Improved Model for Anode Spot Formation in Vacuum Arcs

The evaporation instability model for anode spot formation in high-current vacuum arcs shows one severe deficiency: it needs a critical vapor density at the anode, that is by two orders of magnitude higher than the measured value. The discrepancy can be bridged, if it is assumed that due to the relatively cool anode a low vapor pressure exists near the anode and thus the self magnetic field constricts the arc in the vicinity of the anode considerably. In consequence, the vapor density is higher near the anode than far away from that electrode. The mathematical analysis of that model shows that the predicted constriction near the anode exists indeed. The vapor density obtained at the anode surface is by more than two orders of magnitude higher than in the column and the absolute value is high enough to start the anode spot instability due to evaporation of the anode. The model shows that neither a pure magnetic constriction model nor a pure anode evaporation model can account for the effects observed, but that both effects contribute considerably to the phenomenon of anode spot formation in high-current vacuum arcs.