Particle Simulations of Plasma Wave Instabilities I

1. Name of Database:   Plasma Particle Simulation I : 
                       Computer Simulations of Electrostatic Solitary Waves in the Magnetotail

2. Institution:　Radio Science Center for Space and Atmosphere, Kyoto University

3. Contents of Database: 　

We present particle simulations of one of the most fundamental instabilities in plasmas, i.e., 
two-stream instability induced by two groups of electrons moving with different drift velocities. 
Electrostatic waves grow from the thermal fluctuation noise with the growth rate predicted by 
the linear theory, and saturate due to nonlinear trapping of electrons by the coherent electrostatic 
potentials. After the saturation, the series of the large amplitude potentials coalesce with each 
other to form isolated potentials.  This process was also observed in the past Vlasov code simulations 
and laboratory experiments and were called as electron holes. The plasma wave observation by the 
GEOTAIL spacecraft revealed that there also exist electrostatic solitary waves similar to electrons 
holes in the plasma sheet boundary layer of the Earth’s magnetotail. We performed electrostatic 
particle simulations for various parameters and found conditions for generation of the ESW. The ESW 
is generated as a results of nonlinear coalescence of strong electrostatic waves excited by an 
electrostatic beam instability involving the electron beam drifting relative to the majority of ions 
and another electrons drifting with the ions. We performed two runs with different initial ion thermal 
velocities Vi. One is with Vi = 2.0, and the other is with Vi = 0.1. We assumed the same density ratio 
R = 0.5 for these runs. Namely, two electron beams have the same thermal velocity with drift velocities 
Vd and 0. The evolution of the instability is shown by the phase diagrams of particle in the (X, Vx) 
space at different times. As a necessary condition for formation of the ESW, the ion thermal velocity 
Vi must be large enough so that the electrostatic waves due to the beam instability cannot decay to 
ion acoustic waves.
  
All computations were performed on the KDK computer system at Radio Science Center for Space and 
Atmosphere, Kyoto University.

4. Examples of Database:

The database includes several kinds of plots showing detailed processes of nonlinear evolution of 
electron two-stream instability.  Among them phase space plots showing the locations of electrons 
in the (X, Vx) phase space are most interesting.  An example of the phase space plots is shown below.  
The dots with red, yellow and cyan colors represent ions, electrons moving with ions and electrons 
moving with a drift velocity Vd =20Ve , respectively.  Both groups of electrons have the same thermal 
velocity Ve.  A reduced mass ratio of ions to electrons is assumed to be 100.  The time indicated 
on top of each figure is normalized by the inverse of the total electron plasma angular frequency.  
Namely, “TIME= 6.28” corresponds to one period of the total electron plasma oscillation.



Detailed description of the simulation runs are found in the following reference.

Y. Omura, H. Kojima and H. Matsumoto, Computer Simulation of Electrostatic Solitary Waves: 
A Nonlinear Model of Broadband Electrostatic Noise, Geophysical Research Letters, vol. 21, 
pages 2,923-2,926, 1994.
The simulation code used in producing the present database. is a one-dimensional elelctrostatic coode. 

Detailed description of the code is found in the following reference.
Y. Omura and H. Matsumoto, KEMPO1: Technical Guide to One-Dimensional Electromagnetic Particle Code, 
Computer Space Plasma Physics: Simulation Techniques and Softwares, edited by H. Matsumoto and 
Y. Omura, pages 21-65, Terra Scientific, Tokyo, 1993.
http://www.terrapub.co.jp/e-library/cspp/index.html

5. Contact:

　Yoshiharu Omura
　RASC, Kyoto University, 
　Gokasho, Uji, 611-0011, Japan
　Phone:  +81-774-38-3811
　E-mail:  omura[AT]kurasc.kyoto-u.ac.jp

6. Public Offering of Database:

　http://center.stelab.nagoya-u.ac.jp/web1/sramp/cdrom/sm0004/index.html
　Also see:
　Home Page of Geotail Plasma Wave Instrument
　http://www.rish.kyoto-u.ac.jp/space/gtlpwi/
　　

S-RAMP Database Catalog.

S-RAMP Home Page.