Time-Dependent Description of Cathode Crater Formation in Vacuum Arcs

A dynamic model describing crater formation on the cathode of a metal vapor arc is solved numerically. The model takes into account phase changes, Joule and ionic heating, electron emission, and mass loss due to evaporation and ejection of molten metal. The calculation yields crater radius, crater formation time, erosion rate, and mean spot velocity; the values agree well with available experimental data. The vacuum arc phenomena "minimal arc current" and "spot-splitting current" are explained theoretically. The mean current density in the spot is about 1012 A/m2. The relative importance of ionic heating with regard to Joule heating depends on the cathode material and current density. The increase of crater radius with temperature is not because of reduced heat conduction into the solid.