Effect of a weak ion collisionality on the dynamics of kinetic electrostatic shocks

TL;DR

This paper investigates how weak ion collisionality influences the structure and evolution of electrostatic shocks, revealing that small collisions smooth discontinuities and induce potential oscillations, with effects accumulating over the shock's lifetime.

Contribution

It introduces a semi-analytical model for weakly collisional kinetic shocks, highlighting the impact of finite collisionality on shock dynamics and phase-space structure.

Findings

Collisionality smooths phase-space discontinuities into boundary layers.

Ions diffuse into empty phase-space regions, upsetting charge balance.

Shock evolution depends more on collisional age than on collisionality.

Abstract

In strictly collisionless electrostatic shocks, the ion distribution function can develop discontinuities along phase-space separatrices, due to partial reflection of the ion population. In this paper, we depart from the strictly collisionless regime and present a semi-analytical model for weakly collisional kinetic shocks. The model is used to study the effect of small but finite collisionalities on electrostatic shocks, and they are found to smooth out these discontinuities into growing boundary layers. More importantly, ions diffuse into and accumulate in the previously empty regions of phase space, and, by upsetting the charge balance, lead to growing downstream oscillations of the electrostatic potential. We find that the collisional age of the shock is the more relevant measure of the collisional effects than the collisionality, where the former can become significant during the lifetime of the shock, even for weak collisionalities.