Semiempirical Model of the Microcrater Formation in the Cathode Spot of a Vacuum Arc

A semiempirical hydrodynamic model based on the cellular structure of the cathode spot (CS) of a vacuum arc has been developed to describe the formation of a microcrater on the cathode and the initial axisymmetric stage of the formation of liquid-metal jets. The model includes experimentally obtained characteristics of the CS plasma interacting with the cathode, such as the pressure exerted by the plasma on the cathode and the power dissipated in the cathode. In the context of a 2-D axisymmetric problem statement of charge, heat, and mass transfer in a cathode, the formation of a crater on a copper cathode has been simulated for a constant current carried by an individual CS cell. It has been shown that for the cell current ranging between 1.6 and 7 A and the time of current flowthrough a cell ranging between 15 and 60 ns; the crater diameter is 3-7 μm. In these cases, the current density at the center of a CS cell is ~10
¹²
A/m
²
, and the average current density in a cell, determined using the crater diameter, is ~10
¹¹
A/m
²
. The obtained results are in agreement with experimental data on the crater size, CS lifetime, and CS current density at near-threshold arc currents.