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
Max-Planck-Institut für Plasmaphysik, EURATOM Association
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 !
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Basic question
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
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Diffusion in graphite
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
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
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?
Non-Arrhenius temperature dependence
Max-Planck-Institut für Plasmaphysik, EURATOM Association
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)
Max-Planck-Institut für Plasmaphysik, EURATOM Association
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
Max-Planck-Institut für Plasmaphysik, EURATOM Association
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
Max-Planck-Institut für Plasmaphysik, EURATOM Association
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)
Max-Planck-Institut für Plasmaphysik, EURATOM Association
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
Max-Planck-Institut für Plasmaphysik, EURATOM Association
PIC simulation: RF capacitive discharge
Lower electrode
Negative charge due to higherelectron mobility
Levitation in strong sheathelectric field
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Dusty (complex) plasmas
Max-Planck-Institut für Plasmaphysik, EURATOM Association
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)
Max-Planck-Institut für Plasmaphysik, EURATOM Association
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
Max-Planck-Institut für Plasmaphysik, EURATOM Association
2D-3D axisymmetric fully kinetic PIC model
electron density
Francesco Taccogna, University of Bari
Max-Planck-Institut für Plasmaphysik, EURATOM Association
2D-3D axisymmetric fully kinetic PIC model
potential
Max-Planck-Institut für Plasmaphysik, EURATOM Association
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)
Max-Planck-Institut für Plasmaphysik, EURATOM Association
2D fluid codes
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Molecular physics: quite high recombination rates
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
Max-Planck-Institut für Plasmaphysik, EURATOM Association
2D fluid codes
0
3D effects in stellarators (W7-X)
plasma core (non-ergodic)
ergodic region
island (non-ergodic)
Divertors
Max-Planck-Institut für Plasmaphysik, EURATOM Association
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
Max-Planck-Institut für Plasmaphysik, EURATOM Association
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
Max-Planck-Institut für Plasmaphysik, EURATOM Association
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
Max-Planck-Institut für Plasmaphysik, EURATOM Association
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
Max-Planck-Institut für Plasmaphysik, EURATOM Association
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
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Computational process
vacuum finite-
Island structures smeared out
Max-Planck-Institut für Plasmaphysik, EURATOM Association
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
Max-Planck-Institut für Plasmaphysik, EURATOM Association
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 )
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Power loading on the divertor plates