  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. At last, under the assumption of thermal 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, which will be used
in a forthcoming paper to study the shock tube problem.
