22E05
Large-scale Particle-in-Cell simulations of electron accelerations
at high Mach number collision-less shocks
超並列版電磁プラズマ粒子コードによる
高マッハ数無衝突衝撃波における電子加速
Yosuke Matsumoto1 and Masahiro Hoshino2
松本洋介1, 星野真弘2
1. Graduate School of Science, Chiba University,Yayoi-cho 1-33, Inage-ku, Chiba 263-8522, Japan
１．千葉大学理学研究科 〒263-8522 千葉市稲毛区弥生町１－３３
2. Graduate School of Science, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan
２．東京大学理学系研究科 〒113-0033 東京都文京区本郷７－３－１
Electron accelerations at high Mach number (M A>15) collision-less shocks are presented by examining
two-dimensional electromagnetic Particle-in-Cell simulations on massively parallel supercomputer
systems. For an increased ion to electron mass ratio (M/m=100) case, the simulation of the high Alfven
Mach number (MA~30) shock resulted in production of accelerated electrons in the shock foot region
where large amplitude electrostatic waves are excited by the reflected ions and incoming electrons. The
acceleration mechanism of the electrons are presented with various M/m and MA cases

1. Introduction
Plasma kinetic processes at collision-less shocks
have been investigated and recognized as importantfor injecting electrons towards so-called thediffusive shock acceleration mechanism. The shocksurfing acceleration is one of the prominentmechanisms that can quickly accelerate theelectrons at the leading edge of the shock footregion by DC electric fields. The underlying
mechanism of the shock surfing acceleration is theplasma kinetic process between the reflected ionsand the incoming electrons that leads to theexcitation of Buneman instability.
Numerical investigations of the shock surfing
acceleration have been reported by Partile-in-Cell(PIC) simulation which follows particles motions
with the electromagnetic field development selfconsistently. Recently, two-dimensional PIC
simulation studies reported contrary results: [1]reported the shock surfing acceleration is effective
in a high Mach number perpendicular shock
evolution while it is not a dominant process or evennot observed in the other PIC simulation results[2,3].
In this paper, we report PIC simulation results ofthe electron acceleration at high Mach number
perpendicular shocks. The dependence of theacceleration mechanism on the ion to electron mass
ratio and the Alfven Mach number is discussed.
2. Numerical method
We examine the shock evolution by a twodimensional Particle-in-Cell simulation code. Thecode solves ion and electron motions along with theelectric and magnetic fields developments. The
electric and magnetic fields are solved implicitly forstability. The calculation of the current density isbased on a charge conservation scheme. The code isparallelized via domain decomposition by using
Message Passing Interface (MPI) and OpenMP
librarlies. The code is efficiently parallelized up to512 processor cores (Figure 1).
The shock is formed by injecting particles fromthe boundary on the left-hand side (x=1) andreflecting particles at the boundary on the righthand side (x=Lx). The injected plasma carries a zcomponent of the magnetic field and thus theconvective electric field Ey=-VxB|y (perpendicularshock). The periodic boundary conditions areapplied at y=1 and Ly. The simulation box sizes inthe x and y directions are Lx=10 v0/gi and Ly=5 i,
respectively, where v0 is the upstream speed, gi is
the ion gyro frequency, and i is the ion inertia
length. The grid size h is set equal to Debye length
in the upstream region.
We have examined several runs with various ion
to electron mass ratios (M/m) and the Alfven Machnumbers (MA), while the upstream and the ratio of
the electron plasma to gyro frequencies pe/ge are
fixed to =0.5 and pe/ge=10.0 among thesimulation runs. The mass ratio varies from 25 to
100 and the Alfven Mach number is increased from15 to 30 for the M/m=100 case. The upstream
parameters are summarized in Table 1. The
maximum computational resource (Run3) are usedFigure 1: (Left) Performance of the PIC code in
GFLOPS vs. number of processor cores. Solid anddashed lines with symbols are the obtained results for
Fujitsu FX1 and Fujitsu HX600, respectively. The
straight lines indicate the 100% efficiency of theparallelization. (Right) Efficiency of the performance vs.
number of processor cores.

with 24001x1024 grid points in which 1010 particles
motions are solved with 512 processor cores on
Fujitsu FX1 supercomputer system at JAXA.
3. Results
Figure 2 shows the electron energy spectra
obtained in the foot and downstream regions of theshock for three simulation runs (Table 1). In all
simulation runs, clear differences in the spectra are
not observed between in the foot and downstream
regions.
By comparing Run1 with Run2, we see a clear
reduction of the maximum energy of the electron as
we increased the mass ratio from 25 to 100 while
MA is fixed to 15. This tread is consistent with therecent two-dimensional simulation study [2].
For M/m=100 case, we have also examined thecase with MA=30 (Run3) and compared with thelower MA case (Run2). We have found that even forthe large M/m case, the high Mach number of 30
can produce much more high energy particles thanlower MA case, even more efficiently than in Run1.
The energy of the electron reaches up to ~7Table I. Upstream parameters

Run1
Run2
Run3M/m MA v0/c  pe/ge
25 15 0.2 0.5 10
100 15 0.1 0.5 10
100 30 0.2 0.5 10

4. Summary
We have examined high Mach number (MA>15)
collision-less shocks in order to investigate electron
accelerations by the shock surfing acceleration
mechanism. Contrary to the previous results that theshock surfing acceleration mechanism in large M/mFigure 2: Energy spectrum of the electron in the foot(solid) and the down stream (dashed) regions of theshock. The energy spectra are shown for Run1 (black),
Run2 (green) and Run3 (magenta).

cases is not important, we have found an efficient
acceleration of the electrons in the M/m=100 casewith MA=30. Thus for larger M/m case, a large MA
shock is required for large amplitude of theinstability that efficiently accelerates the electrons.
Acknowledgments
Computational resources are provided by Fujitsu
FX1 at JAXA and Fujitsu HX600 at Nagoya
Univerisity.
References[1] T. Amano and M. Hoshino, ApJ, 690 (2009), 244[2] M. A. Riquelme and A. Spitkovsky, ApJ, 733 (2011),
63.
[3] T. N. Kato and H. Takabe, ApJ, 721 (2010), 828.