IEA Edge workshop, 11-13 Sept. 2006, Krakow, Poland
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IEA Edge workshop, 11-13 Sept. 2006, Krakow, Poland. XGC gyrokinetic particle simulation of edge plasma. C.S. Chang a and the CPES b team a Courant Institute of Mathematical Sciences, NYU b SciDAC Fusion Simulation Prototype C enter for P lasma E dge S imulation. Contents.

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Xgc gyrokinetic particle simulation of edge plasma

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


Contents

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 roadmap

XGC Development Roadmap

Black: Achieved, Blue: in progress, Red: to be developed


Xgc gyrokinetic particle simulation of edge plasma

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.


Xgc gyrokinetic particle simulation of edge plasma

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

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).


Xgc gyrokinetic particle simulation of edge plasma

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


Xgc gyrokinetic particle simulation of edge plasma

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.


Neoclassical polarization drift de r dt 0 case is shown

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


Xgc gyrokinetic particle simulation of edge plasma

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


Xgc gyrokinetic particle simulation of edge plasma

Er

1

Conventional neoclassical vpol-v|| relation

Breaks down in edge pedestal


Xgc gyrokinetic particle simulation of edge plasma

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)


Xgc gyrokinetic particle simulation of edge plasma

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]


Xgc gyrokinetic particle simulation of edge plasma

Experimental evidences of anisotropic

non-Maxwellian edge ions

(K. Burrell, APS 2003)


Xgc gyrokinetic particle simulation of edge plasma

Edge Er is usually inferred from ZiniEr = rp – VxB.

Inaccuracy due to (p)r  rp ???

K. Burrell, 2003


Xgc gyrokinetic particle simulation of edge plasma

  • 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


Xgc gyrokinetic particle simulation of edge plasma

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


Xgc gyrokinetic particle simulation of edge plasma

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.


Xgc gyrokinetic particle simulation of edge plasma

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.


Xgc gyrokinetic particle simulation of edge plasma

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


Xgc gyrokinetic particle simulation of edge plasma

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


Xgc gyrokinetic particle simulation of edge plasma

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


Xgc gyrokinetic particle simulation of edge plasma

V||

V||, DIII-D

1

N

Strongly sheared V|| <0 around separatrix,

but >0 in the (far) scrape-off.


Xgc gyrokinetic particle simulation of edge plasma

  • 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


Xgc gyrokinetic particle simulation of edge plasma

Edge Er is usually inferred from ZiniEr = rp – VxB.

Inaccuracy due to (p)r  rp ???

K. Burrell, 2003


Xgc gyrokinetic particle simulation of edge plasma

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?


Xgc gyrokinetic particle simulation of edge plasma

t=4i

Strongly sheared ExB rotation in the pedestal

ExB


Xgc gyrokinetic particle simulation of edge plasma

Cartoon poloidal flow diagram in the edge


Xgc gyrokinetic particle simulation of edge plasma

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


Xgc gyrokinetic particle simulation of edge plasma

V|| shows modified behavior with strong neutral collisions:

V||>0 becomes throughout the whole edge (less shear)

V||>0 source


Xgc mhd coupling plan

XGC-MHD Coupling Plan

Black: developed, Red: to be developed


Code coupling

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 simulations new equilibrium from eqdsk xgc profiles

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


Xgc gyrokinetic particle simulation of edge plasma

At each check for

linear MHD stability

At each Update kinetic

information (, D, ,etc),

In phase 2


M3d nonlinear simulation pressure evolution

M3D nonlinear simulationpressure evolution

T = 25

ELM near maximum

amplitude

T = 37

Pressure relaxing

Initial pressure

With pedestal


Pressure profile evolution

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).


Density n r profile evolution

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


Temperature t r profiles

Temperature T(R) profiles

T=0

T=25

T=37


Toroidal current density j r evolution

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


Xgc gyrokinetic particle simulation of edge plasma

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.


Conclusions and discussions

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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