Simulating Propagation of Spots over Cathodes of High-Power Vacuum Circuit Breakers

Cathode attachment of high-current vacuum arcs, e.g., those in high-power vacuum circuit breakers, represents an ensemble of several hundred of spots operating simultaneously. A natural alternative to tracing individual spots is to employ the concept of surface density of spots in the ensemble. Such approach is pursued in this work. An equation governing the surface density of the spots represents a generalization of the convection-diffusion equation describing the random walk of a single cathode spot in low-current vacuum arcs. The drift velocity is associated with the retrograde motion of the spots in a tangential magnetic field, imposed externally and induced by the arc, and was estimated from experimental data relating the spot drift velocity to transversal and axial magnetic fields. The model is in a reasonably good agreement with the experiment, does not require significant computational resources, and produces results that do not require spatial averaging in order to be matched to existing numerical models of the arc on the whole. Consequently, the model can be readily implemented as a module of global numerical models of the interruption process in high-power vacuum circuit breakers.