  The aim of this paper is to study a one dimensional model system of equations
for ionized gas dynamics at high temperature where the gas is a mixture of two
kinds of monatomic gas. In addition to the mass density, pressure, temperature
and particle velocity, degrees of ionization of both gases are also involved.
By assuming that the local thermal equilibrium is attained, Saha's ionization
equations are added. Thus the equations are supplemented by the first and
second law of thermodynamics, a single equation of state and, in addition, a
set of thermodynamic equations. The equations constitute a strictly hyperbolic
system, which guarantees that the initial value problem is well-posed locally
in time for sufficiently smooth initial data. However the geometric properties
of the system are rather complicated: in particular, we prove the existence of
a region where convexity (genuine nonlinearity) fails for forward and backward
characteristic fields. Also we study thermodynamic properties of shock waves by
a detailed analysis of the Hugoniot locus, which is used in a mathematical
study of existence and uniqueness of solutions to the shock tube problem.
