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

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 $v_0$ to their thermal velocity $v_T$. The Poisson equation is solved in a space charge layer near the anode at various values of the electric field $E(0)$, ion velocity $v_i(0)$, and parameter $v_0/v_T$ at the layer–-plasma boundary. It is shown that there exists a minimum velocity $v_i^*(0)$ of ions incoming to the anode layer at which the electric field vanishes at a single point inside the layer. The velocity $v_i^*(0)$ determines the boundary of the existence of the stationary anode layer and depends on the ratio $v_0/v_T$. As $v_0/v_T \to 0$, the value $v_i^*(0)$ asymptotically tends to the ion-sound speed, which agrees with the well-known Bohm criterion. The velocity $v_i^*(0)$ increases with an increase in $v_0/v_T$. For $v_i(0) < v_i^*(0)$, 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 $v_0/v_T$.