Effects of electron trapping and ion collisions on electrostatic shocks

Electrostatic shocks in plasmas have been observed to be able to accelerate particles to twice the shock velocity with a very low energy spread. Shock phenomena are often modeled as exactly collisionless, which is a very good approximation for astrophysical shocks. However, collisions might play a role in shocks created in laboratory plasmas, since very sharp features of the ion distribution function develop due to ions being reflected at the shock front; this ion reflection results in empty regions of phase space with discontinuities at their boundaries. In this thesis the effects of a weak but finite ion collisionality are considered in a time dependent, semi-analytical treatment. The amplitude of the downstream potential oscillation is found to increase approximately as the square root of time as particles are scattered into the originally empty regions of phase space. The corresponding changes in the electrostatic potential lead to an increased size of the trapping regions in the ion phase space. This thesis also studies the effect of electron trapping in the potential oscillations downstream of the shockfront. Two model electron distributions, which are flat in the trapped regions of phase space, are considered. The two models only differ in where the potential threshold for trapping is set; one model allows for trapping at a freely set threshold in order to emulate the effects of far downstream behavior of the shock, while the other model only allows for trapping inside the downstream potential oscillation. In general the effects of electron trapping are to reduce the maximum electrostatic potential, but at the same time increase the range of shock propagation speeds for which electrostatic shock solutions exist. The second electron trapping model also exhibits multiple shock solutions for the same temperature ratio and Mach number in certain parameter regions