A system of ionized gas dynamics

The aim of this paper is to study a system of three equations for ionized gas dynamics at high temperature in one spatial dimension. In addition to the mass density, pressure, and particle velocity, a further quantity is needed, namely, the degree of ionization. The system is supplemented by the first and second law of thermodynamics and by an equation of state; all of them involve the degree of ionization. Finally, under the assumption of local thermodynamic equilibrium, the system is closed by requiring Saha's ionization equation. The geometric properties of the system are rather complicated: in particular, we prove the loss of convexity (genuine nonlinearity) for both forward and backward characteristic fields and hence the loss of concavity of the physical entropy. This takes place in a small bounded region, which we are able to characterize by numerical estimates on the state functions. The structure of shock waves is also studied by a detailed analysis of the Hugoniot locus.