Multi-Scale Kinetic Simulation ofCollisionless Magnetic Reconnection
Keizo Fujimoto1, Makoto Takamoto2
1. Division of Theoretical Astronomy, NAOJ
2. Department of Earth and Planetary Science, Univ. Tokyo
Ref. Fujimoto & Takamoto, Physics of Plasmas 23, 012903 (2016)

Outline Motivation of the current study
 Strategy of multi-scale simulation
 Simulation results --- Multiscale dynamics ofreconnection
 Summary

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Outline Motivation of the current study
 Strategy of multi-scale simulation
 Simulation results --- Multiscale dynamics ofreconnection
 SummarySHH2015 @ NAOJ

3Magnetic Reconnection
Fusion Device

Solar Flares

Auroral Substorms[NASA]ω >> ωcollision
Collisionless plasma
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Multi-Scale Nature of Reconnection
1km

103km

10km

Multi-Scale PIC

Topology

Dissipation Hall effectλDeρe, λeFull PIC

ρi, λi(Particle-In-Cell)

1011km

105km

L

∬

Coulomb mean
free path

MHD(Magnetohydrodynamics)

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Lc

βi ~ 15

MHD vs. Kinetic Reconnection
MHD Reconnection (Petschek Model [Petschek, 1964])
Acceleration atSlow Shock

Compact
diffusion region??

Kinetic Reconnection

 Fast reconnection
 Compact diffusion region Acceleration at slow shock Reproduced in MHD simulation[Ugai & Tsuda, 1977; …etc]
 Slow shocks were observed.
[Feldman et al., 1984; …etc]
 Fast reconnection
 Ion/electron Speiser accel.
 Hall electric current
 Reproduced in PIC simulation[Birn et al., 2001; …etc]
 Hall field was observed.
[Nagai et al., 2001; …etc]

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Purpose of This Study
Understanding of the MHD-scale dynamics of collisionlessreconnection, by means of large-scale PIC simulation.
 Can the Petschek reconnection be achieved?
 How does the kinetic process connect to the MHDprocesses?

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7Outline Motivation of the current study
 Strategy of multi-scale simulation
 Simulation results --- Multiscale dynamics ofreconnection
 Summary

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AMR-PIC Model[Fujimoto, JCP, 2011](Adaptive Mesh Refinement – Particle-in-Cell)
Electron-scale
structure

Particles
𝑑𝑑 𝑣𝑣⃗𝑠𝑠𝑞𝑞𝑠𝑠=
𝐸𝐸 + 𝑣𝑣⃗𝑠𝑠 × 𝐵𝐵𝑑𝑑𝑡𝑡
𝑚𝑚𝑠𝑠
𝑑𝑑 𝑥𝑥⃗𝑠𝑠= 𝑣𝑣⃗𝑠𝑠𝑑𝑑𝑡𝑡

Electric and magnetic fields

Particle splitting

Saving 90% memory

𝜕𝜕𝐵𝐵= −𝛻𝛻 × 𝐸𝐸𝜕𝜕𝑡𝑡
𝜕𝜕𝐸𝐸
1= 𝑐𝑐 2 𝛻𝛻 × 𝐸𝐸 − 𝐽𝐽⃗
𝜀𝜀0𝜕𝜕𝑡𝑡

Current density⃗ 𝑠𝑠 𝑣𝑣⃗ 𝑑𝑑3 𝑣𝑣
𝐽𝐽⃗ = � 𝑞𝑞𝑠𝑠 � 𝑣𝑣𝑓𝑓
𝑠𝑠

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AMR-PIC Simulations

ZZX
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Y

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Performance of AMR-PIC Simulation
Massively parallelized for a reconnection problem.
Strong scaling
Load balancing

Effective parallelism
99.9990%

Removing
Poisson Eq.

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Outline Motivation of the current study
 Strategy of multi-scale simulation
 Simulation results --- Multiscale dynamics ofreconnection
 Summary

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Simulation Setup
With an open boundary condition [Fujimoto, GRL, 2014]
mi/me = 100
Lx×Lz = 660λi×330λi
T = 140 ωci-1
Bx = B0 tanh[z/L]
L = λiMaximum resolution：
32,768 × 16,384

660 c/ωpi# of particles: ~ 2×1010
Memory needed： ~ 2 TB~600 c/ωpi

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Time Evolution of Current Sheet
Out-of-plane JIon outflow speed

660 λi
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Petschek??

Sweet-Parker??

Out-of-Plane J30 λi

Long current sheet
250 λi

Dissipation region is localized.
ER ≈ 0.1Reconnection rate
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Slow Mode Shocks?
Petschek??
Z
Slow shock acceleration?

Slow shock?
R-H
condition

Inflow

Outflow

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Ion Acceleration
AExB

Speiser

SpeiserB

Trajectory A:
1. ExB drift without
acceleration
2. Speiser
acceleration in thecurrent sheet
Trajectory B:
1. Speiser
acceleration in thecurrent sheet
2. Drifting along field
line without
acceleration

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Ion Acceleration
Hot outflow

Consistent with hybrid simulations (Lottermoseret al, 1998) and PIC simulations (Hoshino et al,1998) around the x-line.

Cold inflow

 No ion acceleration at slow
shock-like structure.
 Speiser-type acceleration in
the current sheet.
⇒ Acceleration mechanism
different from the Petschek’s.
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κ2 = Rcurvature/ρgyro <1
Speiser [1965]18

Ideal MHD Condition

Ideal MHD condition breaks down over broad area inthe outflow exhaust.
 Hall term is dominant in the generalized Ohm’s law.
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Hall Current
Equations of motion
Uniform Ez
Z

𝑑𝑑 𝑣𝑣⃗ 𝜔𝜔𝑐𝑐=(𝐸𝐸 + 𝑣𝑣⃗ × 𝐵𝐵)
𝐵𝐵𝑑𝑑𝑡𝑡Electric force

𝑑𝑑 2 𝑣𝑣𝑧𝑧
2=−𝜔𝜔
𝑐𝑐𝑑𝑑𝑡𝑡 2

Ion
ElectronLorentz force

𝐸𝐸𝑦𝑦𝜔𝜔𝑐𝑐 𝑑𝑑𝐸𝐸𝑧𝑧𝑣𝑣𝑧𝑧 ++𝐵𝐵𝑥𝑥
𝐵𝐵𝑥𝑥 𝑑𝑑𝑑𝑑

ExB drift velocity

𝑑𝑑 2 𝑣𝑣𝑧𝑧
2 𝑣𝑣 − 𝑉𝑉≈−Ω
𝑐𝑐 𝑧𝑧
𝑑𝑑𝑑𝑑𝑡𝑡 2𝐸𝐸𝑦𝑦
1
𝑉𝑉𝑑𝑑 = −1 𝐸𝐸𝑧𝑧′ 𝐵𝐵𝑥𝑥
1−𝜔𝜔𝑐𝑐 𝐵𝐵𝑥𝑥

Modified ExB drift velocity

𝐸𝐸𝑧𝑧

No current

YTime evolution ofEz along particle𝑧𝑧
trajectory ≈ 𝑣𝑣𝑧𝑧 𝜕𝜕𝐸𝐸𝜕𝜕𝑧𝑧

𝐸𝐸𝑧𝑧′ =𝐵𝐵𝑥𝑥

𝐸𝐸𝑦𝑦

𝜕𝜕𝐸𝐸𝑧𝑧𝜕𝜕𝜕𝜕SHH2015 @ NAOJ

Non-uniform Ez
𝐸𝐸𝑦𝑦
ZIon𝐵𝐵𝑥𝑥

Electron𝐸𝐸𝑧𝑧

Hall currentY20

Summary
Collisionless reconnection differs from MHD reconnection
even in the region far downstream of the x-line.

Collisionless Reconnection
 No slow shock. Speiser–typeacceleration of ions in the extended
current layer
Hall current

 Hall electric current in broad area inthe outflow exhaust.

MHD Reconnection (Petschek model)
 Plasma acceleration at slowshock Localized current layer aroundthe x-line
Ref. Fujimoto & Takamoto, Physics of Plasmas 23, 012903 (2016)
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