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1 15th May 2012 Association EURATOM-CEA Shaodong Song Observation of Strong Inward Heat Transport with Off-axis ECRH in Tore Supra Heat pinch experiments with MECH in Tore Supra Simulation with Linear Pinch Model Simulation with Critical Gradient Model S.D. Song 1, X.L. Zou 2, G. Giruzzi 2, W.W. Xiao 1, X.T. Ding 1, B.J. Ding 3, J.L. Ségui 2, D. Elbeze 2, F. Clairet 2, T. Aniel 2, P. Moreau 2, J. Bucalossi 2, F. Bouquey 2, R. Magne 2, E. Corbel 2 and 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

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2 15th May 2012 Association EURATOM-CEA Shaodong Song Motivation 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 diffusive convective ……

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3 15th May 2012 Association EURATOM-CEA Shaodong Song Phenomenon Previous experiments DIII-D, RTP, FTU, ASDEX-U Signature of heat pinch Negative effective heat diffusivity Inward shift of the maximum of the T e amplitude compared to dep T.C. Luce (DIII-D) 1992PRLP. Mantica (RTP) 2000PRLP. Mantica (ASDEX-U) 2006PPCF 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

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4 15th May 2012 Association EURATOM-CEA Shaodong Song Experimental Setup in Tore Supra Heating: Ohmic: ~ 0.5 MW ECRH: 118GHz, 2 × 300kW Gyrotrons, deposition width 3~5 cm, O-mode, off-axis, dep ~ 0.5, low frequency modulation (1 Hz) Diagnostics: ECE: for for T e measurement, 32 channels, spatial resolution ~ 2.5 cm, time resolution 1 ms, Reflectometry: for n e measurement, frequency sweeping time 20 ms; spatial uncertainty 1 cm CX spectroscopy for T i measurement. Basic parameters I p ~ 0.7MA, B t ~ 3.7T Two regimes: High density case n e0 3~5 × 10 19 m -3 Low density case n e0 1~3 × 10 19 m -3 Ray tracing of EC waves Power deposition profile

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5 15th May 2012 Association EURATOM-CEA Shaodong Song Experimental Results n e0 = 1.5 ~ 1.8×10 19 m −3 Both T e and n e modulated n e0 = 4 ~ 5.4×10 19 m −3 T e modulated n e less influenced

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6 15th May 2012 Association EURATOM-CEA Shaodong Song T e perturbation during EC Pulse Time-space evolution of T e perturbation Sawteeth do not affect this transport process ECRH driven heat propagates from ECRH position to center in low density case High Density CaseLow Density Case

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7 15th May 2012 Association EURATOM-CEA Shaodong Song Simulation

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8 15th May 2012 Association EURATOM-CEA Shaodong Song 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 CaseLow Density Case

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9 15th May 2012 Association EURATOM-CEA Shaodong Song Linear Pinch Model Linear Pinch Model Analytical solution to the simplified heat transport equation Sensitivity analysis Phase not sensitive to V e Amplitude determined by e, V e Piecewise constant profiles of coefficients Trial-and-error technique

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10 15th May 2012 Association EURATOM-CEA Shaodong Song Simulation with LPM High Density Case Decreasing of heat pinch effect

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11 15th May 2012 Association EURATOM-CEA Shaodong Song Simulation with LPM Low Density Case Decreasing of heat pinch effect

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12 15th May 2012 Association EURATOM-CEA Shaodong Song Critical Gradient Model Critical Gradient Model (CGM) Formulas Threshold of normalized T e 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]

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13 15th May 2012 Association EURATOM-CEA Shaodong Song Simulation with CGM High Density Case

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14 15th May 2012 Association EURATOM-CEA Shaodong Song Simulation with CGM Low Density Case

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15 15th May 2012 Association EURATOM-CEA Shaodong Song Comparison between Models Low Density Case Agreement on e PB between CGM and CRONOS Agreement on e PB between CGM and LPM Agreement between CGM V e eff and LPM V e around ECRH position Additional heat pinch V add in CGM agrees with the one from LPM ( V e )

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16 15th May 2012 Association EURATOM-CEA Shaodong Song 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.

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17 15th May 2012 Association EURATOM-CEA Shaodong Song 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.

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18 15th May 2012 Association EURATOM-CEA Shaodong Song Thank you for your attention!

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