Magnetic Reconnection Associated With Kink
Modes: Three-Dimensional Full Kinetic
Simulations

Keizo Fujimoto1 and Richard D. Sydora2
1. STE Laboratory, Nagoya University
2. Department of Physics, University of Alberta

Magnetic Reconnection in Space[ Magnetospheric substorms ]In order to explain theexplosive energy conversion
by magnetic reconnection, therate of reconnection has to be
sufficiently large(Cowley, 1985)

Erec ~ 0.1 VA0B0,[ Solar flares ]and the fast reconnection has topersist for the time scale of thephenomena in space plasmas
a few minutes 〜 a few hours.
(Carmichael, 1964)2

Diffusion Region
Magnetic dissipation takes placein the diffusion region where theMHD constraints break down.
Magnetic field satisfies thediffusion equation

η : Electric resistivity
It is still an open question how
the resistivity is produced incollisionless plasmas.
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Magnetic Dissipation in 2D System
It has been suggested that magnetic
dissipation in 2D system is provided by
the electron inertia resistivity due to themeandering/Speiser motion of theelectrons.

In order for the inertia resistivity to beeffective, the electron diffusion region
has to be compact,

Speiser [1965]

σ ~ λel < λiwhich is believed to be guaranteed by
the Hall effects [Birn et al., 2001].
COSPAR 20084

Large-Scale Particle-In-Cell Simulations in 2D System[Fujimoto, 2006]~ a few sec

It has been suggested that theelongated diffusion region is unstablein the current density direction, andanomalous resistivity could enhance
the magnetic dissipation.
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Large-Scale Particle-In-Cell Simulations in 3D System
Simulation code: 3D-EM-PIC + AMR (Adaptive Mesh Refinement)¾ D21-0045-08 in the poster session
Bx = B0 tanh(z/λ)
Jy = J0 sech2(z/λ)

Lx×Ly×Lz= 31 λi×7.7 λi×31 λi
Maximum resolution：
Nx×Ny×Nz=1024×256×1024
mi/me = 25
The number of particles ：< 1.5×109

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Structure of Current Sheet, and Reconnection Ratet = 18.0

Ne

In 3D system a kink mode is driven by
the ions drifting in the cross-field
direction. The kink mode deforms thecurrent sheet structure drastically.
Nevertheless, the time profile ofthe reconnection electric field isalmost identical to the run
without the kink mode, and thefast reconnection is achieved.

Erec ~ 0.1

Erec ~ 0.1 VA0B07

Generalized Ohm’s Law(a) With kink mode
Z'ZY'

How is the fast reconnection achieved
Yin the system with kinkmode? mode(b) Withoutkink
Electroninertial effects

COSPAR 20088

2D Simulations in the YZ Plane
In order to clarify the dissipation
mechanism associated with the kink mode,
we perform 2D simulations in the system
where the inertia effects are excluded.
It is confirmed that magnetic dissipation isprovided, with an amplitude independentof the mass ratio.
[Ozaki et al., 1996; Horiuchi and Sato,
1999; Shinohara et al., 2001]

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Y9Plasma Heating due to Wave-Particle Interaction[Electron Temperature]mi/me=400

It is found that the electrons are strongly
heated in the thin current sheet. We alsofind a small-scale kink structure
embedded in the large-scale kinked
current sheet.
Hybrid-scale kink mode: λ ~ (λiλe)1/2[Shinohara et al., 2001; Daughton, 2003]

It is the hybrid-scale kink modethat is responsible for theelectron heating.

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Magnetic Dissipation Associated with Kink Modes
Under a steady-state condition, the energy gain should be balancedwith the energy loss.

If the effective collision converts thebulk energy to the thermal energy,should be satisfied.

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Magnetic Dissipation in 3D System
Anomalous resistivity
Electroninertial effects

Due toanomalous
resistivity

It is found that the anomalous
resistivity enhances the magnetic
dissipation , compensating thereduction in the inertia resistivity, andmakes a significant contribution forrealizing the fast reconnection.

Inertia resistivity +Anomalous resistivity

12Summary and Conclusions
We have performed a 3D PIC simulation in a large system inorder to investigate how kink modes affect magnetic
reconnection.
We found that the kink mode broadens the width of the current
sheet and decreases the inertia resistivity. Instead, the anomalous
resistivity associated with the kink mode compensates thedepletion so as to keep the high reconnection rate.
The present result suggests that the electron dynamics in theelectron diffusion region is automatically adjusted so as toproduce sufficient dissipation for the fast magnetic
reconnection.
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