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.

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The paper deals with the investigation of the impact made by two-dimensional effects on the process of passage of current in a short vacuum arc in an axial magnetic field. A two-fluid mathematical model is used, which is based on hydrodynamic and electrodynamic equations. The axial magnetic field B z affects significantly the magnitude of two-dimensional effects: the two-dimensional effects increase with decreasing B z . The simulation results demonstrate that the contraction of plasma density exceeds that of current density. The distribution of anode drop of potential on the anode surface is nonuniform; in the case of certain (critical) values of current, the anode drop goes to zero on the external boundary of plasma. The dependence of the critical current on B z is determined. The distribution of current density on the starting plane is nonuniform with a maximum on the axis, and the ion trajectories are inclined to the discharge axis. The possibility is discussed of matching the solution in the plasma region of vacuum arc with that for cathode flames.

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