In this paper, for the first time, we present a new model of current distribution in a tungsten sample and of substance evaporation when the surface is heated by an electron beam. The model is based on solving electrodynamics equations in a cylindrical coordinate system using a model temperature distribution in the sample and a thin layer of evaporated tungsten. The model is analyzed in a simplified formulation at constant values of electrical resistance and thermoelectric power in gas and metal. The dependence of the amplitude and isolines of thermal currents on the distribution of temperature at the sample surface is shown. The model parameters are taken from experiments at the Beam of Electrons for materials Test Applications (BETA) facility, created at the Budker Institute of Nuclear Physics of the Siberian Branch of the Russian Academy of Sciences.