Phenomenological approach to simulation of propagation of spots over cathodes of high-power vacuum circuit breakers

A phenomenological description of an ensemble of a large number of spots on negative contacts of high-power vacuum circuit breakers is developed by means of generalization of the concept of random walk of a single cathode spot in low-current vacuum arcs. The model is formulated in terms of a convection-diffusion equation governing the evolution of the number of spots per unit area, taking into account the variation of the number of spots with the arc current and the “retrograde repulsion” between spots. The approach is applied to description of the distribution of cathode spots during the initial expansion process after arc ignition in conditions of two independent experiments simulating high-power switches. A reasonably good agreement between the theory and the experiment is found. The developed model can be used as a module of global numerical models of the interruption process in high-power vacuum circuit breakers.