Numerical simulation of the anode region of a high-current vacuum-arc discharge and the Bohm criterion

Abstract

The anode region of the vacuum-arc discharge in an external magnetic field is studied with allowance for the dependence of the negative anode drop on the ratio of the directed velocity of electrons v0 to their thermal velocity vT. The Poisson equation is solved in a space charge layer near the anode at various values of the electric field E(0), ion velocity vi(0), and parameter v0/vT at the layer-plasma boundary. It is shown that there exists a minimum velocity vi* (0)of ions incoming to the anode layer at which the electric field vanishes at a single point inside the layer. The velocity vi* (0) determines the boundary of the existence of the stationary anode layer and depends on the ratio v0/vT. As v0/vT → 0, the value vi* (0) asymptotically tends to the ionsound speed, which agrees with the well-known Bohm criterion. The velocity vi* (0)increases with an increase in v0/vT. For vt (0) < vi*(0), there are no stationary solutions in the anode layer. The domain of existence of stationary solutions in the anode layer is determined for different values of the parameters E(0) and v0/vT.