1. US SciDAC Fusion Simulation Prototype Center for Plasma edge Simulation -CPES- C.S. Chang a) on behaf of the CPES team a) Courant Institute of Mathematical Sciences, NYU

2. Center for Plasma Edge Simulation 1.Creating a 5d edge kinetic PIC code XGC-NT for dynamical Neoclassical+Turbulence+Neutral simulations (Neoclassical in Phase 0, Electrostatic in Phase 1, Electromagnetic in Phase 2) 2.Developing an integrated simulation framework between XGC-NT and an MHD/2-Fluid ELM code for pedestal-ELM cycle. Purpose: To simulate the L-H transition, pedestal buildup, ELM crash, pedestal scaling, scrape-off physics, divertor physics and wall load, etc. To develop a new predictive integrated (first-principles) edge simulation framework by

3. Participants NYU (Lead Institution)C.S. Chang (Lead PI), H. Strauss, D. Zorin, H. Weitzner, L. Greengard, S. Ku, G. Zaslavski (consultant) Princeton U.Daren Stotler, W. Lee, T.S. Hahm, E. Feibush S. Ethier, R. Samtaney, W. Wang, W. Park MITLinda Sugiyama CaltechJulian Cummings Columbia U.Dave Keyes, Mark Adams U. Colorado Scott Parker, Y. Chen UC IrvineZhihong Lin, Y. Nishimura Lehigh U.Arnold Kritz, Glenn Bateman, A. Pankin Rutgers U.Manish Parashar U. Tennessee at KnoxvilleMicah Beck U. UtahSteve Parker Hinton AssociatesFred Hinton ORNLDave Schultz, S. Klasky, P. Worley, E. D’Azevedo LBNLArie Shoshani and the SDM center Experimental Partners M. Greenwald (MIT), R. Maingi (ORNL), S. Zweben (PPPL), International Experimental Partners Kamada (JT60-U), L. Horton (ASDEX-U), KSTAR

4. The PIC edge kinetic code XGC XGC is a kinetic PIC Fokker-Planck/Poisson code It self-consistently includes the 5D ion and electron kinetics, realistic magnetic and wall geometry, Monte Carlo neutral particle transport with wall recycling, conserving MC collisions, neutral beam source, magnetic ripple, etc. XGC-0 established the self-consistent ion neoclassical pedestal physics with neutral dynamics (2004 IAEA, 2005 Spring TTF and ITPA). XGC-1 includes the mixed-f electron kinetics: Full-f e for neoclassical and Adiabatic-f e for electrostatic turbulence. XGC-1 will have the dynamically evolving B from J boot Flux bd: Heat flux from core, neutral flux from wall

5.   Neutral density and temperature distribution (XGC MC particle simulation for DIII-D)   0.4keV 0 keV Difficult to model it with fluid neutrals when mfp ~ L Ped ToTo 1.04 0.96 1. 1.04 0.96 nono Wall

6. Particle simulation of pedestal buildup by neutral ionization (B 0 = 2.1T, T i =500 eV) [164K particles on 1024 processors] Plasma densityV ExB

7. Fig.3.2.1c. Density pedestal profile evaluated from XGC and Tanh fit (left) and regression analysis of experimental density pedestal width (right) XGC finds neoclassical density pedestal width scaling Δ n  (neo)  M i 1/2 (T i 0.5 -0.23) /B T DIII-D data show (Chang-Groebner)  n  (exp) = 0.075 (T i 0.5 - 0.22)/B T + 0.0092 n/q Scaling with the local variables Excellent Tanh fit nn DIII-D Groebner Pedestal Scaling law from XGC-0

8. Steep-gradient bootstrap current in edge pedestal n TiTi V || J b (XGC)J b (Analytic) 

9. Nonlinearly saturated neoclassical Pedestal buildup by neutral ionization Simulation stopped at green bold line. DIII-D B O =2.1T M i =1 Broader T i pedestal and Higher E i scrape-off

10. Ion loss hole near X-point due to small B p 5 mm at outside midplane Scattering in and out of loss bd is important. C.S. Chang, et al, Phys. Plasmas 9, 3884 (2002)

11. Normalized psi~[0.99,1.00] n(  ) ()() f i0 is non-Maxwellian with a positive flow at the outside midplane 0 V_parallel f KE (keV) lnf K || K perp Passing ions from ped top

12. Normalized psi~[1.00,1.01] n(  ) ()() Outside the separatrix (better separation of hot and cold species) 0 V_parallel Orbit expanded banana effect Passing ions from ped top lnf f

13. Figure 1. pressure at t = 0, 67, and 106 Alfven times ELM simulation with MHD/2fluid codes (M3D and NIMROD) M3D

14. XGC Mesh/Interpolation MHD-L (Linear stability) (2d) n,T Stable? MHD tt Stable? B healed? Mesh/Interpolation n,T,V,, ,D,  Orange : Main simulator Blue: Monitor or Assistant V,E, ,D,  Workflow between XGC and MHD (Plan 1) Yes No (3d) n,T,B,V Start (L-H) Monitor (2d) n,T, B,V XGC stops

15. At each Update kinetic information ( , D, , etc) At each check for linear MHD stability

16. XGC Mesh/Interpolation MHD-L (Linear stability) N,T Stable? XGC Mesh/Interpolation MHD (x i, v i ) (3d) n,T,B tt Stable? B healed? Mesh/Interpolation (3d) E-V, ,  n,T,V,E, ,D,  Orange : Main simulator Blue: Monitor or Closure Assistant XGC evaluates SOL transport during ELM crash. V,E, ,  Workflow between 5d XGC and 3d MHD (Plan 2) (x i, v i ) Yes No (2d) n,T,(3d) B E (3d) N,T,B (x i, v i ) Start (L-H) Monitor (2d) N,T,B

17. Development of XGC-1: Integrated neoclassical and turbulence Full-f ions + full-f electrons will yield the neoclassical background solution with large plasma &  o variation along the open field lines. In the Full-f neoclassical electrons, micro fluctuations are removed to avoid the CFL condition (on the Omega-H mode problem) Adiabatic electrons will then yield electrostatic turbulence on top of the neoclassical solution. n e  exp[(  1 +  0 )/T e ]

18. Verification of XGC-1 using the early time solutions  is higher at high-B side  Transient neoclassical behavior Formation of the negative potential layer just inside the separatrix  H-mode layer Positive potential around the X-point (B P ~0)  Transient accumulation of positive charge

19. Turn off the adiabatic electrons An average of  over a finite poloidal angle keeps the  variation along B, while removing the micro turbulence from the full-f solution To begin with, we average  over flux surface (>1/2) inside the separatrix (let the adiabatic electrons evaluate the small poloidal  variation, later), but keep the  variation along B in the open field line region. Study the neoclasscal physics first

20. 2D Flow profiles from XGC The first self-consistent kinetic solution of edge flow structure We turn the turbulence feature off for this study. Most of the results shown are at 1  ib =2  R/v i, before reaching the steady state, augmented by some runs to 6 – 14  ib. The radial electric field is “near” steady state, but still undergoing GAM.

21. Code Verification of XGC-1 against the analytic neoclassical flow eq in core u i ∥ = (cT i /eB p )[kdlogT i /dr –dlog p i /dr-(e/T i )d  /dr] NN U i|| dT i /dr  0<1% t=14  ib V ExB

22. dT i /dr  0 Verification of XGC-1 against the analytic neoclassical flow eq in core u i ∥ = (cT i /eB p )[kdlogT i /dr –dlog p i /dr-(e/T i )d  /dr] k=0.5 Banana: k=1.17 Plateau: k=-0.5 Collisional: k=-2.1   1 for T i =1 keV n=5  10 19 m -3 0.8 0.9 0.7  0 -30 E r (kV/m) t=7.5  ib

23. Density profile  n ~ 1cm Does not drop as in XGC-0

24. Comparison of  o between m i /m e = 100 and 1000 at t=1  I  100 is reasonable Similar  0 in scrape-off m i /m e =100m i /m e =1000

25. Parallel plasma flow at t=1  i (m i /m e = 100, shaved off at  1x10 4 m/s ) t=1  i t=4  i V ||  10 4 m/s Sheared parallel flow in the inner divertor  counter-current flow near separatrix  co-current flow in scrape-off

26. t=4  i V || <0 in front of the inner divertor does not mean a plasma flow out of the material wall because of the ExB flow to the pump. ExB 

27. Neoclassical: V || <0 around separatrix, but >0 in the (far) scrape-off. But, this picture changes with anomalous diffusion or high neutrals: V || >0 in the whole edge region. V ||, DIII-D V || NN

28. V || shows different behavior with neutral collisions: V || >0 throughout the whole edge

29. Wall  (eV) NN V || >0V || <0 Potential profile roughly agrees with the flow direction in the edge

30. ExB rotation opposes the V || effect: V ExB is to inner divertor (co-I P ) in the near and to outer divertor (counter) in the far scrape-off. Which one is more important? t=4  i ExB

31. In neoclassical edge plasma, the poloidal rotaton from ExB and  p dominates over (B P /B T ) V ||. Is the diamagnetic flow real in the edge (stronger gyroviscous cancellation?)

32. t=1  I Forward  B Reversed B T and I P (V  B away from X-point) t=1  I Backward  B t=1  I Backward  B Lower V || in scrape-off. But, notice the dominance of counter-current flow into the inner divertor and sheard flow in the outer divertor

33. Reversed B T and I P V || V ExB  Toward outer divertor Toward inner divertor Weak ExB

34.  V || Reversed B T and I P V || near separatrix (blue) is toward the inner divertor, but ExB? V ExB near sepatrix is toward outer divertor, connecting to the away V ExB flow in the scrape-off.

35. Cartoon flow diagram in the neoclassical edge

36. 1 keV ion transport at D A ~10m 2 /s over edge Potential hill No potential hill With an H-mode type potential hill

37. Time evolution of an inner-divertor lost orbit under  ’’ < 0 and D=10 m 2 /s D=10 m 2 /s

38. E r xB Shearing increases with T i (ped) (from XGC-0) T i = 0.5 keV 1 keV X-loss

39. Forward  B yields ≈15% greater ExB Shear (from XGC-0)

40. Collisions in a PIC code PIC method has an excellent v-space resolution of neoclassical collisional physics  Many published papers reproducing neoclassical phys. There is room for improvement. PIC Monte Carlo (MC) collisions  MC noise. In order to reduce the collisional MC noise at low energy, XGC uses very frequent collision operations over extended cells (  t c  10 -3  b ).  Cannot use cheap particle pushing techniques New methods are under development to reduce the MC noise and to speed up the simulation by increasing  t c - Gridless FP (E. Yoon-CS Chang), - On Grid (F. Hinton, Lattice-Boltzman), (S. parker, 89) (Albreight, et al, 03), /4 L

41. 100,000 particles 10,000 particles Binary Monte Carlo Collisions (vector) real 74m11.531s 0m 33.788s user 74m11.490s 0m 33.766s sys 0m 0.020s 0m 0.008s Fokker-Planck Weight Collisions (about the same) real 0m 2.728s 0m 2.609s user 0m 2.276s 0m 2.180s sys 0m 0.152s 0m 0.144s Computing time comparison between two nonlinear PIC collision schemes

42. Discussions XGC now has the full-f electron dynamics, in addition to the full-f ion gyrokinetic dynamics XGC can perform an integrated neoclassical + electrostatic turbulence simulation We can turn on or off the turbulence. Trying to distinguish the numerical instabilities from the real physics instabilities before going into the long time simulations and turbulence. We are currently studying the neoclassical solutions. Mesh refinement and convergence studies with different solver routines are under way. We do not worry about the noise problem. Collision is an integrated part of XGC simulation (efficient quiet Nonlinear F-P collision techniques).

43. Discussions (2): ExB XGC-1 in neoclassical mode (without momentum input) shows the importance of the ExB flow, in addition to the v || argument raised by MIT group. There is a global convective circulation pattern of ExB flow in the egde region Negative potential in the pedestal (including the separatrix area) and positive potential in the scrape-off region. A milder pedestal shape produces smaller negative potential in the pedestal.

44. Discussions for future development Speeding up the electron simulation with the electron subcycling technique with less number of e-pushings Advanced particle pushing technique for long time simulation  Predictor-corrector with less frequent collision schemes. The electrostatic steep-gradient gyrokinetic equations are ready. The E&M version is under development. Large  n/n. Do we want the full-f non-Maxwellian electrons which can resolve the  H mode (CFL)? (Take advantage of the peta-scale computing?) Or, use the split-weight delta-f scheme with Maxwellian f e at a greater  t time step?