Mathematical simulation of the distribution of the electron beam current during pulsed heating of a metal target

We study a model of the current distribution during heating of the surface of a tungsten sample under pulsed exposure to an electron beam. The model is based on solving the equations of electrodynamics and the two-phase Stefan problem for calculating the temperature in the sample region using a cylindrical coordinate system. The model parameters were taken from experiments at the «Beam of Electrons for materials Test Applications» (BETA) stand created at the Budker Institute of Nuclear Physics. A particular case of axial symmetry is considered without taking the electromotive forces into account. The current is considered as a possible source of rotation of the substance which is observed in the experiment. The values of the current and the acceleration of matter at a surface temperature of over $6000$ K were obtained. The results of the performed simulation show that, to obtain an acceleration capable of initiating the experimentally observed rotation of the melt, it is necessary to take into account some alternative mechanisms of creating a current in the system with consideration of the evaporation of tungsten above the plate.