Simulating Ignition and Development of Cathode Spots in Vacuum Arcs

A detailed numerical model of individual cathode spots in high-current vacuum arcs is developed. The model takes into account two kinds of plasmas in the vicinity of the spot: an “external” plasma (e.g., a plasma generated for arc triggering, a bulk background plasma, or a plasma cloud left over from a previous spot in the immediate vicinity) and the plasma produced due to ionization of the metal vapor emitted in the spot. Both kinds of plasma provide energy fluxes and exert pressure over the cathode surface. Ions from the external plasma enter the cathode space-charge sheath with Bohm's velocity and are accelerated in the direction of the cathode. The plasma produced in the spot is described by means of the model [1]. Melting of the cathode metal and motion of the melt are described by means of the heat conduction and Navier-Stokes equations, solved with account of Joule heat generation in the cathode body, evolution of the cathode surface, the pressure exerted by the plasma, the Lorentz force, and surface tension. Simulation results are given and analyzed for cathodes with microprotrusions and planar cathodes, both made of copper.