Excited-state densities in a multicathode-spot Al vacuum arc. II. Theoretical approach

Abstract

A model is formulated to calculate excited‐state densities in a multicathode‐spot (MCS) vacuum arc. The model is composed of two components: (1) a semiempirical model for the emission of ions from the cathode surface and subsequent plasma flow and (2) a theoretical model for inelastic collisions, including excitation and ionization, and radiation in the interelectrode plasma. After consideration of characteristic times prevalent in MCS arcs, the model is reduced to a set of P‐1 simultaneous linear equations and one differential equation for each ionic species considered, where P is the number of states considered for that species, where the independent variable is time in the frame of the flowing plasma, or equivalently distance from the cathode, and where the dependent variables are the populations of the various states. The model was used to determine the electron temperature in a MCS Al arc by leaving the electron temperature as a free parameter and choosing the value giving the best agreement with experimentally determined excited‐state populations. For a 10⁷‐A m⁻² arc an electron temperature of 6 eV was determined. It was further concluded that inelastic collisions dominate elastic collisions as an electron energy loss mechanism in this plasma.