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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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


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-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 along ion root (Bedge 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 along ion root (B

Asymmetric excursion

of hot passing ions from

pedestal top due to X-pt

Loss of counter traveling

Banana ions


Conventional knowledge of not only along ion root (B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. along ion root (BdEr/dt <0 case is shown


Verification of XGC-1 along ion root (Bagainst

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


E along ion root (Br

1

Conventional neoclassical vpol-v|| relation

Breaks down in edge pedestal


Enhanced loss hole by fluctuating along ion root (B(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)


f along ion root (Bi0 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]


Experimental evidences of anisotropic along ion root (B

non-Maxwellian edge ions

(K. Burrell, APS 2003)


Edge E along ion root (Br is usually inferred from ZiniEr = rp – VxB.

Inaccuracy due to (p)r  rp ???

K. Burrell, 2003


  • XGC-1 Code along ion root (B

  • 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 along ion root (B

  • 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


Guiding center along ion root (B

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.


Turbulence-averaged edge solutions from XGC along ion root (B

  • 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.


Comparison of along ion root (B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


t=1 along ion root (B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


t=4 along ion root (B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


V along ion root (B||

V||, DIII-D

1

N

Strongly sheared V|| <0 around separatrix,

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


  • ExB profile along ion root (Bwithout 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


Edge E along ion root (Br is usually inferred from ZiniEr = rp – VxB.

Inaccuracy due to (p)r  rp ???

K. Burrell, 2003


In neoclassical edge plasma, the poloidal rotaton along ion root (B

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?


t=4 along ion root (Bi

Strongly sheared ExB rotation in the pedestal

ExB



V along ion root (B||

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


V along ion root (B|| 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 along ion root (B

Black: developed, Red: to be developed


Code coupling
Code coupling along ion root (B

  • 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 simulations along ion root (Bnew equilibrium from eqdsk, XGC profiles

Linear perturbed poloidal magnetic flux, n = 9

Linear perturbed electrostatic potential

Equilibrium

poloidal magnetic flux


At each check for along ion root (B

linear MHD stability

At each Update kinetic

information (, D, ,etc),

In phase 2


M3d nonlinear simulation pressure evolution
M3D nonlinear simulation along ion root (Bpressure evolution

T = 25

ELM near maximum

amplitude

T = 37

Pressure relaxing

Initial pressure

With pedestal


Pressure profile evolution
Pressure profile evolution along ion root (B

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 along ion root (B

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 along ion root (B

T=0

T=25

T=37


Toroidal current density j r evolution
Toroidal current density J(R) evolution along ion root (B

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-M3D workflow along ion root (B

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 along ion root (B

  • 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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