Jump Conditions of a Non-Neutral Plasma Shock with Current and Potential Difference

Jump conditions about the total momentum flux and energy flux in a non-neutral plasma shock with electric current and field are given, which are derived from the double fluid equations and the Poisson equation for electron and ion fluids. Furthermore, We derive the relations between the upstream and downstream velocities and temperatures, and the minimum upstream Mach number for the plasma shock existence M^min₁, which depend on the current through the shock front J₀, the electric potential difference between the upstream and downstream of shock ΔФ, and the ion charge Z.