Searching for the optimal distribution of the axial magnetic field over the electrode radius by numerical simulation of motion of a cathode spot system in the self-consistent magnetic field

The work deals with simulation of cathode spot motion in two-dimensional statement. Plasma jets are infinite conductors with current, the height of the interelectrode gap is disregarded. The calculation proceeds as follows: the initial spot distribution is specified, Biot-Savart-Laplace law is used to calculate for each spot the magnetic field induced by other spots at the location of the spot in question. The motion is simulated in the stepwise manner, which corresponds to generation and extinction of cathode spots. At each step, the spot is shifted on the basis of obtained values of the magnetic field. Consideration includes two different models of cathode spot evolution, the two-threshold one and that of splitting and dying-off of spots with corresponding lifetimes. The steadying process of the voltage across the arc has been studied, yielding the Volt-Tesla characteristics of a spot system. Qualitatively, the behavior of the dependences agrees with the experiment, which is an argument in favor of the assumption that the high-current arc behavior is to a large extent governed by that of a system of individual cathode spots, interacting through the common selfconsistent magnetic field.