３Ｄリコネクション：プラズモイドによって誘発された乱流効果
3D Reconnection: Plasmoid-InducedTurbulence EffectKeizo Fujimoto
Computational Astrophysics Lab., RIKENMulti-Scale Nature of Magnetic Reconnection
i ~ 1(Magnetohydrodynamics)(Particle-In-Cell)

MHD（流体）Full PIC（粒子）磁気拡散 ホール効果∬トポロジーDee, ei, i

L

1km

10km

103km

105km

Lc

Coulomb mean
free path

108km

Coroniti [1985]
2

Impact of Dissipation Mechanism[http://solar-center.stanford.edu/]

The reconnection rate depends on the resistivity model.
(Biskamp,1986; Ugai, 1995)

Global responses in substorm and flares are sensitive to theparameterization of the resistivity.
(Raeder et al.,2001; Kuznetsova et al., 2007)3

Kuznetsova et al., J. Geophys. Res., 2007
Numerical
resistivity only

Nongyrotropiccorrection case

 Slow reconnection
 Quasi-steadyconfiguration
 Fast reconnection
 Quasi-periodic
process

4Dissipation Mechanism in 2D Reconnection
ZX[Cai & Lee, 1997; Hesse et al., 1999]

5

Dissipation Mechanism in 2D Reconnection
eZEyX

FluidParticle[Fujimoto & Sydora, 2009]

Speiser [1965]

Electron inertia resistivity

tr: Transit time through the electron diffusion
region6

Dissipation Mechanism in 2D Reconnection
eZX⇒

Very thin currentlayer!
7Implication of Anomalous Effects:
Lab. Experiment

e >> c/pe[Ji et al., GRL, 2008]8

Implication of Anomalous Effects:
Satellite Observation[Wygant et al, JGR, 2005][Zhou et al, JGR, 2009]9

Implication of Anomalous Effects[Vasyliunas, 1975](Resistive length)
Could be caused by wave-particle
interactions.
10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 ~ 1

kyrLe ~ 1
 ~ lhYY11

3D Reconnection Researches ( ~ 1)
 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)].
12

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 = 25Target in this study
mi/me = 100
13

Simulation Setup
Massively parallel AMR-PIC code [Fujimoto, JCP, 2011]
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

14

AMR-PIC Simulation

15

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

16

Wave Number Spectrum|Ve |ZY

17

Wave-Particle Interactions
3D reconnection2D reconnection

Anomalous effects
φVe

ES turb.

zVe

EM turb.

Bx

18

EM vs. ES Turbulence Effects
EM Turbulence

ES Turbulence19EM Turbulence Effect at the X-line

20

Plasmoid-Induced Turbulence I
(a)

(c)
(a)

(b)
(b)

(c)

21

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

(c)

22

Enhancement of the Reconnection Rate23

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

Two-fluidTwo-fluid
equations
equations

Ion

Inconsistent with drift mode
property
24

Wave Properties: Linear Analyses 2 (mi / me )1/ 4kk (m))1/4
1/4e(mi/m/miee=i=c/pee=c/pe i > e(m))1/4
1/4e(mi/m/mie~~cici
Shear
Shearisis
importantimportantfactor.
factor.

The=1836.
Thewavewavesurvives
surviveseven
evenforform
mi/mi/mee=1836.
25

Conclusion
Large-scale 3D PIC simulations using AMR-PIC code
The EM turbulence effect is enhanced in association withthe plasmoid ejections, which coincides with enhancementof the reconnection rate.

Further investigations are needed to understand thenature of the EM mode.

26

Perspective in Near Future
磁気リコネクションのマクロシステムへの適用
MHDコード スケールフリー 自由な境界条件・初期設定
グローバル構造のモデリング

E + V×B = J
プラズマ運動論効果

PICコード物理的考察

 完全な運動論効果
 詳細なミクロ構造27