S12-4
3D Kinetic Simulation of Collisionless Magnetic Reconnection
無衝突磁気リコネクションの３次元運動論シミュレーション
Keizo Fujimoto
藤本桂三
National Astronomical Observatory of Japan
2-21-1, Ohsawa, Mitaka, Tokyo 181-8588, Japan
国立天文台 〒181-8588 東京都三鷹市大沢2-21-1
A large-scale particle-in-cell simulation has been performed to investigate 3D kinetic process ofcollisionless magnetic reconnection by means of the state-of-the-art supercomputer K. It is found that thewave activities in the thin current layer are enhanced significantly in association with plasmoid ejection. Inparticular, a large-scale mode with kyλi<0.5 deforms the current sheet structure drastically. As a result, theelectron outflow forms a 3D structure reminiscent of the busty bulk flow observed in the Earth magnetotail.
The current simulation suggests the connection between the turbulence in the reconnection layer and thebursty bulk flow.

1. Introduction
Magnetic reconnection is an explosive energy
converter, releasing the magnetic field energy
into plasma kinetic energy. It has been believedthat magnetic reconnection plays significant roles
in dynamical phenomena in space, astrophysical,
and laboratory plasmas. However, the exact roles
were not clearly understood yet. One of the main
issues in the reconnection process is theimportance of the 3D effects in the actualdynamical phenomena. The observations in spaceand laboratory plasmas [e.g., 1, 2] have suggested
that the dissipation process around the x-line isessentially three dimensional. The 3D dissipation
mechanism for anti-parallel reconnection has
been also demonstrated using a large-scaleparticle-in-cell (PIC) simulation [3]. Nevertheless,the impacts of the 3D turbulence around thex-line on the global dynamics are poorly
understood.
In the Earth magnetotail, intermittent fast flows
have been frequently observed within adawn-to-dusk narrow channel of 2-3 Re in
association with the geomagnetic substorms.
These flows are called the bursty bulk flows(BBFs) and are considered to be responsible forthe most part of the momentum transport in themagnetotail [4]. The BBFs are believed to begenerated due to magnetic reconnection. However,the current reconnection model cannot explain
sufficiently such a large-scale 3D structure of theoutflow jets. Although the BBFs have typicallymagnetohydrodynamic (MHD) scale, the MHD
simulations have shown that the structure in thedawn-dusk direction of the outflow jets is very
sensitive to the resistivity model at the x-line [5].

In other words, the BBFs could be a MHD-scale
structure originated from kinetic-scale dynamics.
Therefore, the kinetic simulations are needed toreveal the generation mechanism of the BBFs.
In this paper, we report the initial results of alarge-scale 3D PIC simulation of collisionlessmagnetic reconnection using the state-of-the-art
supercomputer K developed in Japan.
2. Simulation Model
The simulation model employs the adaptive meshrefinement and the particle splitting-coalescencemethod in order to achieve efficient high-resolution
simulations [6]. The system boundaries are periodic
in the x and y directions, and the conducting wall inthe z direction. The simulations are carried out
using a Harris-type current sheet with the magnetic
field Bx(z)=-B0 tanh(z/δ) and the number density
n(z)=n0 sech2(z/δ)+nb tanh2(z/δ), where δ is the halfwidth of the current sheet. We choose δ = 0.5λi and
nb=0.044n0 with λi the ion inertia length based on n0.
The ion-to-electron mass ratio and velocity of lightare mi/me=100 and c/VA=27, respectively, whereVA=B0/(µ0n0mi)1/2 is the Alfven velocity. Thetemperature ratios are T0i/T0e=5.0, Tbi/Tbe=1.0, andTbe/T0e=1.0, where T0s and Tbs are the temperaturesof the species s for the sheet and backgroundplasmas, respectively. The system size is Lx×Ly×Lz=81.9λi×41.0λi×81.9λi that is entirely covered by
the base level cells (the coarsest cells) with ∆LB =0.08λi and can be locally subdivided into finer cells
up to the dynamic range level with ∆LD = 0.02λi, sothat
thehighest
spatialresolution
is104096×2048×4096∼3×10 . The total number ofthe particles reaches ~2 ×1011 for each species.

Fig.1. Power spectrum density (PSD) of Ey around thex-line for the Ly=10λi case (black curve) and the Ly=41λi
case (red curve)

3. Results
Magnetic reconnection is initiated with a small
perturbation to the magnetic field. Figure 1
compares the power spectrum density (PSD) of Eyaround the x-line for the cases of the previous
simulation [3] with Ly=10λi and the current
simulation. The PSD is averaged over the wholesimulation time. Before the onset of a fastreconnection, the lower hybrid drift instability(LHDI) with kyλi≈10 evolves quickly at the edge ofthe current sheet. However, the LHDI hardly has animpact on the reconnection process as shown in theprevious simulation. After the onset of the fastreconnection, a laminar electron current layer isformed and experiences the elongation toward theexhaust. The elongated current layer is unstable forplasmoid formations. Once the plasmoids areejected from the current layer, the wave activities
are significantly enhanced around the x-line. As aresult, the PSD expands to smaller ky (i.e., larger
wavelength). In the previous simulation, because of
the smaller system size in y, the peak in the PSD
appears at kyλi≈1 which corresponds to a current
sheet shear mode. While this mode still exists in thecurrent simulation, another peak arises at larger
scale with kyλi≈0.4 (see Fig.1). The large-scalemode deforms the current sheet structure
significantly around the x-line. Figure 2
demonstrates the large-scale deformation of thecurrent layer due to the plasmoid-driven turbulence.
It is interesting to note that, in association with thelarge-scale mode, the electron outflow develops a
3D structure, so that the outflow speed is larger in
one place than in another along the current sheet.
The large-scale mode isestimated as
λ≈2π/ky=16λi≈1.6Re which is comparable with thescale of the BBF. Therefore, the large-scale mode in
the current layer could be responsible for thegeneration of the BBF observed downstream thex-line.

Fig.2. 3D snapshot of the current sheet around the x-line
indicated by an isosurface of |J| colored by Vex with themagnetic field lines in yellow curve and 2D profiles of Jy
at x=41 and y=35.

4. Conclusions
We have performed a large-scale 3D PIC
simulation of collisionless magnetic reconnection
using the state-of-the-art supercomputer K andcompared with the previous simulation [3]. As inthe previous simulation, the plasmoid ejections
stimulate the wave activity in the thin current layer
formed around the x-line. As a result, the wave
spectrum expands to smaller ky region. In theprevious simulation, the typical large-scale mode
was a current sheet shear mode with kyλi≈1 which
generates the dissipation at the x-line. On the otherhand, in the current simulation, a larger-scale modewith kyλi≈0.4 evolves in addition to the shear modeand deforms the current sheet structure significantly.
In association with the current sheet deformation,the electron outflow also forms a 3D structure
reminiscent of the BBF. Since the large-scale mode
has a scale comparable with that of the BBFs, thepresent simulation suggests that the outflow
structure like the BBFs was generated due to thelarge-scale turbulence formed around the x-line.
The generation mechanism of the large-scale mode
should be investigated more in detail.
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