Should plasma reactivity be taken into account in vacuum arc plasma modeling?

Abstract An assumption often made in models of the diffuse arc plasma in vacuum interrupters is to neglect ionization and recombination reactions in the interelectrode gap. In this work, this assumption is investigated. For this purpose, we derive appropriate characteristic lengths for these phenomena. These lengths are then evaluated assuming that ionization by electron impact and three-body recombination are the main mechanisms, accounting for both direct and stepwise processes, the latter being shown to be dominant. For a copper plasma and typical gap lengths, it is found that ionization and recombination are indeed negligible under supersonic flow conditions. However, these reactions exist in the whole gap under subsonic conditions. Under thermodynamic conditions predicted by models neglecting stepwise processes, it is shown that Cu 3+ ions should be the dominating species in the interelectrode gap. However, this conclusion is in contradiction with recent spectroscopic diagnostics, in which Cu 3+ ions were not found. This contradiction may be resolved by remembering that an account of stepwise ionization will generate an additional loss in the electron energy equation, which leads to a decrease of the electron temperature and therefore, of the Cu 2+ ionization coefficient. Finally, in the subsonic case, since some species have very small ionization lengths, it is shown that a treatment under equilibrium (Saha) conditions is appropriate to understand the charge state distribution.