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

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?


• 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.


• 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


• 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)



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



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)



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



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.

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

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