Theoretical Model of the Retrograde Motion of Cathode Spots of Vacuum Arc

The phenomenon of cathode spot (CS) retrograde motion has been attracting extensive research in the field of vacuum arc. Although a number of theoretical models have been proposed to explain this phenomenon, up to now, the first-principle understanding is still missing. In this work, based on the generalized Ohm’s law, it is proposed that there is a transport current in the explosive emission center when a transverse magnetic field (TMF) is applied. The investigation of the influence of the transport current on the strength of the electric field in the cathode sheath suggests that the transport current affects the ignition of new CS in the retrograde direction. In the framework of the ecton model, combined with the dynamics of explosive emission plasma, the relationship between the strength of applied TMF and the ignition probability of new CS in different directions is established, and the retrograde motion characteristics of CS are simulated using a statistical model. The simulation results show that the directionality of retrograde motion of CS is enhanced with an increase in TMF, and the retrograde motion speed of CS increases with the increase of the applied TMF. When the strength of TMF is small, the motion speed of a single CS has a linear relationship with the strength of TMF, but with the increase of the strength of TMF, the motion speed of a single CS is gradually saturated, which is consistent with experimental facts. The feasibility of the model is verified by comparing the simulation results with relevant experimental results.