XGC gyrokinetic particle simulation of edge plasma

C.S. Changa and the CPESb team

aCourant Institute of Mathematical Sciences, NYUbSciDAC Fusion Simulation Prototype Center for Plasma Edge Simulation

IEA Edge workshop, 11-13 Sept. 2006, Krakow, Poland

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

XGC Development RoadmapFull-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

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

Bananadynamics

Jr = r(Er-Er0)Jloss+Jreturn=0

Electron contributionto macroscopic jr is assumed to be small= validation of NC equil.

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

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).

Sources of co-rotation in pedestal

Asymmetric excursionof hot passing ions from pedestal top due to X-pt

Loss of counter travelingBanana ions

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

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.

>=-4nimic2KNC<||2/B2>/t + 4<Jext >

KNC~102

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

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

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

Simulation

Analytic

Er(V/m)t=30ib

k=k(c)

=0’=0

Conventional neoclassical vpol-v|| relation Breaks down in edge pedestal

Er

1

At 10 cm above the X-point in D3D• Green: without • Red: enhanced loss by

after 4.5x10-4 sec(several toroidal

transit times)

Enhanced loss hole by fluctuating (from XGC)(50 eV, 100 kHz, m=360, n=20)

Interplay between 5Dneoclassical and turbulence

Ku and Chang, PoP 11, 5626 (2004)

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

Experimental evidences of anisotropic non-Maxwellian edge ions

(K. Burrell, APS 2003)

Edge Er is usually inferred from ZiniEr = rp – VxB.Inaccuracy due to (p)r rp ???

K. Burrell, 2003

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

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

Ln ~ 1cm

Densitypedestal

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 ~ 1cmGuiding centerdensities

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 =2R/vi (shorter for full-f and longer for delta-f): Long in a/vi time.

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

100 is reasonable (10 was no good)

(Similar solutions)<0 in pedestal and >0 in scrape-off

mi/me =100 mi/me =1000

Parallel plasma flow at t=1 and 4ib

(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 Co-current flow at pedestal top

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

Strongly sheared V|| <0 around separatrix, but >0 in the (far) scrape-off.

V||, DIII-D

V||

N

1

Wall(eV)

N

V||>0V||<0

ExB profile without p flow roughly agrees with the flow direction in the edge

Sign of strong off-diagonal P component?(stronger gyroviscous cancellation?)

Edge Er is usually inferred from ZiniEr = rp – VxB.Inaccuracy due to (p)r rp ???

K. Burrell, 2003

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?

Strongly sheared ExB rotation in the pedestal

t=4i

ExB

Cartoon poloidal flow diagram in the edge

Wider pedestal Stronger V||>0 in scrape-off, Weaker V|| <0 near separatrix.

V||

N

V||, DIII-D

V||

N

1

Wider pedestal Steeper pedestal

Sharp V|| (and ExB) shearingin H layer

Weak V|| (and ExB) shearingin H layer

0

1

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

V||>0 source

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

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

M3D equilibrium and linear simulationsnew equilibrium from eqdsk, XGC profiles

Equilibriumpoloidal magnetic flux

Linear perturbed poloidal magnetic flux, n = 9

Linear perturbed electrostatic potential

At each Update kineticinformation (, D, ,etc),In phase 2

At each check for linear MHD stability

M3D nonlinear simulation pressure evolution

T = 37 Pressure relaxing

T = 25ELM near maximumamplitude

Initial pressureWith pedestal

Pressure profile evolution

T=0

T=25

T=37

Pressure profile p(R) relaxes toward a state with less pressure pedestal. P(R) is pressurealong major radius (not averaged).

Density n(R) profile evolution

T=0

T=25

T=37

T=0 – initial density pedestal at R = 0.5T=25 – ELM carries density across separatrixT=37 – density relaxes toward new profile

Temperature T(R) profiles

T=0

T=25

T=37

Toroidal current density J(R) evolution

T=0T=37

T=25

T=0 – bootstrap current peak is evident at R = 0.5T=25 – ELM causes current on open field linesT=37 – current relaxes toward new profile

XGC-ET Mesh/Interpolation M3D-L(Linear stability)

P,P||

Stable?

XGC-ET Mesh/Interpolation M3D

(xi, vi), E

E,Bt

Stable?B healed?

Mesh/Interpolation

P,P||, ,

N,T,V,E,,D

Blue: Pedestal buildup stageOrange : ELM crash stage

V,E,,

XGC-M3D workflow

(xi, vi)

(xi, vi)

Yes

Yes

No

No

E,B

E

E,B

(xi, vi)

Start (L-H)

Mesh/Interpolation servicesevaluate macroscopic quantities,too.

Conclusions and Discussions• In the edge, we need to abandon many of the conventional neoclas

sical 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 rotat

ion profiles are important.