磁気リコネクションの大規模粒子シミュレーション
Large-Scale Particle-in-Cell Simulation ofMagnetic Reconnection
Keizo Fujimoto
Computational Astrophysics Lab., RIKEN

Magnetic Reconnection Line：Field line, Contour： neArrow：Ve

Anti-parallel B-field

Particle acceleration

 Change in field line topology
 Plasma acceleration andheating2

Impact of Magnetic Reconnection
Solar Flare

Magnetospheric Substorm

MagneticReconnection（NASA）

Particle acceleration inPulser（NASA）

Fusion device3（NASA）（NIFS）

Main Issues of Magnetic Reconnection
Triggering mechanism
How can reconnection be triggered quickly?
Tearing mode is not sufficient.

g ~ 2(/VA)Rm3/5 = 5.6 months>> a few min

Quasi-steady process of fast reconnection
 : ElectricResistivity

Very small in collisionlessplasmasFluid (MHD) ： Sweet-Parker ER = Rm-1/2 ∝1/2 ? orPetschek
ER = (/4) (ln Rm)-1 ∝ln model(ER: Reconnection rate, Rm: Magnetic Reynolds number)

Plasma acceleration and heating mechanism
4MagnetoHydroDynamic (MHD) Model(1950s-60s)
Sweet-Parker model [1957, 1958]

ER ~ Rm-1/2(Rm = 0LVA/ 

Magnetic Reynolds numberSlow reconnection
Petschek model [1964]

ER ~ (/4) (ln Rm)-1
Fast reconnection
Exact solution of theMHD equations?
[Ono et al., JSPF, 2001]

5

MagnetoHydroDynamic (MHD) Simulations[Ugai & Tsuda, 1977; Sato & Hayashi, 1979; Biskamp, 1986;…](1970s – 80s)

What is the condition for Petschek
reconnection to evolve?
E = J

Depending on the resistivity model.

Uniform  ⇒ Sweet-Parker reconnection
Localized  ⇒ Petschek reconnection[after Ugai & Tsuda, 1977][Ugai, 1995]

Uniform Localized 6

Plasma Particle Simulations (1990s – early 2000s)
WhatWhatisisthe
thecondition
conditionfor
forlocalized
localizedresistivity
resistivityto
toarise?
arise?
What
Whatisisthe
themechanism
mechanismfor
forgenerating
generatingthe
theresistiviyresistiviyinincollisionlesscollisionlessplasmas?
plasmas?
GEM (Geospace Environment Modeling)
Magnetic Reconnection Challenge
Inclusion of the Hall effect is sufficientcondition for the fast reconnection!
[Birn et al., 2001]

Hall

Viscosity

Electron viscosity is dominant at thex-line. [Cai & Lee, 1997; Hesse et al., 1999]
7

After GEM Challenge
The Hall reconnection has not been accepted.
 Unclear theoretical background

Whistler wave

 = k2cee2, Vout ~ VAe, ER∝1/L
 Fast reconnection in electronpositron plasmas[Bessho & Bhatacharjee, 2005]

 No evidence for the steady-state
fast reconnection

Dissipation mechanism is notconsistent with observations.

L[Drake et al., 2008]

Artificial damping
due to cyclic
boundary 3D effects must be important.
8[Hesse et al., 2001]

Multi-Scale & 3D Kinetic Simulations (later 2000s~)
i ~ 1(Magnetohydrodynamics)(Particle-In-Cell)

MHD（流体）Full PIC（粒子）磁気拡散 ホール効果

Dee, e

i, i

1km10km

103km∬
AMR-PIC

トポロジー

L105kmLc

Coulomb mean
free path

108km

Coroniti [1985]
9

2. Development of AMR-PIC code10

AMR-PIC Code
(Adaptive Mesh Refinement – Particle-in-Cell)
Restrictions in PIC code
Electron-scale structurex ≤ De,pet < 1

x/t > c

De,ps ~ 3×102 m
De,lobe ~ 6×103 m

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AMR-PIC Simulation

12

Massively Parallelized AMR-PIC Code[Fujimoto, JCP, 2011]

Fujitsu FX1 @Nagaya Univ.
NodeＣＰＵ(4 cores)

ＣＰＵ(4 cores)

Memory（32G）

Memory（32G）
Parallel fraction:

ＣＰＵ(4 cores)

ＣＰＵ(4 cores)

Memory（32G）

Memory（32G）

99.8%

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3. Large-Scale 2D Simulation

14

Target of This Study
Fujimoto [2006]
GEM [2001][Hesse et al., 2001]

Does the inclusion of the Hall effect really lead to the fastreconnection?
Large-scale simulations to exclude the boundary
condition effects.
15

Simulation Results [Fujimoto, 2006]

Elongation of the electron diffusion
regionReduces the reconnection
rate.

L

16

Plasmoid Ejection [Daughton et al., 2006: Klimas et al., 2008]

 The reconnection rate is enhanced
associated with the plasmoid ejections.
 ER ~ 0.1 on average.
 Mechanism of the plasmoid ejection
and determining the reconnection rate
is not clear.
17

Dissipation Mechanism in 2D Reconnection
Inertia resistivity

eIntense current
Narrow current sheet

e ~ e = c/pe
Vd = Ve – Vi > 2 vth,eTwo-stream instabilities
are expected.
18

Implication of Anomalous Effects:
Lab. Experiment

 >> c/pe[Ji et al., GRL, 2008]19

Implication of Anomalous Effects:
Satellite Observation[Wygant et al, JGR, 2005][Zhou et al, JGR, 2009]20

4. Recent 3D Simulation Results21

Instabilities in the Harris Current Sheet
Tearing instability
Bx = -B0 tanh(z/)Jy = -J0 sech2(z/)ZX

Lower hybrid
drift instability(LHDI)ZKink-typeinstability

ZkyL ~ 1kyrLe ~ 1
 ~ lhYY

22

3D Reconnection Research
 LHDI and magnetic reconnection
Enhances the tearing mode growth rate [Scholer et al. (2003), Ricci et al. (2004)],
No impact on the quasi-steady process [Zeiler et al., (2002), Fujimoto (2009)].

 Kink-type instability and magnetic reconnection
Driftmode Drift kink （k ~ 1,  ~ ci） [Pritchett & Coroniti, 1996]
 Current sheet kink instability (k(ie)1/2 ~ 1) [Suzuki et al., 2002]
 Electromagnetic LHDI (k(ie)1/2 ~ 1) [Daughton, 2003]
Triggers magnetic reconnection [Horiuchi & Sato (1999), Scholer et al. (2003)],
No impact on the quasi-steady process[Pritchett & Coroniti (2001), Karimabadi et al. (2003)],

Gives anomalous dissipation during the quasi-steady reconnection[Fujimoto (2009, 2011)].
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Mass Ratio Dependence of Kink Modek = 1 (: Half width of the current sheet)[Daughton, POP, 1999]

Particle simulation
Cost ∝ (mi/me)5/2

Fujimoto (2009; 2011)

mi/me = 25

Target in this study
mi/me = 10024

Simulation Setup
Bx = -B0 tanh(z/)Jy = -J0 sech2(z/)81 i mi/me = 100
Max resolution:
4096×512×4096 ~ 1010
Max number of particles
Ion + Electron ~ 1011
Max memory used ~ 6TB

10i ~ 1Re

81i ~ 10Re

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Time Evolution of the Current Sheet
Surface: |J|, Line: Field line
Color on the surface: Ey, Cut plane：Jy

26

Wave Number Spectrum|Ve |ZY27

Wave-Particle Interactions3D reconnection

2D reconnection

Anomalous effects
φVe

ES turb.

zVe

EM turb.

Bx

28

EM vs. ES Turbulence Effects
EM Turb

ES Turb

29

EM Turbulence Effect at the X-line

30

Plasmoid-Induced Turbulence I
(a)

(c)
(a)

(b)
(b)

(c)

31

Plasmoid-Induced Turbulence II(a)(c)(a) (b)
(b)

(c)

32

Wave Properties In collaboration with R. Sydora (U. Alberta) = r + iSimulation resultsci < |r| < (cice)1/2
Vph ≈ VA
Linear analyses
Electron(cice)1/2
ciTwo-fluidTwo-fluid
equations
equations

Ion

Inconsistent with drift mode
property
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Wave Properties: Linear Analyses 2 (mi / me )1/ 4

mi/me=100

Shear
Shearisis
importantimportantfactor.
factor.

e=i=c/pee=c/pe i > eThe=1836.
Thewavewaveisisexpected
expectedto
toariseariseforform
mi/mi/mee=1836.
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Summary
The present study has investigated the steady-state process of thefast magnetic reconnection using the newly developed AMR-PIC
code.
 2D reconnection
The electron diffusion region is elongated in the outflow direction,
which throttles the reconnection process. The plasmoid ejection
plays a key role in enhancing the reconnection rate.
 3D reconnection
A low-frequency EM mode arises in the current density direction,
which causes the anomalous force around the x-line. The
plasmoid ejection is again important in enhancing the turbulence.
Further investigation is needed to understand the nature of theEM mode
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