# Article

Plasma Investigations
2006. V. 44. № 1. P. 22–28
Londer Ya.I., Ulyanov K.N.
A two-dimensional mathematical model of a short vacuum arc in external magnetic field: results of numerical calculations
Annotation
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.
Article reference:
Londer Ya.I., Ulyanov K.N. A two-dimensional mathematical model of a short vacuum arc in external magnetic field: results of numerical calculations, High Temp., 2006. V. 44. № 1. P. 22