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XGC gyrokinetic particle simulation of edge plasma

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1 XGC gyrokinetic particle simulation of edge plasma
IEA Edge workshop, Sept. 2006, Krakow, Poland XGC gyrokinetic particle simulation of edge plasma C.S. Changa and 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
Full-f neoclassical ion root code (XGC-0) -Pedestal inside separatrix Buildup of pedestal along ion root by neutral ionization. Non-neoclassical electrons are assumed to follow ions Full-f ion-electron electrostatic code (XGC-1) -Whole edge Neoclassical solution Turbulence solution Study L-H transition Multi-scale simulation of pedestal growth in H-mode XGC-MHD Coupling for pedestal-ELM cycle Full-f electromagnetic code (XGC-2) Black: Achieved, Blue: in progress, Red: to be developed

4 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 Banana dynamics Jr = r(Er-Er0) Jloss+Jreturn=0 Electron contribution to macroscopic jr is assumed to be small = validation of NC equil.

5 [164K particles on 1,024 processors]
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 analytic neoclassical flow eq in core
Verification of XGC-1 against 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 Conventional neoclassical vpol-v|| relation
Breaks down in edge pedestal Er 1

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 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 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. n ~ 1cm Guiding center densities

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 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 t=1i t=4i 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. t=4i ExB ExB

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

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 Strongly sheared ExB rotation in the pedestal


29 Cartoon poloidal flow diagram in the edge

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

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

32 Phs-0: Simple coupling: with M3D or NIMROD
XGC-MHD Coupling Plan Phs-0: Simple coupling: with M3D or NIMROD XGC-0 grows pedestal along neoclassical root. MHD checks instability and crashes the pedestal. The same with XGC-1 and 2. Phs-2: Kinetic coupling: MHD performs the crash XGC supplies closure information to MHD during crash Phs-3: Advanced coupling: XGC performs the crash M3D supplies the B crash information to XGC during the crash Black: developed, Red: to be developed

33 Code coupling Initial state: DIIID g096333 XGC M3D
No bootstrap current or pedestal of pressure, density XGC read g eqdsk file calculate bootstrap current and p/n pedestal profile M3D Read g 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 simulations new equilibrium from eqdsk, XGC profiles
Linear perturbed poloidal magnetic flux, n = 9 Equilibrium poloidal magnetic flux Linear perturbed electrostatic potential

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

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

37 Pressure profile evolution
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=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

40 Toroidal current density J(R) evolution
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 M3D-L XGC-ET Yes XGC-ET M3D
Start (L-H) XGC-ET (xi, vi) P,P|| M3D-L (Linear stability) Mesh/Interpolation E V,E,,  Yes Stable? (xi, vi), E N,T,V,E,,D No XGC-ET M3D (xi, vi) Mesh/Interpolation P,P||, ,  t E,B E,B Stable? B healed? 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.

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