Asymptotic Analysis of the Steady-State Current Flow in a Uniform Multicathode-Spot Generated Vacuum-Arc Plasma Flow

The current distribution in a model multicathode-spot vacuum-arc generated uniform plasma flow is analyzed analytically by studying the asymptotic behavior of the magnetic transport equation in the limit of large electron-flow magnetic Reynolds number. It is found that the radial distribution of the axial current flow imposed at the cathode is maintained throughout most of the interelectrode region, and that a strong constriction of the current flow occurs in a narrow boundary layer adjacent to the anode surface. The results support the general trend observed in previous numerical solutions.