On Collisionless Shocks in a Cold Plasma

Motivated by the problem of shocks in a collisionless plasma, we consider the steady Vlasov-Maxwell system in one space dimension. In the case of a cold plasma, the problem reduces to a set of ordinary differential equations. It is assumed that the upstream state of the plasma is given. The downstream state is investigated using the conservation laws and numerical simulation. It is found that when the masses of positive and negative ions differ, that the downstream behavior can differ from the upstream behavior.