Transient Cathode Spot Operation at a Microprotrusion in a Vacuum Arc

A physical model and system of equations was formulated to describe transient cathode spot evolution at a single protrusion. The model considered the self-consistent processes including protrusion heating, kinetics of cathode vaporization, plasma generation, and current continuity. The time dependencies of spot current, current density, and protrusion size were calculated, taking into account the heat flux from the plasma (surface heat source) and Joule energy (volume source). The plasma density, temperature, degree of vapor ionization, electron current fraction, and cathode erosion rate were calculated as functions of the protrusion size, which reduced in time during the spot operation. It was shown that the spot operation on the protrusion was limited by the disappearance of the protrusion due to cathode erosion. The protrusion disappearance time determined the duration of the transient arc spot at a single protrusion. It was calculated that 1-5 mum protrusions reduce their size significantly due to evaporation in 0.5-10 mus, respectively. The smaller time of protrusion destruction occurs due to it relatively high heating, which was mostly by the heat flux from the surrounding plasma.