1. 23 rd IAEA Fusion Energy Conference, Daejeon, Republic of Korea, October 2010Y. Sarazin 1 / 14 Global Gyrokinetic Simulations 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, C S Chang 5, S Jolliet 6, A Bottino 7, P Angelino 8 1. CEA, IRFM Cadarache, Saint Paul-lez-Durance cedex, France. 2. Center for Astrophys. & Space Sciences, UCSD, La Jolla, California, USA. 3. National Fusion Research Institute, Daejeon, Republic of Korea. 4. CRPP, Assoc. Euratom-Confédération Suisse, EPFL, Lausanne, Switzerland. 5. Courant Institute of Math. Sciences, New York Univ., New York, USA. 6. Japan Atomic Energy Agency, Higashi-Ueno 6-9-3, Tokyo, Japan. 7. Max-Planck IPP, Association Euratom, Garching, Germany. 8. Labo. of Computational Systems Biotech., EPFL, Lausanne, Switzerland. GYSELA

2. 23 rd IAEA Fusion Energy Conference, Daejeon, Republic of Korea, October 2010Y. Sarazin 2 / 14 Introduction Open questions for ITER regarding turbulent transport:  Impact of large scale transport on scaling laws  c  E =F(  *, *, ,…)?  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? 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] [Strugarek '10]

3. 23 rd IAEA Fusion Energy Conference, Daejeon, Republic of Korea, October 2010Y. Sarazin 3 / 14 Main characteristics of 3 gyrokinetic codes 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] GYSELA Semi-Lagrangian ORB5 PIC, optimized loading XGC1 PIC, X-point [Jolliet CPC '07][Chang & Ku PoP '08, '09] [Brizard & Hahm RMP '07] ;  Consistent formulation of Gyrokinetic theory

4. 23 rd IAEA Fusion Energy Conference, Daejeon, Republic of Korea, October 2010Y. Sarazin 4 / 14 Resilience of temperature profile  Modest increase of temperature when Source magnitude S 0 ~P add  Caveat: requires long simulation runs (~  E with  c  E  *  3 ) [Sarazin NF '10]  Consequence: stored energy  less than P add  experimental degradation of  E with P add is recovered GYSELA

5. 23 rd IAEA Fusion Energy Conference, Daejeon, Republic of Korea, October 2010Y. Sarazin 5 / 14  =r/a Inward & outward avalanches  Transport dominated by large scale avalanches (length  corr )  Intermittent (1/f Fourier frequency spectrum)  Propagation velocity  * c s (  10 3 m.s  1 in ITER) Outward/inward fronts - sometimes related to positive/negative E r time (10 4  c  1 ) GYSELA (  * =1/512) ORB5 (  * =1/280) Heat flux [gBohm units]  =r/a 18 16 14 12 10 8 6 4 2 0 16 14 12 10 8 6 4 2 0 0.5 1.0 0.3 0.5 0.7 [Idomura NF '09] [McMillan PoP '09] 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…] [Sarazin NF '10]

6. 23 rd IAEA Fusion Energy Conference, Daejeon, Republic of Korea, October 2010Y. Sarazin 6 / 14  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 Edge turbulence does propagate inwards [Ku NF '09] time [R/v T ]  =r/a Turbulence intensity [Ku NF '09] XGC1 (  * =1/180) XGC1 (  * =1/180)  Reminiscent of inward propagation of temperature front after ELM event on JET [Sarazin PPCF '02] Iso-contours of T e (JET #49637) D  Time [s]

7. 23 rd IAEA Fusion Energy Conference, Daejeon, Republic of Korea, October 2010Y. Sarazin 7 / 14 Gyro-Bohm scaling despite avalanches  Usual framework: Small scale vortices (  corr  i )  local transport  gyroBohm scaling Then: If avalanches feel the system size  breaking of gyroBohm scaling?  Answer is NO: still gyroBohm at small  * (see [Jolliet & Idomura IAEA '10] at intermediate  * ) adapted from [McMillan PRL '10]

8. 23 rd IAEA Fusion Energy Conference, Daejeon, Republic of Korea, October 2010Y. Sarazin 8 / 14 Gyro-Bohm scaling despite avalanches  Usual framework: Small scale vortices (  corr  i )  local transport  gyroBohm scaling Then: If avalanches feel the system size  breaking of gyroBohm scaling?  Answer is NO: still gyroBohm at small  * (see [Jolliet & Idomura IAEA '10] at intermediate  * )  Possible reasons:   corr  i GYSELA Poloidal cross section of  (non axi-symmetric component) Smaller  *  Avalanches are meso-scale

9. 23 rd IAEA Fusion Energy Conference, Daejeon, Republic of Korea, October 2010Y. Sarazin 9 / 14 ctct 4.10 5 2.10 5 GYSELA (  * =1/256, * =0.05) 80 100120 140 160  =r/a Gradient R/L T 8642086420 ExB shearing rate 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  Radial profile:  wave-like pattern  predicted by theory  scales like  i [Diamond, Itoh, Itoh, Hahm PPCF '05] GYSELA

10. 23 rd IAEA Fusion Energy Conference, Daejeon, Republic of Korea, October 2010Y. Sarazin 10 / 14 Poloidal flow neoclassical – shear is NOT [Dif-Pradalier PRL '09]  In turbulent regime (no transport barrier) :  v  still mainly neoclassical:  Difference (v   v  neo ) well captured by Reynolds'stress  Reynolds'stress component  when collisionality   Compare E r from 2 expressions: Turbulent regime       E GYSELA ~  lin  E neo  turbulence drives mean shear

11. 23 rd IAEA Fusion Energy Conference, Daejeon, Republic of Korea, October 2010Y. Sarazin 11 / 14   exact momentum (waves + part.) conservation law  Local toroidal momentum balance well fulfilled: radial current (=0 due to charge conservation) Reynolds' stresspolarization term Local balance of parallel momentum is satisfied [Abiteboul EPS '10] [Diamond-Kim PF '91, Peeters PRL '07 PoP '09, Hahm PoP '08, Gürcan PoP '08 '09, Camenen PRL '09, Mc Devitt PRL '10] GYSELA [Brizard '10, Scott '10, Abiteboul & Garbet '10]  Large contribution from neo. & turb. components of RS tensor

12. 23 rd IAEA Fusion Energy Conference, Daejeon, Republic of Korea, October 2010Y. Sarazin 12 / 14 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] Thermal boundary [Hahm PoP '08, Peeters PoP '09, Garbet "Festival de Théorie" '09] Theoretical QL prediction for  U//  Consistent with QL theoretical prediction

13. 23 rd IAEA Fusion Energy Conference, Daejeon, Republic of Korea, October 2010Y. Sarazin 13 / 14 Avalanches transport both heat & U   Dipolar structure (conservation) of U || associated to 1 st relaxation GYSELA  In saturated non-linear regime: Avalanches of heat also transport // momentum -> OK with exp./theo. ; suggests similar  eff (Prandtl number ~1) -> reminiscent to exp. observations on JET Cross-correlation (Q turb, U || ) GYSELA [Hidalgo PRL '03] [Diamond PoP '08]

14. 23 rd IAEA Fusion Energy Conference, Daejeon, Republic of Korea, October 2010Y. Sarazin 14 / 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  * (<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