In order to utilize metallic plasma of the vacuum arc in practice, it is important to understand not just the nature of cathode spots but also the mechanism of cathode spot multiplication (by splitting and separate spot arise) with arc current variations. The cathode spot splitting determines the total arc plasma generation and energy density distribution at the cathode surface. A physical model is developed to understand the regularity of the cathode spot splitting and its division. This model is based on the analysis of the radial distribution of the self-magnetic field of a single spot current and its constriction at the axis with spot current increasing, which leads to non-uniformity of radial current distribution resulting in division of the primary spot. The proposed mathematical approach allowed us to obtain numerical characteristics of the formation of single spots by taking into account typical protrusion configurations (cylindrical, droplet hemisphere on thin pedicle, and cone) at the cathode surface. The calculations show that during arcing, significant density of background plasma can arise in electrode gaps of about 0.2–0.5 cm. The considered protrusion configurations can be destroyed due to the action of the background plasma. As a result, a relatively high plasma density is generated, which is sufficient to initiate single spots at the cathode in arc time in agreement with experiments. Formation of current per single spot is modeled considering a review of its published experimental data and comparison of pressure of the self-magnetic field generated by spot current with the plasma kinetic pressure. This is done at a distance from the cathode surface where these pressures are equal. To this end, the respective plasma density is determined by calculating the cathode erosion in ions from the area of single spot using the measured total ion current in the arc and the number of spots obtained by the ratio of the arc current to the current per single spot. This study shows that the calculated current per single spot for a wide number of cathode materials is found to be in the range that is experimentally measured in both single spot and fragments of a group spot.
I. I. Beilis (Mon,) studied this question.