Three-dimensional Electromagnetic Particle Codewith Adaptive Mesh Refinement Technique

Keizo Fujimoto1,2,3 and Richard D. Sydora1
1.
2.
3.

Department of Physics, University of Alberta
NiCTResearch Fellow (PD) of the JSPS

Three-dimensional (3D) effects of local plasma kinetic processes are, inmany cases, believed to have a significant impact on the global energy
transport and conversion processes occurring in the solar-terrestrial system.
Magnetic reconnection is one of the most important phenomena which
support the fast energy release associated with the magnetospheric substorm
and solar flares. It facilitates the fast conversion of energy stored in acompressed magnetic field into plasma kinetic and thermal energies. However,its 3D processes are poorly understood. The difficulties are mainly caused due
to its strong nonlinearity and the limited computer resources.
In this study, we successfully constructed a new 3D electromagnetic
particle code using the adaptive mesh refinement (AMR) technique, whichenables efficient kinetic simulations on many plasma processes. We show thecode description, several test simulations, and the performance of the code.

JGU Meeting 2007Restriction in full particle code:
Magnetotail Lobe

[Birdsall & Langdon, 1995]

Grid spacing can becoarser in the lobe region
than in the plasma sheet.
Central Plasma SheetJGU Meeting 2007

Cells are treated as independent
units organized in refinement trees
rather than elements of arrays, sothat a very flexible cell hierarchy
is achieved.

The hierarchical cellstructure is supported bya set of pointers, which isbasically same as thefully threaded tree (FTT)
structure [Khokhlov,1989].

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The mesh splitting in the PIC code leads tothe decrease in the number of superparticles
per cell, which causes the increase in thenumerical noise. Particle splitting andcoalescence is one of the solutions forcontrolling the number of particles per cell.

Basic equations

Mesh splitting criteria

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Harris-type current sheet
mi/me = 100; Ti/Te = 5; c/ve,th = 5;λ/λi = 0.5; nbk = 0.044;
Bx(z) = - B0 tanh[z/λ]n (z) = n0/cosh2[z/λ] + nbk tanh2[z/λ]j (z) = en0(Vi - Ve)/cosh2[z/λ]JGU Meeting 2007

Lx×Ly×Lz = 0.24λi×3.84λi×30.72λizy

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Linear dispersion of the lower hybrid drift instability (LHDI)

Analytical solution [Davidson et al., 1977]

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Lx×Ly×Lz = 15.36λi×0.96λi×15.36λizx

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One of the main differences arising
between 3D and 2D reconnections iswhether the system involves theLHDI or not. The LHDI is caused by
the drifting plasma at the flanks ofthe current sheet and flattens thedensity profile. Due to the resultant
pressure imbalance, the current sheet
is pushed from the both sides by theflank magnetic pressure. As a result,the current density is enhanced at thecenter of the current sheet, whichfacilitates the onset of a fastreconnection.
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Implementing 3D simulations
is generally much harder than 2D
simulations in realistic systems,
since it requires much more cells
and particles. We overcome thisdifficulty by parallelizing thecode, using the OpenMP and themessage passing interface (MPI).
The performance is greatly
enhanced by using a number ofthreads and nodes.
(The performance test was conducted by FUJITSU HPC2500 installed at Nagoya University.)JGU Meeting 2007

We have constructed a new 3D electromagnetic particle code with theadaptive mesh refinement technique.
The code was checked against two kinds of instability: the LHDI, andthe tearing instability. We found that the wave dispersion of the LHDI
obtained from the simulations is consistent with the theoretical prediction.
Furthermore, it is clear that the nonlinear evolution of the tearing
instability in the 3D system is basically identical with the 2D results if theLHDI is not excited. It is also confirmed that the fine meshes are properlydistributed according to the mesh splitting criteria.
We improved the computing performance and efficiency by carefullyparallelizing the code, using the OpenMP and MPI.
Therefore, we can conclude that the code is successfully developed andprovides a high efficiency.
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