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Simulation studies targeted at Shocks, Reconnection and Turbulence

Simulation studies targeted at Shocks, Reconnection and Turbulence. Masaki Fujimoto ISAS, JAXA. Targets, physical regimes and tools. Fluid MHD Hall-MHD(Me=0) Hall-MHD(Me!=0).

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Simulation studies targeted at Shocks, Reconnection and Turbulence

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

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

  6. Simulation Model Shock jump (R-H) conditions B1, n1, u1, Te1, Ti1 Upstream B2, n2, u2, Te2, Ti2 Downstream MA=5 wpe/wce=10 b = 0.125 mi/me=25 Open Boundary || Particle Injection /Ejection + Wave Absorption Open Boundary || Particle Injection /Ejection + Wave Absorption “shock-rest-frame”: Enables us to follow long time evolution

  7. Almost 1D Simulation Results Run A : 10.24×0.64 li =(c/wpi1) Run A 2048 x 1024 cells By/By01 wcit • Cyclic reformation x/li

  8. Run A vxi/Ux1 y/li x/li Debye-scale electrostatic waves (～2.0Ez0) are excited uniformly by current-driven instability vxe/Ux1 x/li

  9. 2D Simulation Results Run A : 10.24×0.64 li =(c/wpi1) Run B : 10.24×5.12 li =(c/wpi1) Run B Run A 2048 x 1024 cells By/By01 wcit • 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]. x/li x/li

  10. Run B Ion x-vx vxi/Ux1 y/li Electron x-vx x/li vxe/Ux1 • Debye-scale electrostatic waves (～4.0Ez0) are excited in a localized region • Generation of non-thermal electrons by surfing acceleration [Hoshino & Shimada ApJ 2002] x/li

  11. Run B vxi/Ux1 y/li x/li vxe/Ux1 • Strong reflection of incoming ions by magnetic pressure gradient force of ripples. • Stronger reflection than quasi-1D case, but only in selected locations. y/li

  12. Electron acceleration: The two-dimensionality makes it happen! vte～3.1vte1 Run B Run A vemax2 ～30Udx12 Electron number ve2/Udx12 vte～2.3vte1(Adiabatic compression only) • Mechanisms for generation of non-thermal electrons: • Non-adiabatic scattering • Surfing acceleration

  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:BX(Z)=B0tanh(Z/D) • Harris current sheet: nCS(Z)=n0/cosh2(Z/D) (D: current sheet half thickness) Ti / Te=8 in the current sheet

  20. Ele. temp. anis. + LHDI effects Z 4D Color: plasma density Black curves: field lines X 0 12D -4D 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.

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

  22. 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 vigorouslarge-scale X-line The island size is ~10 ion-inertial length, it needs to coalescence further

  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)Dx = 10le = 0.1Li (Quarter model) 128 x 64 x 30 x 30 x 30 = 5GB (space) (velocity) Excellent agreement with Dx >> le. (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.

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