Anomalous Resistivity due to Kink Modes:
Three-Dimensional Full Kinetic Simulations ofMagnetic Reconnection

Keizo Fujimoto1,2 and Richard D. Sydora3
1. STE Laboratory, Nagoya University
2. JSPS Research Fellow (PD)
3. Department of Physics, University of Alberta

Magnetic Reconnection in Space[Magnetospheric substorms ]In order to explain theexplosive energy conversion
by magnetic reconnection, afast reconnection with thereconnection rate (normalizedby the upstream values)(http://www2.nict.go.jp/dk/c232/)[Solar flares]

Erec ~ 0.1 VA0B0
has to persist for the time scale ofthe phenomena in space plasmas
a few minutes ～ a few hours.

(http://vestige.lmsal.com/TRACE/)

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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].
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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 SystemSimulation code: 3D-EM-PIC + AMR (Adaptive Mesh Refinement)[Fujimoto and Sydora, 2008]

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 VA0B0

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

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

JpGU Meeting 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 the kink mode
provides magnetic dissipation with anamplitude independent of the mass ratio.
[Ozaki et al., 1996; Horiuchi and Sato,1999; Shinohara et al., 2001]

Z9Y

Magnetic Dissipation Associated with the Kink Mode
[Electron Temperature]mi/me=400

It is found that the electrons are strongly
heated in the thin current sheet. This iscaused due to a stochastic scattering at thecorner of the “small bumps”.
Under a steady state, the energy gain
should be balanced with 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 toanomalousresistivity

It is found that the anomalous
resistivity enhances the reconnection
electric field, and makes a significant
contribution for realizing the fastreconnection, compensating thereduction in the inertia resistivity.

Inertia resistivity +Anomalous resistivity

11Summary and Conclusions
We have performed a 3D PIC simulation in a large system inorder to investigate how the kink modes affect magneticreconnection.
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 theelecron diffusion region is automatically adjusted so as toproduce sufficient dissipation for the fast magnetic
reconnection.
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