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XGC gyrokinetic particle simulation of edge plasma

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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

- 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

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

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 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 (Bi, but also the Er &

rotation physics do not apply to the edge.

Ampere’s law in the plasma core

KNC~102

>=-4nimic2KNC<||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. 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=30ib

k=k(c)

Simulation

Er(V/m)

’=0

=0

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

Comparison of along ion root (Bo between

mi/me = 100 and 1000 at t=1Ib

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 (Bi

t=4i

Parallel plasma flow at t=1 and 4ib

(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 (Bi

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?

Cartoon poloidal flow diagram in the edge along ion root (B

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 along ion root (B

Black: developed, Red: to be developed

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 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 along ion root (Bpressure evolution

T = 25

ELM near maximum

amplitude

T = 37

Pressure relaxing

Initial pressure

With pedestal

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 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

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 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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