Time Evolution of the Distribution Function in the Perpendicular Collisionless Shock Wave

Abstract

Instability of anisotropic ion distribution function in the velocity space and its quasilinear relaxation to saturation of parallel energy growth due to coupling with the ion cyclotron mode with the wave vector parallel to the magnetic field are investigated. The initial ion velocity is assumed to be perpendicular to the magnetic field to model plasma state downstream the shock wave front. A numerical method to solve the integral dispersion equation for growing and decaying modes in a wide range of increments is proposed and tested for some analytic distribution functions. Quasilinear relaxation results in isotropisation of the ion distribution function. It is shown that times exceeding one hundred ion gyrotimes are required to achieve substantial isotropy via ion cyclotron mode coupling for plasmas with β~1.