Dissipation Mechanism in 3D
Magnetic Reconnection

Keizo Fujimoto
Computational Astrophysics Laboratory, RIKEN

Outline Introduction-- Importance of reconnection, Multi-scale nature Dissipation Mechanism in Magnetic Reconnection
in 2D system & in 3D system-- Results from particle-in-cell simulations
 Observational Facts-- In the Earth magnetotail and laboratory experiment Summary & Conclusions

West Lake International Symposium on Space
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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 Magnetoshere)

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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Advantage
・ Repeatability
・ Flexibility in initial &boundary conditions
・ Low cost relatively

Model Proposal
West Lake International Symposium on Space
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How is the fast reconnection triggered?
What is the sufficient condition for the fast and steadyreconnection?
 Which of macro-scale（L >> i） or micro-scale（ L < i ）physics controls the reconnection rate?
 What is the dissipation mechanism at the X-line? （Inertia oranomalous resistivity?） Is reconnection inherently steady or intermittent?
 Is it possible to incorporate correctly the kinetic effects into
fluid simulation models?

How are the electrons and protons accelerated byreconnection?
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Why is the dissipation mechanism important?
Our goal is to understand macroscopic dynamics in a varietyof systems.
Diffusion equation:

: Electric resistivity

Macroscopic parameter resulting
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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We need to know what is happening in themicroscopic region in order to model themacroscopic dynamics.

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Dissipation Mechanism in Magnetic Reconnection
in 2D system & in 3D system-- Results from particle-in-cell simulationsWest Lake International Symposium on Space
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How is the resistivity generated?
The motion of charged particles supporting the current must be disturbed
by “collision”.
Collision with other particles

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

Anomalous resistivity(Wave-particle interaction)

fev
fev

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
Upstream

Acceleration

Downstream

Electrons 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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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 Plane
mi/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

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)West Lake International Symposium on Space
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Meandering Scale & Wavelength Electron meandering scale[Speiser, 1965]

7.7i
Meandering scale ~ Wavelength of the kink mode
Does the wave-particle interaction still occur inhigher mass ratio cases?
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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
[Shinohara et al., 2001;Daughton, 2003]:

 ~ (ie)1/2

Electron HeatingWest Lake International Symposium on Space
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Current Sheet Width (e)2D caseInertia
resistivity

3D caseInertia +anomalous
resistivity
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eObservational Facts-- Current sheet width in the Earth magnetotail andlaboratory experimentWest Lake International Symposium on Space
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In the Earth Magnetotail
Cluster observation of normal electric field in the kinked
current sheet[Wygant et al., 2005]

Spiky normal electric fieldDuration = 1 sec ~ 80 km
3 – 4 c/pe > c/pe
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In the Laboratory Experiment
Laboratory measurement performed on the MRX[Ji et al., 2008]

Current sheet width~ 8 c/pe >> c/pewith electromagnetic waves

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Toward the better understanding of the dissipation
mechanism
The current sheet thicker than c/peWave-particle interaction

 Which unstable modes are responsible for the resistivity?
 How much does the wave-particle interaction contribute tothe total resistivity?
 Observations
 Better space and time resolutions.
 Numerical simulations
More realistic parameters andboundary conditions (Highermass ratio and larger systemsize)
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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 heatingdue 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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Future Study
1.

3D PIC simulations with higher
mass ratio and larger system size.

2.

Application to the MHD-scalesystem.
MHD code Flexible boundary and initialconditions

Global Modeling
E + V×B = J
PIC code
Kinetic effects withmicroscopic structureWest Lake International Symposium on Space
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NASA