US SciDAC Fusion Simulation Prototype Center for Plasma edge Simulation

-CPES-

C.S. Changa) on behaf of the CPES team

a)Courant Institute of Mathematical Sciences, NYU

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

ParticipantsNYU (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. ParkMIT Linda SugiyamaCaltech Julian CummingsColumbia U. Dave Keyes, Mark AdamsU. Colorado Scott Parker, Y. ChenUC Irvine Zhihong Lin, Y. NishimuraLehigh U. Arnold Kritz, Glenn Bateman, A. PankinRutgers U. Manish ParasharU. Tennessee at Knoxville Micah BeckU. Utah Steve ParkerHinton Associates Fred HintonORNL Dave Schultz, S. Klasky, P. Worley, E. D’AzevedoLBNL Arie Shoshani and the SDM center

Experimental PartnersM. Greenwald (MIT), R. Maingi (ORNL), S. Zweben (PPPL), International Experimental PartnersKamada (JT60-U), L. Horton (ASDEX-U), KSTAR

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, r

ealistic 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-fe for neoclassical and Adiabatic-fe for electrostatic turbulence.

• XGC-1 will have the dynamically evolving B from Jboot

• Flux bd: Heat flux from core, neutral flux from wall

Neutral density and temperature distribution (XGC MC particle simulation for DIII-D)

0.4keV

0 keV

Difficult to model it withfluid neutrals when mfp ~ LPed

To

1.04

0.961. 1.04

0.96

no

Wall

Wall

Wall

Particle simulation of pedestal buildup by neutral ionization (B0= 2.1T, Ti=500 eV)[164K particles on 1024 processors]

Plasma density VExB

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

Δn(neo) Mi1/2 (Ti

0.5-0.23) /BT

DIII-D data show (Chang-Groebner)n(exp) = 0.075 (Ti

0.5- 0.22)/BT + 0.0092 n/q

Scaling with the local variables

ExcellentTanh fit

n

DIII-DGroebner

Pedestal Scaling law from XGC-0

0.92 0.94 0.96 0.98 1.00

-4

-2

0

2

4

6

8

10

12

14

16

18

Cur

rent

Den

sity

normalized psi

5.99tau 13.5995tau 23.1995tau 33.5995tau

0.92 0.94 0.96 0.98 1.00

-4

-2

0

2

4

6

8

10

Cu

rre

nt D

en

sity

normalized psi

5.99tau 13.5995tau 23.1995tau 33.5995tau

0.92 0.94 0.96 0.98 1.00

5.00E+018

1.00E+019

1.50E+019

2.00E+019

2.50E+019

3.00E+019

3.50E+019

4.00E+019

4.50E+019

5.00E+019

5.50E+019

6.00E+019

de

nsity

normalized psi

5.99tau 13.5995tau 23.1995tau 33.5995tau

0.92 0.94 0.96 0.98 1.00-5000

0

5000

10000

15000

20000

25000

30000

35000

ve

locity

normalized psi

5.99tau 13.5995tau 23.1995tau 33.5995tau

0.92 0.94 0.96 0.98 1.00

400

500

600

700

800

900

1000

Te

mp

era

ture

(eV

)

normalized psi

5.99tau 13.5995tau 23.1995tau 33.5995tau

0.92 0.94 0.96 0.98 1.00-3000

-2800

-2600

-2400

-2200

-2000

-1800

-1600

-1400

-1200

-1000

-800

-600

-400

-200

0

Po

ten

tia

l(V

)

normalized psi

5.99tau 13.5995tau 23.1995tau 33.5995tau

Steep-gradient bootstrap current in edge pedestal n

Ti

V||

Jb(XGC) Jb(Analytic)

Nonlinearly saturated neoclassical Pedestal buildup by neutral ionization

Simulation stoppedat green bold line.

DIII-D BO=2.1T

Mi =1

Broader Ti pedestal andHigher Ei scrape-off

Ion loss hole near X-point due to small Bp

5 mmat outsidemidplane

Scattering in and out of loss bdis important.

C.S. Chang, et al, Phys. Plasmas 9, 3884 (2002)

Normalized psi~[0.99,1.00]

0 2 4 6 8 10 1243

44

45

46

47

48

49

50

lnf

Energy(KeV)

K_perp energyK_para energy

n()

()

fi0 is non-Maxwellian with a positive flow at the outside midplane

-3 -2 -1 0 1 2 3

0.00E+000

1.00E+020

2.00E+020

3.00E+020

4.00E+020

f

V-para

B

0

V_parallel

f

KE (keV)

lnf

K||

Kperp

Passing ionsfrom ped top

Normalized psi~[1.00,1.01]

0 2 4 6 8 10 12

43

44

45

46

47

48

49

50

51

lnf

Energy (KeV)

K_perp energyK_para enegy

n()

()

Outside the separatrix(better separation of hot and cold species)

-3 -2 -1 0 1 2 3-1.00E+020

0.00E+000

1.00E+020

2.00E+020

3.00E+020

4.00E+020

5.00E+020

6.00E+020

7.00E+020

f

V-para

B

0

V_parallel

Orbit expanded banana effect

Passing ions from ped top

lnf

f

Figure 1. pressure at t = 0, 67, and 106 Alfven times

ELM simulation with MHD/2fluid codes (M3D and NIMROD)

M3D

XGC Mesh/Interpolation MHD-L(Linear stability)

(2d) n,T

Stable?

MHD

tStable?B healed?

Mesh/Interpolation

n,T,V,<E>,,D,

Orange : Main simulatorBlue: Monitor or Assistant

V,E,,D,

Workflow between XGC and MHD (Plan 1)

Yes

Yes

No

No

(3d) n,T,B,V

Start (L-H) Monitor

(2d) n,T, B,V

XGC stops

At each Update kineticinformation (, D, , etc)

At each check for linear MHD stability

XGC Mesh/Interpolation MHD-L(Linear stability)

N,T

Stable?

XGC Mesh/Interpolation MHD

(xi, vi)

(3d) n,T,Bt

Stable?B healed?

Mesh/Interpolation

(3d) E-V, ,

n,T,V,E,,D,

Orange : Main simulatorBlue: Monitor or Closure AssistantXGC evaluates SOL transport during ELM crash.

V,E,,

Workflow between 5d XGC and 3d MHD (Plan 2)

(xi, vi)

Yes

Yes

No

No

(2d) n,T,(3d) B

E

(3d) N,T,B

(xi, vi)

Start (L-H) Monitor

(2d) N,T,B

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.

ne exp[(1+0)/Te]

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 (BP ~0) Transient accumulation of positive charge

• 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

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 1ib =2 R/vi,

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.

Code Verification of XGC-1 against the analytic neoclassical flow eq in core

ui∥= (cTi/eBp)[kdlogTi/dr –dlog pi/dr-(e/Ti)d/dr]

N

Ui|| dTi/dr0<1%

t=14ib

VExB

dTi/dr0

Verification of XGC-1 against the analytic neoclassical flow eq in core

ui∥= (cTi/eBp)[kdlogTi/dr –dlog pi/dr-(e/Ti)d/dr]

k=0.5

Banana: k=1.17Plateau: k=-0.5Collisional: k=-2.1

1 for Ti=1 keV n=51019m-3

0.8 0.90.7

0

-30

Er(kV/m)

t=7.5ib

Density profile

n ~ 1cm

Does not dropas in XGC-0

Comparison of o between mi/me = 100 and 1000 at t=1I

100 is reasonable

Similar<0 in pedestal and >0 in scrape-off

mi/me =100 mi/me =1000

Parallel plasma flow at t=1i

(mi/me = 100, shaved off at 1x104 m/s )

t=1i

t=4i

V|| 104 m/s

Sheared parallel flowin the inner divertor

counter-current flow near separatrix co-current flow in scrape-off

t=4i

V|| <0 in front of the inner divertor does not meana plasma flow out of the material wall becauseof the ExB flow to the pump.

ExB

ExB

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

0.92 0.94 0.96 0.98 1.00-5000

0

5000

10000

15000

20000

25000

30000

35000

ve

locity

normalized psi

5.99tau 13.5995tau 23.1995tau 33.5995tau

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

Wall(eV)

N

V||>0V||<0

Potential profile roughly agrees with the flow direction in the edge

ExB rotation opposes the V|| effect:VExB is to inner divertor (co-IP) in the near and

to outer divertor (counter) in the far scrape-off. Which one is more important?

t=4i

ExB

In neoclassical edge plasma, the poloidal rotaton from ExB and p dominates over (BP/BT) V||.Is the diamagnetic flow real in the edge (strongergyroviscous cancellation?)

t=1I

Forward B

Reversed BT and IP

(VB away from X-point)

t=1I

Backward B

t=1I

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

Reversed BT and IP

V||VExB

Towardouter divertor

Towardinner divertor

Weak ExB

V||

Reversed BT and IP

V|| near separatrix (blue) is toward the inner divertor, but ExB?

VExB near sepatrix istoward outer divertor,connecting to the awayVExB flow in the scrape-off.

Cartoon flow diagram in the neoclassical edge

1 keV ion transport at DA~10m2/s over edge Potential hill

No potential hill

With an H-mode type potential hill

Time evolution of an inner-divertor lost orbitunder ’’ < 0 and D=10 m2/s

D=10 m2/s

ErxB Shearing increases with Ti (ped) (from XGC-0)

Ti=0.5 keV

1 keV

X-loss

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

Collisions in a PIC code• PIC method has an excellent v-space resolution of neoclassic

al 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, XG

C uses very frequent collision operations over extended cells (tc 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 tc - Gridless FP (E. Yoon-CS Chang),

- On Grid (F. Hinton, Lattice-Boltzman), (S. parker, 89) (Albreight, et al, 03),

/4

L

100,000 particles 10,000 particlesBinary Monte Carlo Collisions (vector)

real    74m11.531s 0m 33.788suser   74m11.490s 0m 33.766ssys     0m 0.020s 0m 0.008s

Fokker-Planck Weight Collisions (about the same)real    0m 2.728s 0m 2.609suser    0m 2.276s 0m 2.180ssys   0m 0.152s 0m 0.144s

Computing time comparison between two nonlinear PIC collision schemes

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 r

eal 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).

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.

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 fe at a greater t time step?