A short-arc xenon discharge of high (super-high) pressure, which is widely used as a light source, has been studied taking into account the evaporation of cathode material (thorium) into the discharge volume. The article is a continuation of the experimental study, results of which were published earlier (IEEE Transactions on Plasma Science, July 2019, Vol. 47, Issue 7, pp. 3266-3270). A model of the discharge of real geometry is developed, the ellipsoidal coordinates as the most appropriate being used. The strong influence of thorium on the plasma characteristics is obtained. The most noticeable effect is got for the plasma temperature, which is sufficiently lower near the cathode than in a pure xenon discharge, the electric field strength having higher values and penetrating deeper into the discharge volume, and the density of xenon ions, which is close to zero near the cathode that is completely inexplicable without thorium evaporation into the discharge. The results and the approach can be applied to describe other arc discharge plasmas with electrodes doped with some weakly ionized additives.