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)

Kinetic --- Hybrid(Me=0) full-ptcl Vlasov

Shocks ● ＋● ●

Reconnection ● 　　　　　　　　　　●

Turbulence 　●　　　　　　　　　　　　　　　　　　　　　　　●　　　　　　　　　　●

Shocks

• Electron acceleration in low Mach number perp. Shock

• Large scale 2D full-particle

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

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

Simulation Model• “shock-rest-frame”: Enables us to follow long time evolution

B1, n1, u1, Te1, Ti1

Upstream

B2, n2, u2, Te2, Ti2

Downstream

MA=5 pe/ce=10

= 0.125 mi/me=25

Open Boundary

||Particle

Injection /Ejection

+Wave

Absorption

Shock jump (R-H) conditions

Open Boundary||Particle Injection /Ejection+Wave Absorption

Almost 1D Simulation Results

Cyclic reformation

Run A

x/i

By/By01

Run A : 10.24×0.64 i =(c/pi1)

cit

2048 x 1024 cells

y/ i

Run A

Debye-scale electrostatic waves ( ～ 2.0Ez0) are excited uniformly

by current-driven instability

x/i

v xi/U

x1v xe

/Ux1

x/i

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

By/By01

Run A : 10.24×0.64 i =(c/pi1)Run B : 10.24×5.12 i =(c/pi1)

cit

2048 x 1024 cells

y/ i

Run B

• 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/iv xi

/Ux1

x/i

v xe/U

x1

Ion x-vx

Electron x-vx

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/iv xi

/Ux1

v xe/U

x1

Electron acceleration: The two-dimensionality makes it happen!

Elec

tron

num

ber

ve2/Udx1

2 vte ～ 2.3vte1

(Adiabatic compression only)

vte ～ 3.1vte1

Mechanisms for generation of non-thermal electrons: Non-adiabatic scatteringSurfing acceleration

　 vemax2 ～ 30Udx1

2

Run B

Run A

Reconnection

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

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?

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.

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

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.

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?

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

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 sheetfield lines has been reconnected.

X

Z

0 12D

4D

-4D

Color: plasma densityBlack curves: field lines

When ion temp anis is further added

Lobe field lines are reconnected.

X

Z

0 12D

4D

-4D

Color: plasma densityBlack curves: field lines

plasma density drops down to lobe value at XL

The island size is ~10 ion-inertial length, it needs to coalescence further

Embedded islands:May not coalescenceto form a large scaleX-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

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

Turbulence

• High-resolution MHD simulation of Kelvin-Helmholtz instability

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)

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 　●　　　　　　　　　　　　　　　　　　　　　　　●　　　　　　　　　　●

Ion acceleration in parallel shocks

Need to resolve ion particle dynamics Large upstream region is necessary

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)

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 　●　　　　　　　　　　　　　　　　　　　　　　　●　　　　　　　　　　●

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?

GEM Reconnection Challenge2x3v (5D) 　 x = 10e = 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)

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.

If you are interested in performing cross-scale coupling simulations

We are happy to collaborate with you.