Max-Planck-Institut fr Plasmaphysik, EURATOM Association
Computational Plasmaphysics Ralf Schneider Max-Planck-Institut fr
Plasmaphysik, Euratom-IPP Association, Wendelsteinstra e 1, D-17491
Greifswald, Germany
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Max-Planck-Institut fr Plasmaphysik, EURATOM Association
Computational physics Why numerical methods? Complexity of
equations Example Simulation of experiments To test validity of
theory To gain an idea of experimental performance
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Max-Planck-Institut fr Plasmaphysik, EURATOM Association
Computational physics
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The Computational Stellarator W7-X Max-Planck-Institut fr
Plasmaphysik, EURATOM Association
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Max-Planck-Institut fr Plasmaphysik, EURATOM Association Plasma
Wendelstein 7-X
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slow drift of guiding center Max-Planck-Institut fr
Plasmaphysik, EURATOM Association
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Optimized stellarator
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Plasma in a computational model 10 Variables: densities,
velocities, temperatures 10 billion grid points 100 million time
steps 100 FL oating P oint OP erations /sec / timestep / gridpoint
or 1 billion teraflop/sec Cray T3E with 784 PE (ca. 75 gigaflop) or
500 years computing NOT VERY REALISTIC Max-Planck-Institut fr
Plasmaphysik, EURATOM Association
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Plasma: Max-Planck-Institut fr Plasmaphysik, EURATOM
Association
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Particle aspect of plasma dominates Max-Planck-Institut fr
Plasmaphysik, EURATOM Association
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Plasma is treated as one fluid with infinite conductivity
Max-Planck-Institut fr Plasmaphysik, EURATOM Association
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MHD is basis for all equilibrium calculations
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Existence in 3D ? Theoretical ? Experimental ? Accessible only
by computational models but not before 1975 thus Optimization
started with IBM360/91 W7-AS Design 1978 Max-Planck-Institut fr
Plasmaphysik, EURATOM Association MHD, equilibrium
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p constant on (nested) surfaces labelled by s Poloidal and
toroidal fluxes are invariant functions, together with m(s) the
mass distribution Stationary states of plasma energy (fixed
boundary) MHD force balance r and z periodic functions ( Fourier
series) Hybrid finite elements in s, (artificial) Time-like
iteration Max-Planck-Institut fr Plasmaphysik, EURATOM Association
Equilibria, VMEC
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Max-Planck-Institut fr Plasmaphysik, EURATOM Association
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NESTOR / NESCOIL codes Iterative combination of VMEC &
NESCOIL allows free-boundary computations NEMEC Max-Planck-Institut
fr Plasmaphysik, EURATOM Association Vacuum fields - free-boundary
- coils Boundary Value Problems, Greens Function Last closed
magnetic surface (lcms) defines completely interior plasma
properties Search for external current distributions (i.e. coils)
producing a vacuum field B with boundary conditions on the lcms (n
exterior normal)
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Max-Planck-Institut fr Plasmaphysik, EURATOM Association
VMEC
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Max-Planck-Institut fr Plasmaphysik, EURATOM Association Plasma
configuration given calculate coils to produce it
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Max-Planck-Institut fr Plasmaphysik, EURATOM Association Coils
1-50
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Max-Planck-Institut fr Plasmaphysik, EURATOM Association Is a
given plasma configuration stable against small pertubations? Find
ways to prevent instabilities
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Max-Planck-Institut fr Plasmaphysik, EURATOM Association
Tokamak operation limited by MHD instabilities
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Necessary to design equilibrium with good confinement
properties
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Max-Planck-Institut fr Plasmaphysik, EURATOM Association
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Speedup of equilibrium codes due to Peak speed of cpu: 10 fold
IBM 360/91 Cray-1S 1980 (same parameters) 12 fold Cray-1S
YMP-464(4cpus) 1988 16 fold Cray-1S J916 (16) 1992 28 fold Cray-1S
SX4(2) 1996 500 fold Cray-1S T3E-600(784) 1998 New Codes: 24 fold
BETA MOMCON/FIT 1980 (same equilibrium) 50 fold MOMCON VMEC 1985 30
fold VMEC VMEC2 1989 Better algorithms gave a speedup of around
30.000 ! New hardware ``only`` 5.000... Max-Planck-Institut fr
Plasmaphysik, EURATOM Association Computational Remarks
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Max-Planck-Institut fr Plasmaphysik, EURATOM Association
Turbulence suppression
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Max-Planck-Institut fr Plasmaphysik, EURATOM Association
Turbulence suppression
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Max-Planck-Institut fr Plasmaphysik, EURATOM Association
Gyrokinetic turbulence simulations
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Max-Planck-Institut fr Plasmaphysik, EURATOM Association
Plasma-edge physics
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Max-Planck-Institut fr Plasmaphysik, EURATOM Association Length
scales sputtered and backscattered species and fluxes Plasma-wall
interaction Molecular dynamics Binary collision approximation
Kinetic Monte Carlo Kinetic model Fluid model impinging particle
and energy fluxes
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Carbon deposition in divertor regions of JET and ASDEX UPGRADE
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 fr Plasmaphysik,
EURATOM Association Diffusion in graphite
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Max-Planck-Institut fr Plasmaphysik, EURATOM Association
Diffusion in graphite Internal Structure of Graphite Granule sizes
~ microns Void sizes ~ 0.1 microns Crystallite sizes ~ 50-100
ngstroms Micro-void sizes ~ 5-10 ngstroms Multi-scale problem in
space (1cm to ngstroms) and time (pico-seconds to seconds)
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Max-Planck-Institut fr Plasmaphysik, EURATOM Association
Multi-scale ansatz Mikroscales MC Mesoscales KMC Macroscales KMC
and Monte Carlo Diffusion (MCD)
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Max-Planck-Institut fr 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
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Equilibration of pressure with time Max-Planck-Institut fr
Plasmaphysik, EURATOM Association Time variation of pressure
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Max-Planck-Institut fr Plasmaphysik, EURATOM Association
Molecular dynamics Simulation at 150K, 900K 150K 900K
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Max-Planck-Institut fr Plasmaphysik, EURATOM Association
Molecular dynamics results two diffusion channels no diffusion
across graphene layers (150K 900K) Lvy flights?
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Non-Arrhenius temperature dependence Max-Planck-Institut fr
Plasmaphysik, EURATOM Association Molecular dynamic results
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Max-Planck-Institut fr Plasmaphysik, EURATOM Association
Kinetic Monte Carlo basic idea 0 = jump attempt frequency (s -1 ) E
m = migration energy (eV) T = trapped species temperature (K)
Assumptions: - Poisson process (assigns real time to the jumps) -
jumps are not correlated
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Max-Planck-Institut fr Plasmaphysik, EURATOM Association KMC
results for transgranular diffusion - strong dependence on void
sizes and not on void fraction - saturated H (Tanabe) 0 ~10 5 s -1
and step sizes ~1 (QM?)
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Max-Planck-Institut fr Plasmaphysik, EURATOM Association
Multiscale model Activation energies: trapping-detrapping 2.7 eV
desorption 1.9 eV surface diffusion 0.9 eV, jump attempt frequency,
jump step length for entering the surface for a solute H atom 2.7
eV 0 ~10 13 s -1 ~35 porous graphite structure
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desorption starts between 900 K and 1200 K Max-Planck-Institut
fr Plasmaphysik, EURATOM Association Multiscale model -
results
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Max-Planck-Institut fr Plasmaphysik, EURATOM Association
Multiscale model 900 K, 0.1 ms
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Max-Planck-Institut fr Plasmaphysik, EURATOM Association
Multiscale model 1500 K, 0.001 ms
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Max-Planck-Institut fr Plasmaphysik, EURATOM Association
Multiscale model diffusion types adsorption- desorption 1.9 eV
surface diffusion 0.9 eV
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Applications: Low temperature plasmas (methane, RF discharges)
Complex plasmas (plasma crystals) Parasitic plasmas in the divertor
(radiative ionization) Max-Planck-Institut fr Plasmaphysik, EURATOM
Association PIC(Particle-in-cell)-method Principle:
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n e ~ 10 9 -10 10 cm -3 n n ~ 10 15 -10 16 cm -3 f RF = 13.56
MHz potential n e = 10 10 cm -3, n H 2 = 9.210 14 cm -3, n CH 4 =
710 14 cm -3, p = 0.085 Torr (11 Pa) Model system for chemical
sputtering: methane plasma (2DX3DV PICMCC multispecies)
Collaboration with IEP5, Bochum University (Ivonne Mller)
Max-Planck-Institut fr Plasmaphysik, EURATOM Association PIC
simulation: RF capacitive discharge
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CH 4 + ion energy distribution electron and CH 4 + ion density
Electrons reach electrode only during sheaths collapse Energetic
ions at the wall due to acceleration in the sheath
Max-Planck-Institut fr Plasmaphysik, EURATOM Association PIC
simulation: RF capacitive discharge
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Max-Planck-Institut fr Plasmaphysik, EURATOM Association PIC
simulation: RF capacitive discharge electron velocity
distributionelectron-impact ionization rate Energetic electrons
oscillate between sheaths Ionization spread over the bulk
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Max-Planck-Institut fr Plasmaphysik, EURATOM Association PIC
simulation: RF capacitive discharge electron energy probability
function Figure from V.A. Godyak, et al., Phys. Rev. Lett., 65
(1990) 996. Bi-maxwellian distribution due to stochastic
heating
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Lower electrode Negative charge due to higher electron mobility
Levitation in strong sheath electric field Max-Planck-Institut fr
Plasmaphysik, EURATOM Association Dusty (complex) plasmas
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Max-Planck-Institut fr Plasmaphysik, EURATOM Association PIC
simulation: Plasma crystal - full 3D! Quasi - ordered 3D structure
Top view
Thanks!! Ralf Kleiber, Ulrich Schwenn, Volodja Kornilov, Stefan
Sorge Mathias Borchardt, Jrg Riemann, Alex Runov, Xavier Bonnin
Konstantin Matyash, Neil McTaggart, Manoj Warrier, Francesco
Taccogna Andrea Pulss, Andreas Mutzke, Henry Leyh And many
contributions from colleagues all over the world
