PIC Simulation of a quasi-parallel collisionless shock: Interaction between upstream waves and backstreaming ions

Abstract

We perform a one-dimensional full particle-in-cell (PIC) simulation of a quasi-parallel collisionless shock with the Alfvén Mach number 6.6 and a shock angle of 20 degrees between the upstream magnetic field and the shock normal direction. The backstreaming ions are self-consistently generated by reflections of the incoming ions at the shock. They generate the Alfvénic electromagnetic wave via the right-handed resonant ion-ion instability, as the ions travel toward the upstream region. The energy distribution of the backstreaming ions far upstream splits into two populations as it approaches the shock. The energy threshold of the populations is approximately the energy gained by a single specular reflection at the shock. The maximum energy of the backstreaming ions near the shock is about 10 times larger than the specularly reflected ion energy. Nonlinear phase bunches of the high-energy backstreaming ions and the background ions are found near the shock, due to the resonant and non-resonant trappings by the excited waves, respectively.