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Global Gyrokinetic Simulations of Heat Transport & Plasma Rotation

Global Gyrokinetic Simulations of Heat Transport & Plasma Rotation. Y Sarazin 1 , V Grandgirard 1 , J Abiteboul 1 , S Allfrey 1 , X Garbet 1 , Ph Ghendrih 1 , G Latu 1 , A Strugarek 1 , G Dif-Pradalier 2 , P H Diamond 2,3 , B F McMillan 4 , T M Tran 4 , L Villard 4 , S Ku 5 ,

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Global Gyrokinetic Simulations of Heat Transport & Plasma Rotation

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  1. Global Gyrokinetic SimulationsofHeat Transport & Plasma Rotation Y Sarazin1, V Grandgirard1, J Abiteboul1, S Allfrey1, X Garbet1, Ph Ghendrih1, G Latu1, A Strugarek1, G Dif-Pradalier2, P H Diamond2,3, B F McMillan4, T M Tran4, L Villard4, S Ku5, C S Chang5, S Jolliet6, A Bottino7, P Angelino8 GYSELA • CEA, IRFM Cadarache, Saint Paul-lez-Durance cedex, France. • Center for Astrophys. & Space Sciences, UCSD, La Jolla, California, USA. • National Fusion Research Institute, Daejeon, Republic of Korea. • CRPP, Assoc. Euratom-Confédération Suisse, EPFL, Lausanne, Switzerland. • Courant Institute of Math. Sciences, New York Univ., New York, USA. • Japan Atomic Energy Agency, Higashi-Ueno 6-9-3, Tokyo, Japan. • Max-Planck IPP, Association Euratom, Garching, Germany. • Labo. of Computational Systems Biotech., EPFL, Lausanne, Switzerland.

  2. [Strugarek '10] New generation of gyrokinetic codes able to address these issues … thanks to the large increase of HPC resources(PetaFlop scale) GYSELA [Grandgirard JCP '06], ORB5 [Jolliet CPC '07], XGC1 [Chang PoP '08], ELMFIRE [Heikkinen JCP '08], GT5D [Idomura NF '09], global-GENE [Görler '09, Lapillonne '10], multi scale TRINITY [Barnes '10], FEFI [Scott CPP '10] Introduction Open questions for ITER regarding turbulent transport: • Impact of large scale transport on scaling laws wctE=F(r*,n*,b,…)?  meso-scale avalanches / ZF interaction => gyro-Bohm scaling • Generation & magnitude of poloidal/toroidal rotation? Critical for turbulence saturation & MHD stability  Turbulence-generated poloidal & toroidal corrugations • How to trigger & maintain transport barriers?

  3. Consistent formulation of Gyrokinetic theory [Brizard & Hahm RMP '07] ; Main characteristics of 3 gyrokinetic codes ORB5 PIC, optimized loading XGC1 PIC, X-point GYSELA Semi-Lagrangian All three codes are (for simulations used) Full-f(no scale separation fluctuations/equilibrium)Flux driven Electrostatic, adiabatic electrons, collisionalGlobal geometry [Grandgirard JCP '06, PPCF '08] [Jolliet CPC '07] [Chang & Ku PoP '08, '09]

  4. Consequence: stored energy  less than Padd  experimental degradation of tE with Padd is recovered [Sarazin NF '10] Resilience of temperature profile • Modest increase of temperature when Source magnitude S0~Padd Caveat: requires long simulation runs (~tE with wctE ~ r*-3) GYSELA

  5. Inward & outward avalanches • Transport dominated by large scaleavalanches (length >> Dcorr) • Intermittent (1/f Fourier frequency spectrum) • Propagation velocity ~  r* cs(~ 103 m.s-1 in ITER) Outward/inward fronts - sometimes related to positive/negative Er [Idomura NF '09] [McMillan PoP '09] [Sarazin NF '10] 18 16 14 12 10 8 6 4 2 0 16 14 12 10 8 6 4 2 GYSELA (r*=1/512) ORB5 (r*=1/280) Exp. Evidences: [Politzer PRL '00, Tamura IAEA '10,Endler JNM '99, Rudakov PPCF '01, Boedo PoP '01, Grulke PoP '06, Antar PoP '07, Müller PoP '07, Zweben PPCF '07, Fedorczak JNM '09, Pedrosa EPS '10, etc…] time (104 wc-1) Heat flux [gBohm units] 0.3 0.5 0.7 0 0.5 1.0 r=r/a r=r/a

  6. Iso-contours of Te (JET #49637) Da Time [s] • Reminiscent of inward propagation of temperature front after ELM event on JET [Sarazin PPCF '02] Edge turbulence does propagate inwards Turbulence intensity [Ku NF '09] • Common understanding: • Local transport assumption • Edge = core boundary condition • Simulation with prescribed H-mode pedestal (XGC1): Edge ITG turbulence observed to propagate inwards  destabilization of the core XGC1 (r*=1/180) time [R/vT] [Ku NF '09] r=r/a

  7. Gyro-Bohm scaling despite avalanches • Usual framework: Small scale vortices (Dcorrri)  local transport  gyroBohm scaling Then: If avalanches feel the system size  breaking of gyroBohm scaling? • Answer is NO: still gyroBohm at small r* (see [Jolliet & Idomura IAEA '10] at intermediate r*) adapted from [McMillan PRL '10]

  8. GYSELA Poloidal cross section of df (non axi-symmetric component) Smaller r* Gyro-Bohm scaling despite avalanches • Usual framework: Small scale vortices (Dcorrri)  local transport  gyroBohm scaling Then: If avalanches feel the system size  breaking of gyroBohm scaling? • Answer is NO: still gyroBohm at small r* (see [Jolliet & Idomura IAEA '10] at intermediate r*) • Possible reasons: • Dcorrri • Avalanches are meso-scale

  9. GYSELA (r*=1/256,n*=0.05) 8 6 4 2 0 Gradient R/LT 4.105 2.105 ExB shearing rate wct 80 100 120 140 160 r=r/a • Radial profile: • wave-like pattern  predicted by theory • scales like ri [Diamond, Itoh, Itoh, Hahm PPCF '05] GYSELA Wave-like structure of ZF controls avalanche size • Zonal Flows radially localized • Limit extension of avalanches • "Staircase" structure  Framework for non-local formulation of transport [Dif-Pradalier PRE '10] THC/P4-06

  10. Turbulent regime (r*=1/128; n*=0.5) • Compare Er from 2 expressions:  gEGYSELA ~ glin> gEneo  turbulence drives mean shear Poloidal flow neoclassical – shear is NOT • In turbulent regime (no transport barrier): • vq still mainly neoclassical: • Difference (vq-vqneo) well captured by Reynolds'stress • Reynolds'stress component  when collisionality  [Dif-Pradalier PRL '09]

  11. Large contribution from neo. & turb. components of RS tensor Local balance of parallel momentum is satisfied •  exact momentum (waves + part.) conservation law • Local toroidalmomentum balance well fulfilled: radial current (=0 due to charge conservation) Reynolds' stresspolarization term [Brizard '10, Scott '10, Abiteboul & Garbet '10] [Diamond-Kim PF '91, Peeters PRL '07 PoP '09, Hahm PoP '08, Gürcan PoP '08 '09, Camenen PRL '09, Mc Devitt PRL '10] [Abiteboul EPS '10] GYSELA

  12. Consistent with QL theoretical prediction [Hahm PoP '08, Peeters PoP '09, Garbet "Festival de Théorie" '09] Theoretical QL prediction for GU// Thermal boundary U|| from supra-thermal & barely passing particles • Co-current toroidal spin-up carried out by particles supra-thermal barely passing cf. [Fenzi '10 this conf. EX/3-4]

  13. In saturated non-linear regime: Avalanches of heat also transport // momentum -> OK with exp./theo. ; suggests similar ceff (Prandtl number ~1) -> reminiscent to exp. observations on JET [Diamond PoP '08] [Hidalgo PRL '03] Cross-correlation (Qturb, U||) GYSELA Avalanches transport both heat & U|| • Dipolar structure (conservation) of U|| associated to 1st relaxation GYSELA

  14. Conclusions • New generation of global full-f GK codes(GYSELA, ORB5, XGC1, …)  Turbulent transport: excellent qualitative agreement • Transport dominated by meso-scale transport events: inward & outward avalanches -> non local / non diffusive  new paradigm for core-edge interactions & transients • Gyro-Bohm effective diffusivity at sufficiently small r* (<1/250)  critical role of zonal flow radial profile • Poloidal rotation mainly neoclassical – shear is NOT (turbulence) • Many players / rich physics in toroidal momentum balance Supra-thermal particles drive co-current spin-up Transport of U|| correlated to heat transport

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