Theory of space-charge sheaths on cathodes of vacuum arcs

The model of a collisionless near-cathode space-charge sheath with ionization of atoms emitted by the cathode surface is considered. It was found that such sheath represents a double layer with a potential maximum, with the ions which are produced before the maximum returning to the cathode surface and those produced after the maximum escaping into the plasma. Distributions across the sheath have been calculated of ion, electron, and atomic densities, electrostatic potential and electric field. Also calculated have been integral parameters of the sheath. The results may be readily incorporated into models of near-cathode layers of discharges burning in cathode vapor. Besides, these results may be employed for qualitative analysis. In particular, the results indicate that the ion backflow coefficient in such discharges is at least 53%. As an example of application of the theory, calculation results on spots on copper cathodes of vacuum arcs are given and a favorable agreement with available experimental data is found.