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Max-Planck-Institut für Plasmaphysik, EURATOM Association

Max-Planck-Institut für Plasmaphysik, EURATOM Association. Computational Plasmaphysics. Ralf Schneider. Max-Planck-Institut für Plasmaphysik, Euratom-IPP Association, Wendelsteinstra  e 1, D-17491 Greifswald, Germany. Max-Planck-Institut für Plasmaphysik, EURATOM Association

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Max-Planck-Institut für Plasmaphysik, EURATOM Association

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  1. Max-Planck-Institut für Plasmaphysik, EURATOM Association Computational Plasmaphysics Ralf Schneider Max-Planck-Institut für Plasmaphysik, Euratom-IPP Association, Wendelsteinstrae 1, D-17491 Greifswald, Germany

  2. Max-Planck-Institut für Plasmaphysik, EURATOM Association Computational physics • Why numerical methods? Complexity of equationsExample Simulation of experiments • To test validity of theory • To gain an idea of experimental performance

  3. Max-Planck-Institut für Plasmaphysik, EURATOM Association Computational physics

  4. Max-Planck-Institut für Plasmaphysik, EURATOM Association The Computational Stellarator W7-X

  5. Max-Planck-Institut für Plasmaphysik, EURATOM Association Plasma Wendelstein 7-X

  6. Max-Planck-Institut für Plasmaphysik, EURATOM Association slow drift of guiding center

  7. Max-Planck-Institut für Plasmaphysik, EURATOM Association Optimized stellarator

  8. Max-Planck-Institut für Plasmaphysik, EURATOM Association Plasma in a computational model • 10 Variables: densities, velocities, temperatures • 10 billion grid points • 100 million time steps • 100 FLoatingPointOPerations/sec / timestep / gridpoint • or 1 billion teraflop/sec • Cray T3E with 784 PE (ca. 75 gigaflop) or500 yearscomputing • NOT VERY REALISTIC

  9. Max-Planck-Institut für Plasmaphysik, EURATOM Association Plasma:

  10. Max-Planck-Institut für Plasmaphysik, EURATOM Association Particle aspect of plasma dominates

  11. Max-Planck-Institut für Plasmaphysik, EURATOM Association Plasma is treated as one fluid with infinite conductivity

  12. Max-Planck-Institut für Plasmaphysik, EURATOM Association

  13. Max-Planck-Institut für Plasmaphysik, EURATOM Association MHD is basis for all equilibrium calculations

  14. Max-Planck-Institut für Plasmaphysik, EURATOM Association

  15. Max-Planck-Institut für Plasmaphysik, EURATOM Association MHD, equilibrium • Existence in 3D ? • Theoretical ? • Experimental ? • Accessible only by computational models • but • not before 1975 • thus Optimization started with IBM360/91 • W7-AS Design 1978

  16. Max-Planck-Institut für Plasmaphysik, EURATOM Association Equilibria, VMEC Stationary states of plasma energy (fixed boundary) MHD force balance pconstant on (nested) surfaces labelled bys Poloidal and toroidal fluxes are invariant functions, together withm(s) the mass distribution • randzperiodic functions (Fourier series) • Hybrid finite elements in s, (artificial) Time-like iteration

  17. Max-Planck-Institut für Plasmaphysik, EURATOM Association

  18. Max-Planck-Institut für 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 fieldBwith boundary conditions on the lcms (n exterior normal) NESTOR / NESCOIL codes Iterative combination ofVMEC & NESCOIL allows free-boundary computationsNEMEC

  19. Max-Planck-Institut für Plasmaphysik, EURATOM Association VMEC

  20. Max-Planck-Institut für Plasmaphysik, EURATOM Association Plasma configuration given calculate coils to produce it

  21. Max-Planck-Institut für Plasmaphysik, EURATOM Association Coils 1-50

  22. Max-Planck-Institut für Plasmaphysik, EURATOM Association Is a given plasma configuration stable against small pertubations? Find ways to prevent instabilities

  23. Max-Planck-Institut für Plasmaphysik, EURATOM Association Tokamak operation limited by MHD instabilities

  24. Max-Planck-Institut für Plasmaphysik, EURATOM Association

  25. Max-Planck-Institut für Plasmaphysik, EURATOM Association Necessary to design equilibrium with „good“ confinement properties

  26. Max-Planck-Institut für Plasmaphysik, EURATOM Association

  27. Max-Planck-Institut für Plasmaphysik, EURATOM Association

  28. Max-Planck-Institut für Plasmaphysik, EURATOM Association Computational Remarks 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 ...

  29. Max-Planck-Institut für Plasmaphysik, EURATOM Association Turbulence suppression

  30. Max-Planck-Institut für Plasmaphysik, EURATOM Association Turbulence suppression

  31. Max-Planck-Institut für Plasmaphysik, EURATOM Association Gyrokinetic turbulence simulations

  32. Max-Planck-Institut für Plasmaphysik, EURATOM Association Plasma-edge physics

  33. Max-Planck-Institut für Plasmaphysik, EURATOM Association Length scales sputtered and backscattered species and fluxes Plasma-wall interaction Kinetic Monte Carlo Fluid model Kinetic model Molecular dynamics Binary collision approximation impinging particle and energy fluxes

  34. 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, Garching)

  35. 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)

  36. Max-Planck-Institut für Plasmaphysik, EURATOM Association Multi-scale ansatz Mikroscales MC Mesoscales KMC Macroscales KMC and Monte Carlo Diffusion (MCD)

  37. 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

  38. Max-Planck-Institut für Plasmaphysik, EURATOM Association Time variation of pressure • Equilibration of pressure with time

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