Edge plasma physics – a bridge between several disciplines

Edge plasma physics – a bridge between several disciplines

Ralf Schneider

IPP-Teilinstitut Greifswald, EURATOM Association, Wendelsteinstraße 1, D-17491 Greifswald, Germany

Max-Planck-Institut für Plasmaphysik, EURATOM Association

Ralf Schneider

and K. Matyash, N. McTaggart, M. Warrier, X. Bonnin, A. Runov, M. Borchardt, J. Riemann, A. Mutzke, H. Leyh,

D. Coster, W. Eckstein, R. Dohmen

and many other colleagues from USA, Europe and Japan

Strongly non-linear parallel heat conduction by Coulomb collisions:

Extreme anisotropy:

25

|| T

74|| 1010


Magnetic confinement

Can we manage the power load at the plates?

Development of computational tools to model this power loading.

Estimate of power load:

EX

heat

Rn

PQ

22

2

7 35 MWmQ XW !


Basic question


Plasma-edge physics


Length scales

Carbon deposition in divertor regions of JET and ASDEX UPGRADE

Carbon deposition in divertor regions of JET and ASDEX UPGRADE

JET JET

ASDEX UPGRADE

ASDEX UPGRADE

Achim von Keudell (IPP, Garching) V. Rohde (IPP,

Garching)

Paul Coad (JET)

Major topics: tritium codeposition

chemical erosion


Diffusion in graphite


Diffusion in graphite

Internal Structure of Graphite

Granule sizes ~ microns

Void sizes ~ 0.1 microns

Crystallite sizes ~ 50-100 Ångstroms

Micro-void sizes ~ 5-10 Ångstroms

Multi-scale problem in space (1cm to Ångstroms) and time (pico-seconds to seconds)


Molecular dynamics – HCParcas code

Developed by Kai Nordlund, Accelarator laboratory, University of Helsinki

- Hydrogen in perfect crystal graphite – 960 atoms

- Brenner potential, Nordlund range interaction

- Berendsen thermostat, 150K to 900K for 100ps

- Periodic boundary conditions


Molecular dynamics – Simulation at 150K, 900K

150K 900K


Molecular dynamics results

Two diffusion channels

No diffusion across graphene layers (150K – 900K)

Lévy flights?

Non-Arrhenius temperature dependence


Molecular dynamic results

Assume:- Poisson process (assigns real time to the jumps)- The jumps are not correlated

0 = Jump attempt frequency (s-1)Em = Migration Energy (eV)T = Trapped species temperature (K)


Kinetic Monte Carlo - description

BKL algorithm (residence time algorithm A.B. Bortz, M.H. Kalos, J.L. Lebowitz, J. Comp. Phys. 17 (1975) 10Theoretical foundations of dynamical Monte Carlo simulations, K.A. Fichthorn and W.H. Weinberg, J. Chem. Phys. 95 (2) (1991) 1090-1096


KMC (DiG) results

K.L. Wilson et al., Trapping, detrapping and release of implanted hydrogen isotopes, Nucl. Fusion 1: 31-50 Suppl. S 1991

- Strong dependenceon void sizes and not on void fraction

- Saturated H (Tanabe) 0~105s-1 and step sizes ~1Å

TRIM, TRIDYN: much faster than MD (simplified physics)

- very good match of physical sputtering- dynamical changes of surface

composition


Binary collision approximation

ne ~ 109-1010 cm-3

nn ~ 1015 -1016 cm-3

fRF = 13.56 MHz potential

ne = 1010 cm-3, nH2 = 9.2·1014 cm-3,

nCH4 = 7·1014 cm-3, p = 0.085 Torr (11 Pa)

Model system for chemical sputtering: methane plasma(2DX3DV PICMCC multispecies)

Collaboration with IEP5, Bochum University (Ivonne Möller)


PIC simulation: RF capacitive discharge

CH4+ ion energy distributionelectron and CH4

+ ion density

Electrons reach electrode only during sheaths collapse

Energetic ions at the wall dueto acceleration in the sheath


PIC simulation: RF capacitive discharge

Lower electrode

Negative charge due to higherelectron mobility

Levitation in strong sheathelectric field


Dusty (complex) plasmas


PIC simulation: Plasma crystal - full 3D!

Quasi - ordered 3D structure

Top view

electric thrusters: exhaust velocity larger than in conventional chemical systems --> much lower mass of propellant

exhaust

cathode

anode(neutral

propellant)

stationary plasma thruster(electron closed drift or Morozov type)


Plasma thruster SPT-100

jexB forces toward the exhaust producing the thrust

radial B-field: e-confined; e-impact ionization increasedpositive ions not confined; accelerated by E field

SPT-100 parameters

dimensions: Rin=30 mm, Rout=50 mm, L=25 m

mass flow rate and power: dm/dt=5 mg/s, P=300W

discharge parameters: Bmax=200 G, V=300 V, Id=3.2

propulsion performances: Isp=1600 s, T=40 mN, T=0.33

Computational model parameters- Geometrical reducing factor: f=0.2- Grid points: 50x40- Cell size: x=3D

- Time step: t=p-1/3

- Weight of macroparticle: wp=105, wN=107

- Number of macroparticles: N=105

- Number of time step to reach staedy state: Nt=105

- Computational time: 30 hh on 2.5 Ghz

- secondary electrons emitted from the wall (BN, Al2O3, SiO2): probabilistic model - all collisions included- ion-wall sputtering: TRIDYN- geometrical scaling: constant Knudsen (/L) and Larmor (rL/L) parameters

electron density

Francesco Taccogna, University of Bari


2D-3D axisymmetric fully kinetic PIC model

electron density

Francesco Taccogna, University of Bari


2D-3D axisymmetric fully kinetic PIC model

potential


Divertors

Tokamak Stellarator (W 7-X)

pump

pump

Plasma core

pump

B2-Eirene, UEDGE, …

Finite volume codes for mixed conduction convection problems

- Neutral physics (momentum losses, volume recombination, operational scenarios, geometry optimization)- Impurities (radiation, flows)


2D fluid codes


Molecular physics


Molecular physics: quite high recombination rates


Molecular physics

Inclusion of drifts and currents: flows, radial electric field

Radial electric field:Closed field lines – neoclassicalOpen field lines – SOL physics

Radial electric field shear layer close to separatrix (flow pattern)

Potential


2D fluid codes

Plasma

Divertor


Divertor Structures


Plasma Wendelstein 7-X

0

3D effects in stellarators (W7-X)

plasma core (non-ergodic)

ergodic region

island (non-ergodic)

Divertors


3D transport in the plasma edge

Scrape Off Layer

Plasma core

Wall

Parallel direction

Rad

ial d

irec

tio

n

Ergodic region

|| flr D

Enhancement of radial transport

due to contribution from parallel transport

Rechester Rosenbluth, Physical Review Letters, 1978

Electron temperature

r


Transport in an ergodic region

Kolmogorov length LK is a measure of field line ergodicity

0

1log

SLK

10

S

exponential divergence

Typical value in W7-X : LK = 10 – 30 m


Kolmogorov length

central cut

backward cut

forward cut

x1

x2

x3

333231

232221

131211

ggg

ggg

ggg

g ij

One coordinate aligned with the magnetic field to minimize numerical diffusion

Area is conserved

Use a full metric tensor

Local system shorter than Kolmogorov length to handle ergodicity


Local magnetic coordinate system

1) Optimized mesh (finite-difference scheme)

/10 1

,100 ,2 ,

24||

||||

||

smmm

NRNLL

numerics

2) Monte-Carlo combined with InterpolatedCell Mapping

High accuracy transformation of theperpendicular coordinates of a particle

(mapping between cuts) needed!(bicubic spline interpolation)

Solutions:

Problem: numerical diffusion induced by interpolation on the interface


Local magnetic coordinate system

Field line tracing code

Triangulation code Metric coefficients code

Transport code

333231

232221

131211

ggg

ggg

ggg

g ij

Mesh data file

Neighborhood array data fileMetric coefficients data file

Temperature solution

Magnetic field configuration data file

Mesh optimization

1

2

3

5 4

6

7


Computational process


3D solution for W7-X

vacuum finite-

Island structures smeared out


Vacuum and finite solutions on a cut

Normalized field line length

T (

eV)

Ergodic effects lead to 3D modulation of long open field lines

Cascading of energy from ergodic to open field lines


W7-X finite case

Feeding fluxes determined by field line length

No power load problem for W7-X

Parallel flux density

Length of open field line (m)

Flu

x d

ensi

ty (

MW

/m2 )

Power load )sin(12||

dx

TTQ

Length of open field line (m)

Vacuum case

Finite β case

Engineering limit

Vacuum case

Finite β case

Flu

x d

ensi

ty (

MW

/m2 )


Power loading on the divertor plates

Complex multi-scale physics requires complex computational tools


Summary

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Edge plasma physics – a bridge between several disciplines

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