Plasma spatial characteristics of a short-arc xenon discharge of high (super-high) pressure, which is widely used as a light source, are studied taking into account the evaporation of cathode material, thorium (such light sources usually have tungsten cathodes doped with thorium), into the discharge volume. To solve the problem five equations are written and resolved for the main plasma characteristics: the strength of the electric field, plasma temperature, concentration of thorium atoms and densities of thorium and xenon ions. The consideration is carried out on the base of the model developed for the discharge of real geometry, the ellipsoidal coordinates as the most appropriate being used. This representation makes it possible to obtain straight away the spatial distribution of the electric field strength in ellipsoidal coordinates that, in turn, defines the other plasma characteristics and, first of all, the plasma temperature. The spatial distributions of the electric field strength, plasma temperature, concentration of thorium atoms and densities of thorium and xenon ions are obtained for the typical conditions of xenon short-arc lamps. The radial distribution of thorium atoms near the cathode shows a very interesting dependence with a maximum, which at first glance is rather unexpected. This fact is interpreted using physical considerations and geometric picture of the evaporation of thorium atoms from the cathode. The obtained data are important for the optimization of optical, lighting, and energetic characteristics of light sources on the base of arc discharges in rare gases. The data can also be fruitful for the study of other high current high pressure discharges with electrodes doped with some lightly ionized additives (thorium, rare earth elements etc.).