A Model of the Multicathode-Spot Vacuum Arc

A model is proposed for the multicathode-spot (MCS) vacuum arc. A zero-order model is first constructed, whereby the interelectrode plasma is produced by the multitude of cathode spots, and flows to the anode upon which it condenses. The electron density is calculated by assuming that the plasma is uniform within a cylinder bounded by the electrodes and using experimental data for the ionic velocities and ion current fraction obtained in single cathode spot arcs. The electron density thus obtained is proportionate to the current density, and is equal to 5 × 10²⁰ m^–3 in the case of a 10⁷-A/m² Cu arc. The model predictions are a factor of 3–4 lower than measured values. Firstorder perturbations to the zero-order model are considered taking into account inelastic electron-ion collisions, plasma-macroparticle interactions, the interaction of the self-magnetic field with the plasma and electric current flows, and the interaction with the anode. Inelastic collisions tend to increase the ionicity of the plasma as a function of distance from the cathode, in agreement with spectroscopic observations. Macroparticles are heated by ion impact until they have significant evaporation rates. The vapor thus produced is ultimately ionized, and most probably accounts for the discrepancy between the zero-order prediction of electron densities and the measured values. Constrictions near the anode in both the plasma and electric current flows have been calculated. An overabundant electron current supply forces the anode to assume a negative potential with respect to the adjacent plasma. The anodic heat flux will be dominated by ionic heating at lower values of electron temperature, and electronic heating at higher values. Sputtering from the anode is responsible for the local peak in neutral density observed near the anode.