Oblique Ion Two-Stream Instability in the Foot Region of a Collisionless   Shock
  Electrostatic behavior of a collisionless plasma in the foot region of high Mach number perpendicular shocks is investigated through the two-dimensional linear analysis and electrostatic particle-in-cell (PIC) simulation. The simulations are double periodic and taken as a proxy for the situation in the foot. The linear analysis for relatively cold unmagnetized plasmas with a reflected proton beam shows that obliquely propagating Buneman instability is strongly excited. We also found that when the electron temperature is much higher than the proton temperature, the most unstable mode is the highly obliquely propagating ion two-stream instability excited through the resonance between ion plasma oscillations of the background protons and of the beam protons, rather than the ion acoustic instability that is dominant for parallel propagation. To investigate nonlinear behavior of the ion two-stream instability, we have made PIC simulations for the shock foot region in which the initial state satisfies the Buneman instability condition. In the first phase, electrostatic waves grow two-dimensionally by the Buneman instability to heat electrons. In the second phase, highly oblique ion two-stream instability grows to heat mainly ions. This result is in contrast to previous studies based on one-dimensional simulations, for which ion acoustic instability further heats electrons. The present result implies that overheating problem of electrons for shocks in supernova remnants is resolved by considering ion two-stream instability propagating highly obliquely to the shock normal and that multi-dimensional analysis is crucial to understand the particle heating and acceleration processes in shocks. 
Yutaka Ohira and Fumio Takahara