24P154-P
Simulation of charged particles motion around a fine particle
by using GRAPE.
重力多体問題専用計算機を用いた微粒子近傍の荷電粒子運動シミュレーション
Yasunori Mizuno, Takeshi Yokitani, Kosuke Sawamoto, Hiroshi Inutsuka
and Hiroshi Yamaguchi*
水野保則, 斧谷毅，澤本晃佑，犬塚 博, 山口 浩*
Shisuoka Univ., Hamamatsu Metrix Co., Ltd.*
3-5-1, Johoku naka-ku, Hamamatsu, Shizuoka, 432-8561, Japan
1-4-10-10, Shinmiyakoda, kita-ku, Hamamatsu, Shizuoka, 431-2103, Japan*
静岡大学 〒432-8561 浜松市中区城北3-5-1
浜松メトリックス株式会社 〒431-2103 浜松市北区新都田1-4-10-10*

We performed a simulation of charged particles motion around a fine particle using a special purpose
computer for the gravity named GRAPE. It is fast to calculate the gravitaional interaction on 1 TFlops.
The distribution of the charged particles around a fine particl is simulated by using the individual time
step method. The charged particles distribution of the simulation results are close to the actual physicalphenomenon without spread out greatly.

1. Introduction
The gravity simulator named GRAPE-6 (G6) isachieved, by connecting a lot of pipeline
processors for special
use of the gravity,
computing speed to 985Gflops (≒1 Tflops) perunit. It includes many large-scale integration
chips for calculation of specific analyticalexpression such as 1/r2 interactions. G6 iscurrently being used for the simulation of star andstar cluster interactions, as well as galaxy andgalaxy group interactions [1][2].
Our group has used G6 for simulation of
Coulombic interactions, which have the same
central-force form as gravitational interaction.
These simulations have been conducted toinvestigate particle motion in plasmas.
Three-dimensional
simulations
using
thegravitational force as a proxy for the Coulomb
force have proved successful. This approach has
been used to simulate the diffusion of electron
clouds, plasma oscillations in terms of particle
motion, the behavior of dust clouds inmicro-gravity environments, and the simulationof a Coulomb crystal [3][4].
When G6 is applied to a plasma phenomenon,
the simulation must solve a problem peculiar toplasma such as having much number of theparticles and Debye shielding phenomenon.
Therefore we try the reproduction of Debye
shielding phenomenon on the computer now
using G6.

In our Debye shielding simulation, we reproduce
the cover effect which has the tens of thousands ofneighboring charged particles for one charged fineparticle on the computer. Because an charged
particle has large acceleration as it approaches tofine particles, the charged particle is splashed athigh speed in the infinite distance. As a result, mostcharged particles are scattered by the simulation oflong time, and there becomes no charged particles
around the fine particle. Therefore we devised amethod to add mechanism of the charged particles
generation and extinction to this simulation.
Furthermore, we devised the method to reflect ancharged particle on a spherical boundary. However,in actual plasma space, the presence of the plasmaboundary is hard to consider.
So, this time we focus on the motion of eachcharged particle, and we report the result ofsimulations with individually time step for eachparticle updates.
2. Method of the simulation
The initial distribution of simulation is distributedin the spherical space of the radius 10λe (Debyelength) by 3058 (density of charged particles
1023[m-3]) charged particles uniformly. A
positively-charged fine particle is put in the centerof the spherical space. A time step (△t) of thesimulation was made 1/100ωpe (plasma frequency).
The spatial distribution of charged particles arounda fine particle calculated 103 steps is compared withthe initial distribution or others.
Furthermore, the simulation time step of thecharged particles which approached a center fineparticle was short, and the simulation time step of
the charged particles which leave a center fineparticle was extended. Short time step is set up in
1/2 of the extended time step, at this time. From
now on, this is written with the individual time step
method.
3. Result of the simulation
The result of the simulation is shown in figure 2
and 3. The distribution of the three-dimensionalcharged particles is projected on the x-y plane, and
it is drawing on all the figures. Figure 1 shows theinitial distribution of charged particles before thesimulation. Charged particles are distributed with
10λe around the fine particle uniformly.
The distribution of charged particles after 103
steps is shown in the figure 2. The scale of x and yaxis is being indicated by a same scale to comparewith a figure 1. Spatial distribution of the charged
particles spreads out greatly because an charged
particle may get the repulsive force of the charged
particles and acceleration for the outside due to theinteraction with a center fine particle.
Figure 3 is the result of the simulation which used
the individual time step method. The charged
particles within 5λe from the center fine particle isbeing simulated in the step of 1/2△ t and thoseouter of 5λe from it is calculating in the step of 1.0△t. A result of simulation by the individual time
step doesn't spread out greatly, and it is distributedin the form which is close to the actual plasma
phenomenon. Details of the electrical potential
distribution and energy distribution are reported in aposter.

Fig.1.

Initial distribution of charged particles.

Fig. 2. Charged particles distribution after 103 steps.

Fig.3. Charged particles distribution after 103
steps using the individual time step method.
References[1] M. Taiji and J. Makino, A special-purpose computer
system for astro-physical many-body simulation, Jpn.
Plasma Fusion Res. 72(1996) 920-925.
[2] J. Makino, T. Fukushige, M. Koga and K. Namura,
GRAPE-6: Massively-Parallel Special-Purpose
Computer for Astrophysical Particle Simulation,Publ. Astron. Soc. Jpn. 55 (2003) 1163-1187.
[3] Y. Mizuno, Y. Cao, K. Yamamoto, H. Inuzuka, Y.
Liu and K. Yazawa, How to compute the plasma
particle movement using a special-purpose computerfor gravitational many-body problems, IEEJ Trans.
FM, 124 (2004) 344-345.
[4] K. Yamamoto, Y. Mizuno, S. Hibino, H. Inuzuka, Y.
Liu and K. Yazawa, Simulation of dusty plasmausing a special-purpose computer system designed
for gravitational N-body problems, Phys. Plasmas,
13 (2004) 344-345.