1. Kinetic Approach to microscopic-macroscopic coupling in fusion plasmas Koichi Noguchi Physics & Astronomy Dept., Rice Univ. Giovanni Lapenta Plasma Theory Group, Theoretical Division, LANL, USA Collaborators: J.U Brackbill (Particle Solutions), W. Daughton (U Iowa), S. Markidis (UNM), P. Ricci (Dartmouth), R. Nebel, E. Evstatiev, J. Park (LANL)

2. Motivation: simulation of burning plasmas Lavender Field, Provence, near ITER

3. Outline 1. Multiscale processes in plasmas, the case of ITER 2. The implicit moment PIC method 3. Benchmarks 4. Applications: – 3D reconnection – Reconnection in low beta plasmas – Fusion applications

4. 1 – Multiple scales Fusion Devices Space Role of micro-macro coupling

5. Scales involved in plasma physics 10 -2 10 -3 10 5 10 -3 Pressure tensor 10 -3 10 -7 Resistivity 10 -8 10 -1 10 4 10 -4 Electron inertia 10 -6 10 1 10 6 10 -2 Hall Solar interiorSolar coronaEarth magnetotail ITER (D @ 10keV) Length scale Scales where the various terms become important (SI UNITS)

6. ITER: Multiscale - Multiphysics Ions: D @ 10keV α: fusion generated Source: ITER web site

7. Eliminates the smaller scales Quasineutrality is imposed Reduces the velocity space to 2D Some high order non-linearity are neglected Gyrokinetic PIC In ITER  D =0.1 cm,  He =10 cm and gyroaverage could have problems

8. Multiscale coupling in space plasmas High  Collisionless Small scales, non gyromotion Macro/micro coupling Methods developed there could be used for ITER. Gombosi et al., Univ. Michigan G. Lapenta, AGU Fall meeting, 2004 Example of CELESTE3D

9. 2 – Simulating micro-macro coupling A possibility: implicit moment PIC Description of implicit moment PIC

10. Fundamental Equations (Classical) We consider collisionless plasmas Vlasov-Poisson model - Vlasov equation - Maxwell equations (Newton equations) Eulerian formulation Lagrangian formulation

11. Explicit PIC Computational Cycle

12. Time step and grid spacing limit: – Explicit stability constraints – Implicit accuracy conditions Summary of the Stability constraints

13. Maxwell equations: implicit second order formulation for the field E Newton equations: implicit form Solver: Implicit moment method Implicit formulation (Classical) Particle mover Field Solver

14. Implicit Moment Method Fluid equations

15. ITER: Multiscale - Multiphysics Gyrokineti c Implicit Moment PIC   Gyrokinetic D,T

16. 4 – V&V and applications 1. Reconnection physics in 3D 2. Parallelization & Relativity 3. Inertial Electrostatic Confinement

17. Explicit: Pritchett, JGR 106, 3783 (2001) Implicit: CELESTE3D Explicit [Pritchett, JGR, 106, 3783 (2001)] Grid 512 X 256 grid, 9,000,000 particles, Time step: massively parallel computer Celeste3D [Ricci et al., GRL, 29, 2088, (2002)] Grid: 64X64 200,000 particles, Time step: Workstation TEST: GEM challenge Electron outflowIon density Ion outflowBz x x x x Implicit: CELESTE3D x T=0 T=8 T=16 T=32 T=24 T=48 z

18. Performance – See Poster New PRASEK project: – CELESTE – FLIP (MHD) – DEMOCRITUS (plasma- material interaction, kinetic) – GLOW (plasma-material interaction, fluid) – Relativity C++ object oriented Parallel (logarithmic axis)

19. Maxwell equations: New scheme for current prediction Newton equations: Implicit form, relativistic Solver: Implicit moment method, Newton-Krylov method, Energy conserving method New Relativistic Formulation Particle mover Field Solver

20. Test: relativistic 1D two-stream instability Growth Rate : Im(  p )  V 0 =0.9c, 100,000 particles, 128 mesh, Te=0.01eV  t  p =0.01 (Explicit), 0.2 (Implicit)  0 E 2 )/2 t  p

21. Can we use CELESTE in low beta, high toroidal field? Electron acceleration Explicit Implicit B T =0 B T =B P B T =10B P V ye M i /M e =180

22. Summary Question: how can we study burning plasmas kinetically Possibility: consider implicit moment PIC Fully kinetic Able to capture micro-macro modeling Extensive application to space plasma physics Conclusions: The method is mature Recent upgrades Parallelization Relativity Suite of relevant applications

23. R&D100 prize in 2005 CartaBlanca: A High-Efficiency, Object- Oriented, General-Purpose Computer Simulation Environment PARSEK General tool for PIC simulations Includes: Implicit kinetic PIC (Celeste) Implicit fluid PIC (Flip) Plasma-material interface (Democritus)

25. Waves Light Langmuir whistler Ion acoustic Brackbill, Forslund JCP, 1985

26. Orbits -Gyromotion No averaging, accuracy determined by  t,  x Accurate gyroradius and drift motions at large  t Valid at all beta Valid at all: ρk ┴ Short scales are not eliminated and the energy channel towards them remains open

27. Drifts and Gyroradius Implicit corrected for Method III Implicit (described above) Method II Leap-Frog BorisMethod I Vu, Brackbill, JCP, 116, 384 (1995)

28. 3D reconnection: micro-macro coupling Large scale processes Small scale processes Question: Is the small/large scale coupling captured?

29. Simulation of the small scale processes (LHDI) Free energy: diamagnetic drift Driving: density gradient Stabilization: high beta Frequency: Wavelength: Direction: Seen in space and experiments (e.g. MRX) Present only on the edges of the sheet Requires a kinetic treatment Simulation with L=d i Daughton, Lapenta, Ricci, JCP, 116, 384 (1995)

30. Effect of microinstabilities captured correctly.55 1.1 2.2 L/ρ i L explicit implicit Current intensification Temperature anisotropy Reconnection is enhanced (Poster: FZ1.00008)

31. Can we use CELESTE in low beta, high toroidal field? We considered reconnection with different: – B toroidal (guide field) – Using a Harris equilibrium We computed: – Reconnection rate – Onset – Ion/electron decoupling mechanism – Break-up mechanism As B T increases we kept the same  t, even while the gyrofrequency increased. Reconnection rate Explicit Implicit B T =0 B T =B P B T =10B P

32. IEC Simulation – See posters: BP1.137-138 LP1.107