Plasmoid-Induced Turbulence in
3D Kinetic Reconnection

Keizo Fujimoto1, Richard D. Sydora2
1. Division of Theoretical Astronomy, NAOJ
2. Department of Physics, University of Alberta

Multi-Scale Nature of Reconnection
1km

10km

103km

Topology

Dissipation Hall effectDee, e
Full PIC(Particle-In-Cell)

i, i

1011km

105km∬L
MHD(Magnetohydrodynamics)

Lc

Coulomb mean
free pathi ~ 1[NASA]2

Impact of Dissipation Mechanism
Ugai, Phys. Plasmas, 1995
MHD simulations
Uniform Localized Slow Reconnection

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

Nongyrotropic
correction case

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

4Dissipation in 2D Kinetic Reconnection
Ze

BzZ

BxYX

Ey

PIC simulations
at x-line

X

Electron viscosity[Cai & Lee, 1997; Hesse et al., 1999]

Speiser [1965]

Inertia resistivity
FluidParticle[Fujimoto & Sydora, 2009]tr: Transit time throughthe diffusion region5

Inertia Resistivity & Current Sheet Widthat the x-line
outside the current layer

Very thin currentlayer!

⇒eZX

6

Implication of Anomalous Effects:
Lab. Experiment
e >> c/pe[Ji et al., PRL, 2004][Ji et al., GRL, 2008]7

Implication of Anomalous Effects:
Satellite ObservationLHci[Wygant et al, JGR, 2005][Zhou et al, JGR, 2009]8

Implication of Anomalous Effects
at the x-line
outside the current layer[Vasyliunas, 1975](Resistive length)
Could be caused by wave-particle
interactions.
9Dynamical Current SheetThin current layer:(2D PIC simulation)

Elongation

Plasmoid formation
10

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

Lower hybrid
drift instability(LHDI)

Z

Kink-typeinstabilityZ

kyL ~ 1kyrLe ~ 1
 ~ lh

YY

11

AMR-PIC Simulations[Fujimoto, JCP, 2011]12

Simulation Setup
Bx = -B0 tanh(z/)Jy = -J0 sech2(z/)Fujitsu FX1
81 imi/me = 100
Max resolution:
4096×512×4096 ~ 1010
Max number of particles
Ion + Electron ~ 1011

10i ~ 1Re

Max memory used
81i ~ 10Re~ 6TB
13

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

14

Wave Activity

15

Anomalous Momentum Transport

Anomalous effects

16

Anomalous Transport at the X-line

17Plasmoid-Induced Turbulence*t = 1.6 ci-1
LXO = 0.95 i*

LXOInformation
propagates at
Vp ~ VA*(B* = 0.5B0)
18

Plasmoid-Induced Turbulence
Plasmoid formation
Wave
amplification
Local turbulence
enhancement
Propagation along
the field line
Intensified turbulenceat the x-line
19

Wave Properties = r + iSimulation resultsci < |r| < ＬＨ
Vph ≈ VAＬＨ

Linear analyses
Profiles taken fromsimulation
Electronci

Two-fluidTwo-fluid
equations
equations

Ion

20Linear Analyses
1/4
1/4
kk (m)(mi/m/me)iee=c/pe i > e

1/4(m/m)(mi i/mee)1/4

Peak velocities
are fixed.
Shear
Sheardriven
drivenmode
moderather
ratherthan
thandrift
driftmodemode~~cici
The=1836.
Thewavewavesurvives
surviveseven
evenforform
mi/mi/mee=1836.
21

Summary
Large-scale 3D PIC simulations using AMR-PIC codeThe EM turbulence has a significant impact on thedissipation mechanism during the fast reconnection, inassociation with plasmoid formations.
The properties of the EM mode responsible for theturbulent electron flow.
ci < r < LH
Shear driven instability
Large growth rate even for mi/me=183622