2D semiempirical model of the formation of an elementary crater on the cathode of a vacuum arc

A semiempirical hydrodynamic model based on the cellular structure of the cathode spot of a vacuum arc has been developed to describe the formation of a microcrater on the cathode and the initial stage of the formation of liquid-metal jets. The model includes experimentally obtained characteristics of the cathode spot plasma interacting with the cathode, such as the pressure exerted by the plasma on the cathode and the energy balance in the arc. In the context of a 2D axisymmetric statement of the problem of electric heat and mass transport in a cathode, the formation of a crater on a copper cathode has been simulated for a constant current carried by a elementary cathode spot cell. It has been shown that for the cell current ranging between 1.6 and 7 A and the time of current flow through the cell ranging between 15 and 60 ns, the crater diameter is 3÷7 μm. The crater depth is determined mainly by the current density in the cell. For all calculation variants where a micrometer-size crater was formed in several tens of nanoseconds, the maximum current density in a cell was (1÷3)·10 ⁸ A/cm ² .