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Simulation studies targeted at Shocks, Reconnection and
Turbulence
Masaki Fujimoto
ISAS, JAXA
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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 ● ● ●
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Shocks
• Electron acceleration in low Mach number perp. Shock
• Large scale 2D full-particle
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Reconnection
• Reconnection trigger: how to make it happen in an ion-scale (thick) current sheet
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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?
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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.
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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
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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.
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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?
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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
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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
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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
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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
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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
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Turbulence
• High-resolution MHD simulation of Kelvin-Helmholtz instability
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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)
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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 ● ● ●
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Ion acceleration in parallel shocks
Need to resolve ion particle dynamics Large upstream region is necessary
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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)
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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 ● ● ●
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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?
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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)
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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.
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If you are interested in performing cross-scale coupling simulations
We are happy to collaborate with you.