On the Distribution Function of Particles at Quasi-parallel Collisionless Shocks

Abstract

The departure of particle distributions from the Maxwellian is commonly observed in space plasmas. These non-Maxwellian distributions which are typical for plasmas that are not in thermal equilibrium, can be modeled with Kappa distribution function. Kinetic simulations of quasi-parallel collisionless shocks show that proton distribution is a composite of thermal, supra-thermal, and non-thermal parts, which correspond to thermalized, pre-accelerated, and diffusive-shock-accelerated protons, respectively. By using particle-in-cell shock simulations, we show that Kappa distribution adequately fits thermal and supra-thermal parts together, as one continuous distribution in early proton spectra. We find that the index kappa of the distribution increases with the distance from the shock, following the decrease in supra-thermal part. In the far downstream, initially strong supra-thermal part almost completely fades, leaving the proton distribution composed of a Maxwellian and a power-law.