XGC gyrokinetic particle simulation of edge plasma

1. IEA Edge workshop, 11-13 Sept. 2006, Krakow, Poland XGC gyrokinetic particle simulation of edge plasma C.S. Changaand the CPESb team aCourant Institute of Mathematical Sciences, NYU bSciDAC Fusion Simulation Prototype Center for Plasma Edge Simulation

2. Contents • XGC GK particle code development roadmap • XGC-0 and XGC-1 • Unconventional and strong edge neoclassical physics to be coupled to edge turbulence • XGC-1 Full-f Gyrokinetic Edge Simulation (PIC) • Potential profile • Rotation profile • Movie of particle motion

3. XGC Development Roadmap Black: Achieved, Blue: in progress, Red: to be developed

4. Banana dynamics • XGC-0 Code • For pedestal physics inside separatrix • Particle-in-cell, conserving MC collisions • 5D (3D real space + 2D v-space) • Full-f ions and neutrals (wall recycling) • Neoclassical root is followed • Macroscopic electrons follow ion root (weak turbulence) • Realistic magnetic and wall geometry containing X-point • Heat flux from core • Particle source from neutral ionization Jr = r(Er-Er0) Jloss+Jreturn=0 Electron contribution to macroscopic jr is assumed to be small = validation of NC equil.

5. XGC-0 simulation of pedestal buildup by neutral ionization along ion root (B0= 2.1T, Ti=500 eV) [164K particles on 1,024 processors] Plasma density VExB

6. Unconventional and strong edge neoclassical physics • b ~ Lp (Nonlinear neoclassical) f0 fM, P I p/r • E-field and rotation can be easily generated from boundary effects • Unconventional and strong neoclassical physics is coupled together with unconventional turbulence (strong gradients, GAM, separatrix & X, neutrals, open field lines, wall effect, etc).

7. Sources of co-rotation in pedestal Asymmetric excursion of hot passing ions from pedestal top due to X-pt Loss of counter traveling Banana ions

8. Conventional knowledge of not only i, but also the Er & rotation physics do not apply to the edge. Ampere’s law in the plasma core KNC~102  >=-4nimic2KNC<||2/B2>/t  + 4<Jext > • Due to the sensitive radial return current (large dielectric response), net radial current (or dEr/dt) in the core plasma is small. Consider the toroidal component of the force balance equation (-sum) • Since J is small, only the (small) off-diagonal stress tensor can raise or damp • the toroidal rotation in the core plasma. • In the scrape-off region, J|| return current can be large. • Thus, Jr can easily spin the plasma up and down. • In pedestal/scrape-off, Si (Neoclassical momentum transport) can be large. •  Highly unconventional and strong neoclassical physics.

9. Neoclassical Polarization Drift.dEr/dt <0 case is shown

10. Verification of XGC-1against analytic neoclassical flow eq in core ui∥= (cTi/eBp)[kdlogTi/dr –dlog pi/dr-(e/Ti)d/dr] Analytic t=30ib k=k(c) Simulation Er(V/m) ’=0 =0 

11. Er 1  Conventional neoclassical vpol-v|| relation Breaks down in edge pedestal

12. Enhanced loss hole by fluctuating (from XGC) (50 eV,100 kHz, m=360, n=20) • At 10 cm above the • X-point in D3D • Green: without  • Red: enhanced • loss by  Interplay between 5D neoclassical and turbulence after 4.5x10-4 sec (several toroidal transit times) Ku and Chang, PoP 11, 5626 (2004)

13. fi0 is non-Maxwellian with a positive flow at the outside midplane K|| lnf n() Kperp KE (keV) Passing ions from ped top () f 0 V_parallel Normalized psi~[0.99,1.00]

14. Experimental evidences of anisotropic non-Maxwellian edge ions (K. Burrell, APS 2003)

15. Edge Er is usually inferred from ZiniEr = rp – VxB. Inaccuracy due to (p)r  rp ??? K. Burrell, 2003

16. XGC-1 Code • Particle-in-cell • 5D (3D real space + 2D v-space) • Conserving plasma collisions • Full-f ions, electrons, and neutrals (recycling) • Neoclassical and turbulence integrated together • Realistic magnetic geometry containing X-point • Heat flux from core • Particle source from neutral ionization

17. Early time solutions of turbulence+neoclassical • Correct electron mass • t = 10-4 ion bounce time • Several million particles •  is higher at high-B side •  Transient neoclassical behavior • Formation of a negative • potential layer just inside • the separatrix  H-mode layer • Positive potential around • the X-point (BP ~0) •  Transient accumulation • of positive charge Density pedestal Ln ~ 1cm

18. Guiding center densities n ~ 1cm XGC simulation results: The initial H-mode like density profile has not changed much before stopping the simulation (<~10 bi), neutral recycling is kept low.

19. Turbulence-averaged edge solutions from XGC • The first self-consistent kinetic solution of edge potential and flow structure • We average the fluctuating  over toroidal angle and over a poloidal extent to obtain o. (1/2 flux-surface in closed and ~10 cm in the open field)  Remove turbulence and avoid the “banging” instability • Simulation is for 1 to 30 ion bounce time ib =2R/vi (shorter for full-f and longer for delta-f): Long in a/vi time.

20. Comparison of o between mi/me = 100 and 1000 at t=1Ib 100 is reasonable (10 was no good) mi/me =100 mi/me =1000 (Similar solutions) <0 in pedestal and >0 in scrape-off

21. t=1i t=4i Parallel plasma flow at t=1 and 4ib (mi/me = 100, shaved off at 1x104 m/s) • Counter-current flow near separatrix • Co-current flow in scrape-off • Co-current flow at pedestal top V|| 104 m/s Sheared parallel flow in the inner divertor

22. 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 ExB

23. V|| V||, DIII-D 1 N Strongly sheared V|| <0 around separatrix, but >0 in the (far) scrape-off.

24. ExB profile without p flow roughly agrees • with the flow direction in the edge • Sign of strong off-diagonal P component? (stronger gyroviscous cancellation?) V||<0 V||>0 (eV) Wall N

25. Edge Er is usually inferred from ZiniEr = rp – VxB. Inaccuracy due to (p)r  rp ??? K. Burrell, 2003

26. In neoclassical edge plasma, the poloidal rotaton from ExB can dominate over (BP/BT) V||. What is the real diamagnetic flow in the edge? (stronger gyroviscous cancellation?) How large is the off-diagonal pressure?

27. t=4i Strongly sheared ExB rotation in the pedestal ExB

29. Cartoon poloidal flow diagram in the edge

30. V|| V|| V||, DIII-D 1 N N Wider pedestal  Stronger V||>0 in scrape-off, Weaker V|| <0 near separatrix. Weak V|| (and ExB) shearing in H layer Sharp V|| (and ExB) shearing in H layer Wider pedestal Steeper pedestal 0 1

31. V|| shows modified behavior with strong neutral collisions: V||>0 becomes throughout the whole edge (less shear) V||>0 source

32. XGC-MHD Coupling Plan Black: developed, Red: to be developed

33. Code coupling • Initial state: DIIID g096333 • No bootstrap current or pedestal of pressure, density • XGC • read g096333 eqdsk file • calculate bootstrap current and p/n pedestal profile • M3D • Read g096333 eqdsk file • Read XGC bootstrap current and pedestal profiles • Obtain new MHD equilibrium • Test for linear stability - found unstable • Calculate nonlinear ELM evolution

34. M3D equilibrium and linear simulationsnew equilibrium from eqdsk, XGC profiles Linear perturbed poloidal magnetic flux, n = 9 Linear perturbed electrostatic potential Equilibrium poloidal magnetic flux

35. At each check for linear MHD stability At each Update kinetic information (, D, ,etc), In phase 2

36. M3D nonlinear simulationpressure evolution T = 25 ELM near maximum amplitude T = 37 Pressure relaxing Initial pressure With pedestal

37. Pressure profile evolution T=0 T=37 T=25 Pressure profile p(R) relaxes toward a state with less pressure pedestal. P(R) is pressure along major radius (not averaged).

38. Density n(R) profile evolution T=37 T=0 T=25 T=0 – initial density pedestal at R = 0.5 T=25 – ELM carries density across separatrix T=37 – density relaxes toward new profile

39. Temperature T(R) profiles T=0 T=25 T=37

40. Toroidal current density J(R) evolution T=0 T=37 T=25 T=0 – bootstrap current peak is evident at R = 0.5 T=25 – ELM causes current on open field lines T=37 – current relaxes toward new profile

41. XGC-M3D workflow Start (L-H) P,P|| M3D-L (Linear stability) (xi, vi) XGC-ET Mesh/Interpolation E V,E,,  Yes Stable? N,T,V,E,,D (xi, vi), E No M3D XGC-ET (xi, vi) Mesh/Interpolation P,P||, ,  t E,B Stable? B healed? E,B No (xi, vi) Yes Mesh/Interpolation E,B Blue: Pedestal buildup stage Orange : ELM crash stage Mesh/Interpolation services evaluate macroscopic quantities, too.

42. Conclusions and Discussions • In the edge, we need to abandon many of the conventional neoclassical rotation theories • Strong off-diagonal pressure (non-CGL) • Turbulence and Neoclassical physics need to be self-consistent. • In an H-mode pedestal condition, • V|| >0 in the scrape-off, <0 in near separatrix, >0 at pedestal shoulder. • >0 in the scrape-off plasma, <0 in the pedestal • Global convective poloidal flow structure in the scrape-off • Strong sheared ExB flow in the H-mode layer • Good correlation of ExB rotation with V|| • Flow pattern is different in an L-mode edge • Weaker sheared flow in H-layer • High neutral density smoothens the V|| structure and further reduces the shear in the pedestal region • Sources of V||>0 exist at the pedestal shoulder. • Nonlinear ELM simulation is underway (M3D, NIMROD) • XGC-MHD coupling started. Correct bootstrap current, Er, and rotation profiles are important.