Kinetic Modeling of Collisionless
Magnetic Reconnection in ThreeDimension

Keizo Fujimoto
Division of Theoretical Astronomy, NAOJ

Outline Introduction
 Particle-in-Cell (PIC) model with adaptive meshrefinement (AMR)
 3D kinetic modeling of reconnection(Instabilities, turbulence, and anomaloustransport at the x-line) Summary

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Outline Introduction
 Particle-in-Cell (PIC) model with adaptive meshrefinement (AMR)
 3D kinetic modeling of reconnection(Instabilities, turbulence, and anomaloustransport at the x-line) Summary

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Magnetic Reconnection in Space
Auroral Substorms[NASA]

Solar Flares
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Multi-Scale Nature of Reconnection
1km

103km

10km

Topology

Dissipation Hall effectλDeρe, λe
Full PIC

ρ i, λ i

1011km

105km

L

∬

Coulomb mean
free path

MHD(Particle-In-Cell)(Magnetohydrodynamics)

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Lcβi ~ 1[NASA]
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Kuznetsova et al., J. Geophys. Res., 2007
Numerical
resistivity only

Nongyrotropic
correction case

Microscopic processes arevery important even for
global dynamics!
 Slow reconnection
 Quasi-steady
configuration Fast reconnection
 Quasi-periodicprocess

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Outline Introduction
 Particle-in-Cell (PIC) model with adaptive meshrefinement (AMR)
 3D kinetic modeling of reconnection(Instabilities, turbulence, and anomaloustransport at the x-line) Summary

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AMR-PIC Model [Fujimoto, JCP, 2011](Adaptive Mesh Refinement – Particle-in-Cell)∆x ≲ 3λDe∝ ne-1/2
λDe,lobe ~ 6×103 m
λDe,ps ~ 3×102 m

Electron scale

Removing
unnecessary cells.

Particle splitting-coalescence

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AMR-PIC SimulationsZZX
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9Data Structure
Similar to a fully
threaded tree(FTT) structure(Khokhlov, 1998).

[Fujimoto & Machida, JCP, 2006]

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10Basic Equations

The same as usual PIC
Superparticle
S: Shape function

Superparticles (Buneman-Boris method)

EM Field (Yee-Buneman scheme)

ChargeConservation
Method[Villasenor &Buneman, 1992]〇 Local operations

Facilitate parallel computation

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Adaptive Block Technique [Fujimoto, JCP, 2011]
Base-level cells in the entire domain are sorted in anappropriate order: That is similar to Morton order,
 So that the block surface is assmall as possible,
 Especially in the central current
sheet, the surface must be small.

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12Performance of the AMR-PIC Model[Fujimoto, JCP, 2011]

Fujitsu FX1@Nagaya Univ.

NodeＣＰＵ(4 cores)

ＣＰＵ(4 cores)

Memory（32G）

Memory（32G）ＣＰＵ(4 cores)

ＣＰＵ(4 cores)

Memory（32G）

Memory（32G）

Parallel fraction:

Load balancing

99.8%
RemovingPoisson Eq.

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Outline Introduction
 Particle-in-Cell (PIC) model with adaptive meshrefinement (AMR)
 3D kinetic modeling of reconnection(Instabilities, turbulence, and anomaloustransport at the x-line)
Origin of resistivity…
 Summary

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Reconnection Rate and Resistivity ηVinReconnection rate2δzx2lVout[Vasyliunas, 1975]

Depending on width and length of the dissipation region.
2D caseInertia resistivity limit

3D, Multi scale, Nonlinear,
Kinetic ⇒ Large-scale PIC
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Inconsistent withObservations

Anomalous dissipation?
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Width of e- layer δeLaboratory Experiment

ωLHExperiment
8c/ωpe2D PIC
1.6c/ωpec/ωpe[Ji et al, GRL, 2008]• δe >> c/ωpe• Active ωLH waves
ASTRONUM2014@Long Beach, USA[Ji et al, PRL, 2004]
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Satellite Obs. in Earth’s Magnetotail

Eyδe >> c/ωpe

ωLH
ωci

[Wygant et al, JGR, 2005][Zhou et al, JGR, 2009]
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3D AMR-PIC of Anti-Parallel Reconnection
mi/me = 100~ 1011 particles~ 6 TB memory

Surface: |J|, Line: Field line
Color on the surface: Ey, Cut plane：Jy

ASTRONUM2014@Long Beach, USA[Fujimoto & Sydora, PRL,2012]18

Generalized Ohm’s Law [Fujimoto & Sydora, PRL, 2012]
3D reconnection

2D reconnection

Anomalous effects
δφVeES turb.

zVe

EM turb.

δBx

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Anomalous Transport at the X-line

Turbulence is enhanced by plasmoid ejections.
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Linear Analyses of the Wave [Fujimoto & Sydora, in prep]
The mode is not the Drift Kink,
not the LHDI,
but the Current Sheet Shear Inst.

𝝎𝝎 = 𝝎𝝎𝒓𝒓 + 𝒊𝒊𝜸𝜸

Double CS
Current Sheet ShearSingle CSc/ωpe

Drift Kink
Single CS, k=1

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Comparison with 3D Simulationsω = ωr + iγ

Simulation resultsωci < |ωr| < ωＬＨVph ≈ VA
ωＬＨ

Linear analyses
Profiles taken fromsimulation
Electronωci

Two-fluidequations
Ion

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Summary Adaptive mesh refinement (AMR) has been
implemented in the electromagnetic particle-in-cell(PIC) model to achieve large-scale simulations ofmagnetic reconnection.
 The AMR-PIC simulations indicate that the dissipation
process of collisionless reconnection is threedimensional. The current sheet shear instability isdominant around the x-line. The turbulence is enhancedby the plasmoid ejections.

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