1. 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

2. Strongly non-linear parallel heat conduction by Coulomb collisions: Extreme anisotropy: Max-Planck-Institut für Plasmaphysik, EURATOM Association Magnetic confinement

3. Can we manage the power load at the plates? Development of computational tools to model this power loading. Estimate of power load: ! Max-Planck-Institut für Plasmaphysik, EURATOM Association Basic question

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

5. Max-Planck-Institut für Plasmaphysik, EURATOM Association Length scales

6. 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 für Plasmaphysik, EURATOM Association Diffusion in graphite

7. 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)

8. 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

9. Max-Planck-Institut für Plasmaphysik, EURATOM Association Molecular dynamics – Simulation at 150K, 900K 150K 900K

10. Max-Planck-Institut für Plasmaphysik, EURATOM Association Molecular dynamics results Two diffusion channels No diffusion across graphene layers (150K – 900K) Lévy flights?

11. Non-Arrhenius temperature dependence Max-Planck-Institut für Plasmaphysik, EURATOM Association Molecular dynamic results

12. Assume: - Poisson process (assigns real time to the jumps) - The jumps are not correlated  0 = Jump attempt frequency (s -1 ) E m = 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) 10 Theoretical foundations of dynamical Monte Carlo simulations, K.A. Fichthorn and W.H. Weinberg, J. Chem. Phys. 95 (2) (1991) 1090-1096

13. 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 dependence on void sizes and not on void fraction - Saturated H (Tanabe)  0 ~10 5 s -1 and step sizes ~1Å

14. 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

15. 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 = 9.2·10 14 cm -3, n CH 4 = 7·10 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 Möller) Max-Planck-Institut für Plasmaphysik, EURATOM Association PIC simulation: RF capacitive discharge

16. 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 für Plasmaphysik, EURATOM Association PIC simulation: RF capacitive discharge

17. Lower electrode Negative charge due to higher electron mobility Levitation in strong sheath electric field Max-Planck-Institut für Plasmaphysik, EURATOM Association Dusty (complex) plasmas

18. Max-Planck-Institut für Plasmaphysik, EURATOM Association PIC simulation: Plasma crystal - full 3D! Quasi - ordered 3D structure Top view

19. 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 j e xB forces toward the exhaust producing the thrust radial B-field: e-confined; e-impact ionization increased positive ions not confined; accelerated by E field SPT-100 parameters dimensions: R in =30 mm, R out =50 mm, L=25 m mass flow rate and power: dm/dt=5 mg/s, P=300W discharge parameters: B max =200 G,  V=300 V, I d =3.2 propulsion performances: I sp =1600 s, T=40 mN,  T =0.33

20. 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: w p =10 5, w N =10 7 - Number of macroparticles: N=10 5 - Number of time step to reach staedy state: N t =10 5 - Computational time: 30 hh on 2.5 Ghz - secondary electrons emitted from the wall (BN, Al 2 O 3, SiO 2 ): 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

21. electron density Francesco Taccogna, University of Bari Max-Planck-Institut für Plasmaphysik, EURATOM Association 2D-3D axisymmetric fully kinetic PIC model potential

22. Max-Planck-Institut für Plasmaphysik, EURATOM Association Divertors Tokamak Stellarator (W 7-X) pump Plasma core pump

23. 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

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

25. Max-Planck-Institut für Plasmaphysik, EURATOM Association Molecular physics: quite high recombination rates

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

27. Inclusion of drifts and currents: flows, radial electric field Radial electric field: Closed field lines – neoclassical Open 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

28. Plasma Divertor Max-Planck-Institut für Plasmaphysik, EURATOM Association Divertor Structures

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

30. 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

31. Scrape Off Layer Plasma core Wall Parallel direction Radial direction Ergodic region 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

32. Kolmogorov length L K is a measure of field line ergodicity exponential divergence Typical value in W7-X : L K = 10 – 30 m Max-Planck-Institut für Plasmaphysik, EURATOM Association Kolmogorov length

33. central cut backward cut forward cut x1x1 x2x2 x3x3 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

34. 1) Optimized mesh (finite-difference scheme)  2) Monte-Carlo combined with Interpolated Cell Mapping High accuracy transformation of the perpendicular 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

35. Field line tracing code Triangulation code Metric coefficients code Transport code Mesh data file Neighborhood array data file Metric 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

36. Max-Planck-Institut für Plasmaphysik, EURATOM Association 3D solution for W7-X

37. vacuum finite-  Island structures smeared out Max-Planck-Institut für Plasmaphysik, EURATOM Association Vacuum and finite  solutions on a cut

38. 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

39. Feeding fluxes determined by field line length No power load problem for W7-X Parallel flux density Length of open field line (m) Flux density (MW/m 2 ) Power load Length of open field line (m) Vacuum case Finite β case Engineering limit Vacuum case Finite β case Flux density (MW/m 2 ) Max-Planck-Institut für Plasmaphysik, EURATOM Association Power loading on the divertor plates

40. Complex multi-scale physics requires complex computational tools Max-Planck-Institut für Plasmaphysik, EURATOM Association Summary