A Two-Dimensional Mathematical Model of a Short Vacuum Arc in External Magnetic Field

A mathematical model of a short high-current vacuum arc is developed. The model involves equations of motion and continuity for electrons and ions, as well as electrodynamic equations. The boundary conditions are formulated on the cathode and anode boundaries of plasma and on the side surface of plasma. The model is based on the method of trajectories, in the case of which a set of partial equations can be reduced to a set of ordinary differential equations written for derivatives along ion trajectories. The model is used to determine the region of steady-state solutions and to calculate the distribution of the parameters of arc plasma in this region.