Hydrodynamics of the Molten Metal During the Crater Formation on the Cathode Surface in a Vacuum Arc

2-D axially symmetric hydrodynamic model has been developed to describe the formation of a crater and liquid-metal jets on a vacuum arc cathode using Navier-Stokes equations for an incompressible viscous fluid with a free surface and a heat conduction equation taking convective heat transfer into account. The formation of an elemental crater on a copper cathode during the operation of a cathode spot cell has been numerically simulated by varying the heat flux and the pressure produced by the cathode spot plasma. Based on the simulation results, we can distinguish three different modes of the crater formation process: 1) no splashing; 2) inertial splashing; and 3) active splashing. It has been shown that a crater with metal jets forced away can be formed within 30 ns of plasma action if the heat flux density is above 10¹² W/m² and the pressure is above 10⁸ Pa.