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.