Edge plasma physics – a bridge between several disciplines

1. 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, J. Riemann, A. Mutzke, H. Leyh, D. Coster, W. Eckstein, R. Dohmen and many other colleagues from USA, Europe and Japan Ralf Schneider IPP-Teilinstitut Greifswald, EURATOM Association, Wendelsteinstraße 1, D-17491 Greifswald, Germany

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

3. 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: !

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

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

6. 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)

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 • - 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

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

12. 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

13. 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

14. 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

15. 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= 1010 cm-3, nH2 = 9.2·1014 cm-3, nCH4 = 7·1014 cm-3, p = 0.085 Torr (11 Pa) ne~ 109-1010 cm-3 nn~ 1015 -1016 cm-3 fRF= 13.56 MHz potential

16. Max-Planck-Institut für Plasmaphysik, EURATOM Association PIC simulation: RF capacitive discharge electron and CH4+ion density CH4+ ion energy distribution Electrons reach electrode only during sheaths collapse Energetic ions at the wall due to acceleration in the sheath

17. 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

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

19. Max-Planck-Institut für Plasmaphysik, EURATOM Association Plasma thruster SPT-100 radial B-field: e-confined; e-impact ionization increased positive ions not confined; accelerated by E field jexB forces toward the exhaust producing the thrust 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 electric thrusters: exhaust velocity larger than in conventional chemical systems --> much lower mass of propellant stationary plasma thruster(electron closed drift or Morozov type) exhaust anode (neutral propellant) cathode

20. 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

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

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

23. 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)

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. Max-Planck-Institut für Plasmaphysik, EURATOM Association 2D fluid codes Potential 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)

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

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

30. Max-Planck-Institut für Plasmaphysik, EURATOM Association 3D transport in the plasma edge 3D effects in stellarators (W7-X) ergodic region plasma core (non-ergodic) island (non-ergodic) Divertors

31. Max-Planck-Institut für Plasmaphysik, EURATOM Association Transport in an ergodic region Wall Scrape Off Layer Ergodic region Radial direction Plasma core Parallel direction r Enhancement of radial transport due to contribution from parallel transport Electron temperature Rechester Rosenbluth, Physical Review Letters, 1978

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

33. Max-Planck-Institut für Plasmaphysik, EURATOM Association Local magnetic coordinate system Local system shorter than Kolmogorov length to handle ergodicity forward cut One coordinate aligned with the magnetic field to minimize numerical diffusion x2 Area is conserved x3 Use a full metric tensor x1 central cut backward cut

34. Max-Planck-Institut für Plasmaphysik, EURATOM Association Local magnetic coordinate system Problem: numerical diffusion induced by interpolation on the interface Solutions: 2) Monte-Carlo combined with Interpolated Cell Mapping 1) Optimized mesh (finite-difference scheme)  High accuracy transformation of the perpendicular coordinates of a particle (mapping between cuts) needed! (bicubic spline interpolation)

35. 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 6 Transport code 7 Metric coefficients data file Neighborhood array data file Temperature solution

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

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

38. Max-Planck-Institut für Plasmaphysik, EURATOM Association W7-X finite  case T (eV) Normalized field line length Ergodic effects lead to 3D modulation of long open field lines Cascading of energy from ergodic to open field lines

39. Max-Planck-Institut für Plasmaphysik, EURATOM Association Power loading on the divertor plates Power load Parallel flux density Vacuum case Finite β case Vacuum case Finite β case Flux density (MW/m2) Flux density (MW/m2) Engineering limit Length of open field line (m) Length of open field line (m) Feeding fluxes determined by field line length No power load problem for W7-X

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