Phasespace transport of a quasi-neutral multi-fluid plasma over the solar wind MHD termination shock

We study the physics of a multi-ion MHD shock, i.e. an MHD shock feature that forms when a supersonic flow of mixed ion populations is forced to adapt itself to a pressure obstacle further downstream. We shall describe this situation by using a multi-fluid approach for a mixture of ion populations with different specific masses and charges per ion species. First we calculate the effective electric potential that forces the plasma bulk to decelerate to the downstream bulk flow velocity which also then defines that system into which the downstream magnetic field is frozen-in. Then we calculate the unavoidable ion-specific overshoot velocities and gain from them, requesting energy conservation, the ion-specific contributions to the downstream thermal energies and pressures. The aim thereby is to find the solution for the MHD status of the downstream flow of the plasma mixture, specifically for a proton-electron plasma. We derive an implicit equation for the effective compression ratio and explicit relations for the different, downstream ion and electron temperatures as function of the multi-fluid compression ratio s. The resulting actual multi-fluid compression ratio s _eff is found by adding up all the partial downstream pressures and comparing it with the upstream ram pressure. As we can show, the electron pressure is the dominant contribution to the total downstream plasma pressure.