Dissipation Mechanism in 3D
Collisionless Magnetic Reconnection

Keizo Fujimoto
Computational Astrophysics Laboratory, RIKEN

Outline Introduction-- Importance of reconnection, Multi-scale nature Dissipation Mechanism in Magnetic Reconnection,comparing 2D and 3D reconnections-- Results from particle-in-cell simulations
 Summary & Conclusions

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Introduction-- Why is reconnection important?
-- Why do we need to study the dissipation mechanism?

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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 inherently multi-scale process.
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Reconnection (in Solar Flares)(Carmichael, 1964)

 Leads to rapid energy release, Strongly accelerates the electrons and protons.

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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 resulting
from microscopic (kinetic)
We needprocesses.
to know the

microscopic physics to model
In the MHD framework…
the macroscopic dynamics.
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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Dissipation Mechanism in Magnetic Reconnection,comparing 2D and 3D reconnections-- Results from particle-in-cell simulations

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How is the resistivity generated?
The motion of charged particles supporting the current must be disturbed
by “collision”.

feCollision with other particlesv
 How does the “collision” occur in collisionless plasmas?
= How does the momentum transport occur?

fe

Inertia resistivityv

Anomalous resistivity(Wave-particle interaction)fe

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

Refinement cells are
selectively allocatedaround the X-line andseparatrices.

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2D Reconnection
fevElectrons are…
 Coherently accelerated
in the diffusion region,
 Not thermalized.
Inertia resistivity
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Electron Inertia Resistivity[Speiser, 1970; Tanaka, 1995; Fujimoto & Sydora, 2009]

The electrons must be
accelerated quickly up to ahigh velocity.

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

Is such a thin current sheet really stable in 3D system?
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Time Evolution of the Current Sheet in 3D system
mi/me = 25, Lx×Ly×Lz = 31×7.7×31(a) tci = 6(b) tci = 18

Bx = -B0 tanh(z/)Jy = -J0 sech2(z/)

Z

Y
(a)

(b)

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

ER ~ 0.1

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

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Dissipation Mechanism in 3D Reconnection[Fujimoto, 2009]

Long-stay electrons

Inflow

Outflow
Pey’z’The electrons are intensely
thermalized as well as
accelerated in bulk.
Pey’z’(2D reconnection case)
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Current Sheet Width (e)e

2D caseInertia
resistivity

3D caseInertia +anomalous
resistivity
Broader current sheets have been observed in the Earth magnetotail[Wygant et al., 2005] and laboratory experiment [Ji et al., 2008].
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In the Cases with Lager mi/me (> 100)
 2D simulations in the YZ plane
Temparature: mi/me=400

Hybrid-scale kink mode
 ~ (ie)1/2

Electron Heating
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Toward Larger-Scale Simulations with Larger mi/me
Massively parallel computing of 3D AMR-PIC model
Larger computer resources
including more memory
capacity and CPUs.

The present code has achievedvery good scalability.

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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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Toward the better understanding of the dissipation
mechanism
The current sheet thicker than c/pe

Wave-particle interaction

 Which unstable modes are responsible for the resistivity?
 How much does the wave-particle interaction contribute to
the total resistivity?
 Observations
 Better space and time resolutions.
 Numerical simulations
More realistic parameters andboundary conditions (Higher
mass ratio and larger systemsize)
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