Simulation results

We have performed a large number of simulation runs for many point in the two-dimensional parameter space with different initial values of Ve/Vd and Vi/Vd, where Vi and Ve are the thermal velocities for ions and electrons, respectively, and Vd is the drift velocity of electrons. We assume a single ions species of protons. The charge neutrality condition of the plasma gives ni = ne. We assume a real mass ratio for protons and electrons, i.e., mi / me = 1836, which gives the ratio of the ion to electron plasma frequencies, Πi / Πe = 0.0233. The time is normalized by 1/Πe, and velocities are normalized by the drift velocity Vd. The distance is normalized by Vd / Πe. We only solve the electrostatic mode in the direction parallel to the static magnetic field in this paper. Therefore, the polarization is purely parallel to the static magnetic field, and the magnitude of the magnetic field does not contribute to the electron dynamics. In this simple model, the controling parameters of the Buneman instabilities are the thermal velocities of ions and electrons, i.e., Ve/Vd and Vi/Vd. Since we normalize velocities by the drift velocity Vd, the thermal velocities of ions and electrons are specified with a reference to the drift velocity Vd = 1.

The simulation results are presented by animations of plots consisting of the following four panels. From the top, they are:


List of simulation results

Vi
/
Vd		 0.24 vi=0.24,ve=0.1




0.2





0.14 vi=0.14,ve=0.1




0.1 vi=0.1,ve=0.1
vi=0.1,ve=0.1(open)



vi=0.1,ve=20(open)
0.06 vi=0.06,ve=0.1(1)
vi=0.06,ve=0.1(2)
vi=0.06,ve=0.1(open)




0.038
vi=0.038,ve=0.3(1)
vi=0.038,ve=0.3(2)



0.02
vi=0.02,ve=0.35
vi=0.02,ve=0.35(open)
 vi=0.02,ve=0.6
vi=0.02,ve=0.6(open)

vi=0.02,ve=3
vi=0.02,ve=3(open)
0.014

vi=0.014,ve=0.6(1)
vi=0.014,ve=0.6(2)


0.01 vi=0.01,ve=0.1
vi=0.01,ve=0.1(open)
vi=0.01,ve=0.7(1)
vi=0.01,ve=0.7(2)

vi=0.01,ve=2
vi=0.01,ve=2(open)(1)
vi=0.01_ve=2(open)(2)
0.005


vi=0.005,ve=1.2
vi=0.005,ve=1.2(long)(1)
vi=0.005,ve=1.2(long)(2)
vi=0.005,ve=1.2(open)
 vi=0.005,ve=1.25
(x=512)
(x=1024)
(x=2048)
0.0005 vi=0.0005,ve=0.1






0.1 0.3 - 0.35 0.5 - 0.7 1.2 1.25 2 -


Ve/Vd

Ve: Electron thermal velocity
Vi: Ion thermal velocity
Vd: Drift velocity of electrons relative to ions at rest

no sign: Periodic system
long: Very long periodic system
open: Open system

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