Particle phase space oscillations of the two-stream instability under strong initial perturbation

The instability generated by two-stream system is a common plasma instability in geospace. Electrostatic solitary waves that are observed in the Earth's magnetotail, plasma sheet boundary layer, the Earth's bow shock, the solar wind, the cusp, and in the auroral acceleration region, are generated by the two-stream instability. The geo-space environment is neither uniform nor stationary, so the initial perturbation should be considered in the study of two-stream system evolution. Based on our developed kinetic particle-in-cell model, we investigate the instability of the two-stream system with strong initial perturbation. We find that particles oscillate in the phase space. The oscillation frequency is related with the spatial wavenumber of initial perturbation. The frequency component of electric field and electric energy also exists. By linear theory, we obtain the oscillation frequency. It is consistent with the oscillation frequency obtained by particle-in-cell simulation. This frequency consists of two components: one is the Langmuir frequency of the system, the other is a frequency offset related to the spatial wavenumber of the initial perturbation. We change the plasma frequency, and confirm the conclusion. Our results indicate that the initial perturbation condition is very important to the instability of the two-stream system, and advance our understanding on the process and consequence of the evolution of the two-stream system in the Earth's magnetosphere.