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Max-Planck-Institut für Plasmaphysik, EURATOM Association
Edge plasma physics –
a bridge between several disciplines
Ralf Schneider
and K. Matyash, N. McTaggart, M. Warrier, X. Bonnin,
A. Runov, M. Borchardt,
Riemann, A. Mutzke, H. Leyh,
Ralf J.
Schneider
D. Coster, W. Eckstein, R. Dohmen
and many other colleagues from USA, Europe and Japan
IPP-Teilinstitut Greifswald, EURATOM Association, Wendelsteinstraße 1, D-17491 Greifswald,
Germany
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Magnetic confinement
Strongly non-linear parallel heat
conduction by Coulomb collisions:
Extreme anisotropy:
 ||  T
||  10 10  
4
7
5
2
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Basic question
Can we manage the power load at the
plates?
Development of computational tools to
model this power loading.
Estimate of power load:
Pheat
Q 
2nX  2R   E
QW 7 X  35MWm2
!
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Plasma-edge physics
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Length scales
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Diffusion in graphite
Carbon deposition in divertor regions of JET and
ASDEX UPGRADE
Major topics: tritium codeposition
chemical erosion
JET
Paul Coad
(JET)
ASDEX
UPGRADE
Achim von Keudell (IPP,
Garching)
V. Rohde (IPP,
Max-Planck-Institut für Plasmaphysik, EURATOM Association
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)
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Molecular dynamics – HCParcas code
- Hydrogen in perfect crystal graphite –
960 atoms
- Brenner potential, Nordlund range
interaction
- Berendsen thermostat, 150K to 900K
for 100ps
- Periodic boundary conditions
Developed by Kai Nordlund, Accelarator laboratory, University of Helsinki
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Molecular dynamics – Simulation at 150K, 900K
150K
900K
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Molecular dynamics results
Two diffusion channels
No diffusion across graphene layers (150K – 900K)
Lévy flights?
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Molecular dynamic results
Non-Arrhenius temperature dependence
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Kinetic Monte Carlo - description
0 = Jump attempt frequency (s-1)
Em = Migration Energy (eV)
T = Trapped species temperature (K)
Assume:
- Poisson process (assigns
real time to the jumps)
- The jumps are not
correlated
BKL algorithm (residence time algorithm A.B. Bortz, M.H. Kalos, J.L. Lebowitz, J. Comp. Phys.
17 (1975) 10
Theoretical foundations of dynamical Monte Carlo simulations, K.A. Fichthorn and W.H.
Weinberg, J. Chem. Phys. 95 (2) (1991) 1090-1096
Max-Planck-Institut für Plasmaphysik, EURATOM Association
KMC (DiG) results
- Strong dependence
on void sizes and
not on void fraction
- Saturated H (Tanabe)
0~105s-1 and step
sizes ~1Å
K.L. Wilson et al., Trapping, detrapping and release of implanted hydrogen isotopes, Nucl.
Fusion 1: 31-50 Suppl. S 1991
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Binary collision approximation
TRIM, TRIDYN: much faster than MD (simplified physics)
- very good match of physical
sputtering
- dynamical changes of surface
composition
Max-Planck-Institut für Plasmaphysik, EURATOM Association
PIC simulation: RF capacitive discharge
Model system for chemical sputtering: methane plasma
(2DX3DV PICMCC multispecies)
Collaboration with IEP5, Bochum University (Ivonne Möller)
ne ~ 109-1010 cm-3
nn ~ 1015 -1016 cm-3
fRF = 13.56 MHz
ne = 1010 cm-3, nH2 = 9.2·1014 cm-3,
nCH4 = 7·1014 cm-3, p = 0.085 Torr (11 Pa)
potential
Max-Planck-Institut für Plasmaphysik, EURATOM Association
PIC simulation: RF capacitive discharge
electron and CH4+ ion density
Electrons reach electrode only
during sheaths collapse
CH4+ ion energy distribution
Energetic ions at the wall due
to acceleration in the sheath
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Dusty (complex) plasmas
Lower electrode
Negative charge due to higher
electron mobility
Levitation in strong sheath
electric field
Max-Planck-Institut für Plasmaphysik, EURATOM Association
PIC simulation: Plasma crystal - full 3D!
Top view
Quasi - ordered 3D structure
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Plasma thruster SPT-100
electric thrusters: exhaust velocity larger than in
conventional chemical systems --> much lower mass of
propellant
stationary plasma thruster(electron
closed drift or Morozov type)
radial B-field: e-confined; e-impact
ionization increased
positive ions not confined; accelerated
by E field
anode
jexB forces toward the exhaust
(neutral
producing the thrust
propellant)
exhaust
SPT-100 parameters
dimensions:
mass flow rate and power:
Rin=30 mm, Rout=50 mm, L=25 m
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
cathode
Max-Planck-Institut für Plasmaphysik, EURATOM Association
2D-3D axisymmetric fully kinetic PIC model
- 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
Computational model parameters
- Geometrical reducing factor:
f=0.2
- Grid points:
50x40
- Cell size:
x=3D
- 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
electron density
Francesco Taccogna, University of
Bari
Max-Planck-Institut für Plasmaphysik, EURATOM Association
2D-3D axisymmetric fully kinetic PIC model
electron density
potential
Francesco Taccogna, University of
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Divertors
Tokamak
Stellarator (W 7-X)
pump
Plasma core
pump
pump
Max-Planck-Institut für Plasmaphysik, EURATOM Association
2D fluid codes
B2-Eirene, UEDGE, …
Finite volume codes for mixed
conduction convection problems
- Neutral physics (momentum losses,
volume recombination, operational
scenarios, geometry optimization)
- Impurities (radiation, flows)
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Molecular physics
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Molecular physics: quite high recombination rates
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Molecular physics
Max-Planck-Institut für Plasmaphysik, EURATOM Association
2D fluid codes
Inclusion of drifts and currents: flows, radial electric field
Potential
Radial electric field:
Closed field lines – neoclassical
Open field lines – SOL physics
Radial electric field shear layer
close to separatrix (flow pattern)
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Divertor Structures
Divertor
Plasma
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Plasma Wendelstein 7-X
Max-Planck-Institut für Plasmaphysik, EURATOM Association
3D transport in the plasma edge
3D effects in stellarators (W7-X)
ergodic
region
plasma
core
(nonergodic)
island
(nonergodic)
  0
Divertors
Max-Planck-Institut für Plasmaphysik, EURATOM Association
r
Transport in an ergodic region
Wall
Radial direction
Scrape Off
Layer
Enhancement of
radial transport
due to
contribution from
parallel transport
Ergodic
region
 r  D fl ||
Plasma
core
Parallel direction
Electron
temperature
Rechester Rosenbluth, Physical Review Letters,
1978
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Kolmogorov length
Kolmogorov length LK is a measure of field line ergodicity
S
0
exponential divergence
1
S
LK 
 1 
log 
 0 
Typical value in W7-X : LK = 10 – 30 m
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Local magnetic coordinate system
forward cut
Local system shorter than Kolmogorov
length to handle ergodicity
x2
One coordinate aligned with the magnetic
field to minimize numerical diffusion
x3
x1
central cut
backward cut
Area is conserved
Use a full metric tensor
 g 11 g 12 g 13 
 21 22 23 
ij
g  g g g 
 g 31 g 32 g 33 


Max-Planck-Institut für Plasmaphysik, EURATOM Association
Local magnetic coordinate system
Problem: numerical diffusion induced by interpolation on the interface
Solutions:
1) Optimized mesh (finite-difference scheme) 2) Monte-Carlo combined with Interpolated
Cell Mapping
  L||
  1m m

, L||  2RN , N  100,
 ||
  || numerics  104 m 2 / s
High accuracy transformation of the
perpendicular coordinates of a particle
(mapping between cuts) needed!
(bicubic spline interpolation)
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Computational process
1
Mesh
optimization
2
Field line tracing code
Magnetic field
configuration data file
3
5
4
Metric coefficients code
Triangulation code
Mesh data file
 g 11 g 12 g 13 


g ij   g 21 g 22 g 23 
 g 31 g 32 g 33 


Metric coefficients data file
6
Transport code
7
Neighborhood array data file
Temperature
solution
Max-Planck-Institut für Plasmaphysik, EURATOM Association
3D solution for W7-X
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Vacuum and finite  solutions on a cut
vacuum
finite-
Island structures smeared
out
Max-Planck-Institut für Plasmaphysik, EURATOM Association
T (eV)
W7-X finite  case
Normalized field line length
Ergodic effects lead to 3D modulation
of long open field lines
Cascading of energy from
ergodic to open field lines
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Power loading on the divertor plates
Power load
Vacuum case
Finite β case
Engineering limit
Length of open field line (m)
Feeding fluxes determined
by field line length
Flux density (MW/m2)
Flux density (MW/m2)
Parallel flux density
Q  ||
T2  T1
sin( )
dx
Vacuum case
Finite β case
Length of open field line (m)
No power load
problem for W7-X
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Summary
Complex multi-scale physics requires complex computational tools