Cathode Spot Development on a Bulk Cathode in a Vacuum Arc

A transient model of spot on a bulk cathode is developed, considering the initial adjacent plasma generated during arc triggering. A self-consistent approach is described and a closed mathematical solution is presented to understand the transient cathode phenomena and the time-dependent cathode potential drop (CPD), considering the kinetics and gas dynamics of the cathode plasma flow. The time-dependent spot development is calculated by considering different existing lifetimes tau of an initial plasma adjacent to the cathode for Cu, Cr, and W and 10-A spot current. The lifetime t is in the range of 2-100 ns. The solution shows that for Cu, the cathode temperature increased from 3500 to 4300 K with spot time. The CPD decreased with spot time from initial values 100-45 V (depending on tau) to 14-15 V at steady state. The solution for a refractory W cathode is obtained using a previously developed virtual cathode model. Calculation shows that a spot current density of similar to 10(7) A/cm(2) can support the spot initiation in a time of 2 ns considering W cathode vaporization with plasma generation by atom ionization. When tau increased from 2 ns to the 2 mu s range, the W cathode temperature decreased from similar to 10 000 K to a relatively low level of 7500 K.