1. Simulation studies targeted at Shocks, Reconnection and Turbulence Masaki Fujimoto ISAS, JAXA

2. Targets, physical regimes and tools Fluid MHD Hall-MHD(Me=0) Hall-MHD(Me!=0) Kinetic --- Hybrid(Me=0) full-ptcl Vlasov Shocks ● ＋ ● ● Reconnection ● ● Turbulence ● ● ●

3. Shocks Electron acceleration in low Mach number perp. Shock Large scale 2D full-particle

4. Solar wind Global Magnetosphere Re ~ 6350km MHD scale: Discontinuities in Density, Pressure and Magnetic field. Electron-scale Micro Turbulences ~ Electron Debye length Ion-scale Structures Ripples ~ Ion inertia Ion Reflection ~ Ion gyro-radius cross-scale coupling at perpendicular shocks

5. Cross-scale Coupling at Perpendicular Collisionless Shocks Macro scale Discontinuity Fluid R-H (shock jump) condition ES instability Electron cyclotron resonance Electron acceleration and diffusion Ion reflection and inertia Reformation and Rippling Meso scale Micro scale Initial & boundary conditions Modification of conditions & structures

6. Simulation Model “shock-rest-frame”: Enables us to follow long time evolution B 1, n 1, u 1, T e1, T i1 Upstream B 2, n 2, u 2, T e2, T i2 Downstream M A =5  pe /  ce =10  = 0.125 m i /m e =25 Open Boundary || Particle Injection /Ejection + Wave Absorption Shock jump (R-H) conditions Open Boundary || Particle Injection /Ejection + Wave Absorption

7. Almost 1D Simulation Results Cyclic reformation Run A x/ i B y /B y01 Run A : 10.24×0.64 i =(c/  pi1 )  ci t 2048 x 1024 cells

8. y/ i Run A Debye-scale electrostatic waves ( ～ 2.0E z0 ) are excited uniformly by current-driven instability x/ i v xi /U x1 v xe /U x1 x/ i

9. 2D Simulation Results Cyclic reformation of a perpendicular shock at downstream ion cyclotron freq. Transition from reformation phase to turbulent phase in Run B [Hellinger et al. GRL 2008; Lembege et al. JGR 2009]. Run A x/ i Run B x/ i B y /B y01 Run A : 10.24×0.64 i =(c/  pi1 ) Run B : 10.24×5.12 i =(c/  pi1 )  ci t 2048 x 1024 cells

10. y/ i Run B Debye-scale electrostatic waves ( ～ 4.0E z0 ) are excited in a localized region Generation of non-thermal electrons by surfing acceleration [Hoshino & Shimada ApJ 2002] x/ i v xi /U x1 x/ i v xe /U x1 Ion x-vx Electron x-vx

11. y/ i Run B Strong reflection of incoming ions by magnetic pressure gradient force of ripples. Stronger reflection than quasi-1D case, but only in selected locations. x/ i y/ i v xi /U x1 v xe /U x1

12. Electron acceleration: The two-dimensionality makes it happen! Electron number v e 2 /U dx1 2 v te ～ 2.3v te1 (Adiabatic compression only) v te ～ 3.1v te1 Mechanisms for generation of non-thermal electrons:  Non-adiabatic scattering  Surfing acceleration v emax 2 ～ 30U dx1 2 Run B Run A

13. Reconnection Reconnection trigger: how to make it happen in an ion-scale (thick) current sheet

14. Formulation of the Problem: Background Not all the triggering process leads to MHD-scale reconnection. This is very true if the initial current sheet thickness is of ion-scale What kind of triggering process can lead to MHD-scale reconnection?

15. Formulation of the Problem: Background A single X-line seems to dominate in the MHD-stage of reconnection We do NOT think that there has been only one X-line from the beginning.

16. Formulation of the Problem: Background The triggering process we have in our mind: - A finite lateral extent (quite large in terms of the ion-scale unit) of the current sheet is pinched - Multiple X-lines are formed - Multiple magnetic islands goes under coalescence process - Eventually one X-line dominates

17. Formulation of the Problem: Background The other issue: The initial thickness of the current sheet would not be as thin as electron-scale but would be of ion-scale. Current sheet thickness of ion-scale: Very thin seen from an observer but is rather thick from the viewpoint of reconnection triggering.

18. Formulation of the Problem: THE Problem Can magnetic islands grow and merge lively in an ion-scale current sheet to eventually form a vigorous X-line that has MHD-scale impact? Only tearing: NO! Then what if with the aid of - electron temperature anisotropy (perp>para) and - non-local effects of LHDI at the edges - anything else needed?

19. Simulation setup  Three-dimensional (3D) full-particle simulation  Harris magnetic field:B X (Z)=B 0 tanh (Z/D)  Harris current sheet: n CS (Z)=n 0 / cosh 2 (Z/D) (D: current sheet half thickness) Ti / Te=8 in the current sheet

20. Ele. temp. anis. + LHDI effects Magnetic island is immature. Plasma density at X-line is not as low as the lobe, that is, not the whole current sheet field lines has been reconnected. X Z 0 12D 4D -4D Color: plasma density Black curves: field lines

21. When ion temp anis is further added Lobe field lines are reconnected. X Z 0 12D 4D -4D Color: plasma density Black curves: field lines plasma density drops down to lobe value at XL

22. The island size is ~10 ion-inertial length, it needs to coalescence further Embedded islands: May not coalescence to form a large scale X-line In the presence of Ti – anis, lobe field lines are reconnected. This exposed islands are known to go under lively coalescence to form a vigorous large-scale X-line

23. The conjecture To be tested soon by the new SX9 system at ISAS. May turn out to prove an unexpectedly important role of the ion temperature anisotropy in reconnection triggering

24. Turbulence High-resolution MHD simulation of Kelvin-Helmholtz instability

25. Coupling to non-MHD physics well expected. Indeed: Two-fluid simulations (with finite electron mass) do show coupling to reconnection inside a KHV Full particle simulations show electron acceleration in a KH+RX process (A case of turbulent acceleration)

26. Targets, physical regimes and tools Fluid MHD Hall-MHD(Me=0) Hall-MHD(Me!=0) Particle --- Hybrid(Me=0) full-ptcl Vlasov Shocks ● ＋ ● ● Reconnection ● ● Turbulence ● ● ●

27. Ion acceleration in parallel shocks Need to resolve ion particle dynamics Large upstream region is necessary

28. Interlocked simulation: Hybrid + Hall-MHD (Me=0) Near shock-front region: hybrid, including ion particle dynamics Far upstream: Hall-MHD (ions are treated as fluid)

29. Targets, physical regimes and tools Fluid MHD Hall-MHD(Me=0) Hall-MHD(Me!=0) Particle --- Hybrid(Me=0) full-ptcl Vlasov Shocks ● ＋ ● ● Reconnection ● ● Turbulence ● ● ●

30. Vlasov Simulation Noiseless. –No enhanced thermal (random) fluctuations due to finite number of particles. –Strong nonphysical effects in PIC model with low spatial resolutions. Easy to parallelize with the domain decomposition method. – Eularian variables only. Drawbacks: – Huge computer resources for 6D simulations are needed. – Numerical techniques are still developing. Why Vlasov?

31. GEM Reconnection Challenge 2x3v (5D)  x = 10 e = 0.1Li (Quarter model) 128 x 64 x 30 x 30 x 30 = 5GB (space) (velocity) Excellent agreement with  x >> e. (Umeda, Togano & Ogino, CPC, in press, 2008)

32. As yet at a demonstration level, but … Parallelization straight forward May become the standard scheme when parallel computers become more massive. Getting prepared for the new era to come.

33. If you are interested in performing cross-scale coupling simulations We are happy to collaborate with you.