Modeling of cathode spot crater formation and development in vacuum arc

A two-dimensional (2D) rotary axisymmetric model has been developed to describe the formation and development of cathode spot in vacuum arc. The model includes hydrodynamic equations and heat transfer equation which considers surface evaporation and Joule heating. Parameters used in this model, such as the distributions of pressure, energy flux density, and current density, come from experiments and other researchers' work. In this model, cathode spot maintains 30 ns and during this time, all parameters are fixed. The simulation results show that when the energy flux density is 1.5-3 × 1012 W, discharge current is 1-6 A and the pressure is 1-3 × 108 Pa, the crater radius is 1.4-4.1 µm, the crater depth is 1.4-2.1 µm, the velocity of liquid metal is 154-428 m s−1 and the maximum temperature is 2145-5342 K which is located in the area with radius 0.5-1.5 µm. Besides, on the chromium cathode, the maximum temperature is higher mainly because of the lower thermal conductivity.