Stepwise and Statistical Simulation on the Random and Retrograde Motion of a Single Cathode Spot of Vacuum Arc

In this paper, the influence of an external transverse magnetic field, in parallel with the cathode surface, on the ignition probabilities of a cathode spot (CS) in the Amperian and retrograde directions is developed assuming that the ignition probability of a new CS is proportional to the magnetic pressure around the old one. Furthermore, both stepwise and statistical models are established to simulate the random and retrograde motions of a single CS of vacuum arc, assuming that the 2-D motion of the CS in the xy plane is equivalent to the synthesis of two independent 1-D movements along the xand y-axis, respectively. With both models, the random and retrograde motions of a single Cu CS are simulated step by step and statistically, respectively. It was found that stepwise simulation results agree well with the statistical results, and they are also consistent with the relevant experimental results. The difference in retrograde motion velocity between the present stepwise model and that assuming that a new CS can be ignited in any direction around the old one is discussed.