A two-dimensional mathematical model of a short vacuum arc in external magnetic field: results of numerical calculations

Abstract

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.

A theoretical study of the impact of magnetic field of Hall current on the parameters of a high-current vacuum-arc discharge

“…For this purpose, it is necessary that the density of VAD current would decrease from the center to periphery by quite a definite law. In so doing, no strong contraction of current is observed [3,4].…”

“…A set of magnetohydrodynamic equations was used in [3,4] for developing a two-dimensional two-fluid mathematical jet model of VAD. The set of equations included equations of continuity, motion, and energy for electrons and ions.…”

“…In a high-current VAD, the magnetic force j θ B z almost fully balances the force j z B θ (pinch effect), and the radial electric field decreases to values at which the mode of current flow with equipotential anode is possible [3,4]. Therefore, the principle of almost complete compensation of radial magnetic forces is effective in a high-current VAD with axial magnetic field.…”

“…Such models have been developed [2][3][4][5][6][7][8] and are used for the calculations of various modes of VAD. These models are based on different mathematical approaches and are characterized by different ways of taking into account the impact made by the intrinsic magnetic field of discharge current.…”

“…These models are based on different mathematical approaches and are characterized by different ways of taking into account the impact made by the intrinsic magnetic field of discharge current. For example, in the case of the models of [3,4,6,8], only the azimuthal field of discharge current and external axial magnetic field are taken into account, i.e., the magnetic field of discharge current is included only in part. In these models, the effect of magnetic field of Hall current is ignored.…”