Critical flow of high-speed ions in a high-current vacuum-arc discharge

A physical model of vacuum arc is developed, which is used to construct a quasi-one-dimensional model and a two-dimensional two-fluid mathematical model. The two-dimensional magnetohydrodynamic model is based on the method of trajectories, according to which a set of partial equations is reduced to a set of ordinary differential equations written for derivatives along the lines of current. The quasi-one-dimensional model is based on the principle of compensation of radial magnetic forces, which is valid for a short high-current vacuum arc in axial magnetic field. A criterion is obtained, which defines the range of validity of the quasi-one-dimensional model in external axial magnetic field $B_0$. Calculations are performed of the dependence of critical current on $B_0$ for discharge gaps of different geometries. The calculation results agree with experiment.