heat transport equation • Sensitivity analysis • Phase not sensitive to Ve • Amplitude determined by ce, Ve • Piecewise constant profiles of coefficients • Trial-and-error technique

10. Simulation with LPM Decreasing of heat pinch effect High Density Case

11. Simulation with LPM Decreasing of heat pinch effect Low Density Case

12. Critical Gradient Model • Critical Gradient Model (CGM) Formulas • Threshold of normalized Te gradient found in both experiments and numerical simulations • CGM used as a paradigm • Transient effect • Perturbative diffusivity • Pseudo pinch [F. Imbeaux 2001 PPCF, X. Garbet 2004 PPCF]

13. Simulation with CGM High Density Case

14. Simulation with CGM Low Density Case

15. Comparison between Models • Agreement on cePB between CGM and CRONOS • Agreement on cePB between CGM and LPM • Agreement between CGM Veeff and LPM Ve around ECRH position • Additional heat pinch Vadd in CGM agrees with the one from LPM (Ve) Low Density Case

16. Conclusions and Prospects • Experimental observations • Different behaviors in high and low density cases • Low density case: inward shift of maximum compared to the ECRH position observed • Simulation with LPM • High density case: • A heat pinch is needed at around r = 0.2 • Diffusive model sufficient around ECRH position; • Low density case: • Heat pinch with larger value is needed around ECRH position. • Simulation with CGM • High density case: • Pure diffusive CGM can almost recover the Te and harmonic profiles, except on the amplitude profile inside r = 0.15; • Low density case: • Pure diffusive CGM can recover data outside r = 0.3. • Additional pinch is needed for r < 0.3.

17. Conclusions and Prospects • Future work • More experiments on heat and particle transport in HL-2A using these techniques. • Simulation • Quasi-linear model: QuaLiKiz [C. Bourdelle 2002 NF] • Non-linear codes: GYSELA [V. Grandgirard 2007 PPCF] • Heat pinch • More ECRH power on HL-2A; • Correlation between heat pinch and density gradient length [L. Wang 2011 NF]; • Find the negative diffusivity in the core region outside uncertainties.

18. Thank you for your attention!