Dissipation Mechanism in 3D
Magnetic Reconnection

Keizo Fujimoto
Computational Astrophysics Laboratory, RIKEN

Reconnection (in the Earth Magnetosphere)

Coroniti [1985]

105 km

10 km

103 km Can induce global-scale convection causing change inthe field line topology,
 Is intrinsically multi-scale process.
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Why is the dissipation mechanism important?
Our goal is to understand macroscopic
dynamics in a variety of systems.
Diffusion equation:

: Electric resistivity

Macroscopic parameter
originating from microscopic(kinetic) processes.

In the MHD framework…
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)
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How is the resistivity generated?
The motion of charged particles supporting the current density must bedisturbed by “collision”.
Collision with other particles

fev How does the “collision” occur in collisionless plasmas?
= How does the momentum transport occur?

feInertia resistivity

Anomalous resistivity(Wave-particle interaction)v
fe

US-Japan Workshop on Magnetic Reconnectionv

Simulation Model
PIC + Adaptive Mesh Refinement (AMR)[Fujimoto & Machida, JCP, 2006; Fujimoto & Sydora, CPC, 2008]

Refinement cells are
selectively allocatedaround the X-line andseparatrices.

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2D Reconnection
Upstream

Acceleration

Downstream

Electrons are…
 Coherently accelerated
in the diffusion region,
 Not thermalized.
Inertia resistivity
US-Japan Workshop on Magnetic ReconnectionElectron Inertia Resistivity[Speiser, 1970; Tanaka, 1995; Fujimoto & Sydora, 2009]The electrons must be
accelerated quickly up toelectron Alfven velocity.

eMagnetotail： ~ 10km (⇔105km)
Solar Flare： ~ 10-5km (⇔104km)

Is such a thin current sheet really stable in 3D system?
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Unstable Modes Expected in the Current Sheet
Tearing instability
Bx = -B0 tanh(z/)Jy = -J0 sech2(z/)ZX

Lower hybrid
drift instability(LHDI)

Z

Kink-typeinstabilityZ

kyL ~ 1kyrLe ~ 1
 ~ lhY

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YTime Evolution of the Current Sheet in the YZ Planemi/me = 25, Lx×Ly×Lz = 31×7.7×31(a) tci = 6(b) tci = 14(c) tci = 18ZY(a)(b) (c)Lower hybrid drift instability (LHDI)
Kink-type instability
Induction field due to tearing instability
Kink instability coexists with the tearing
mode.

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Reconnection Rate & Current Sheet Width

If the inertia resistivity alone supported
the dissipation, the ER would besignificantly reduced.

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Dissipation Mechanism in 3D Reconnection[Fujimoto, POP, 2009]

High-energy electrons

Pey’z’The electrons are intensely
thermalized as well as
accelerated in bulk.
Pey’z’(2D reconnection case)
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Meandering Scale & Wavelength Electron meandering scaleym[Speiser, 1965]

7.7i0Meandering scale ~ Wavelength of the kink mode
Does the wave-particle interaction still occur inhigher mass ratio cases?
US-Japan Workshop on Magnetic ReconnectionMassively parallel AMR-PIC code
Fujitsu FX1
NodeＣＰＵ(4 core)ＣＰＵ(4 core)

Memory（32G）

Memory（32G）

ＣＰＵ(4 core)ＣＰＵ(4 core)

Memory（32G）

Memory（32G）

Parallel fraction:

99.8%

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Load Balancing Technique
Example of 8-node parallelization
Fixed block

Adaptive block

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Large-scale 3D simulation: First result
mi/me = 100,

Lx×Ly×Lz = 41i×5.1i×41i

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Current Sheet Width (e)2D caseInertia
resistivity

3D caseInertia +anomalous
resistivity
US-Japan Workshop on Magnetic ReconnectioneIn the Earth Magnetotail
Cluster observation of normal electric field in the kinked
current sheet[Wygant et al., 2005]

Spiky normal electric field
Duration = 1 sec ~ 80 km
3 – 4 c/pe > c/peUS-Japan Workshop on Magnetic Reconnection

Summary and Conclusions
The present study has investigated the dissipation mechanism in 3D magnetic
reconnection in comparison with 2D reconnection, using a large-scale PIC
simulations.

Reconnection rate
ER ~ 0.1 both the cases of 2D and 3D reconnections

Dissipation mechanism
2D reconnection

Inertia resistivity

3D reconnection

Inertia resistivity +Anomalous resistivity (Electron heating
due to wave-particle interaction)

Current sheet width larger than c/pe
Both the 3D simulation and observation studies indicate the existence ofsome wave-particle interaction at the X-line.
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