Multiple solutions in the theory of dc glow discharges and cathodic part of arc discharges. Application of these solutions to the modeling of cathode spots and patterns: a review

A new class of stationary solutions in the theory of glow discharges and plasma-cathode interaction in ambient-gas arc discharges has been found over the past 15 years. These solutions exist simultaneously with the solution given in textbooks, which describes a discharge mode with a uniform or smooth distribution of current over the cathode surface, and describes modes with various configurations of cathode spots: normal spots on glow cathodes, patterns of multiple spots recently observed on cathodes of glow microdischarges and spots on arc cathodes. In particular, these solutions show that cathode spots represent a manifestation of self-organization caused by basic mechanisms of the near-cathode space-charge sheath; another illustration of the richness of the gas discharge science. As far as arc cathodes are concerned, the new solutions have proved relevant for industrial applications. This work is dedicated to reviewing the multiple solutions obtained to date, their systematization, and analysis of their properties and physical meaning. The treatment is performed in the context of general trends of self-organization in bistable nonlinear dissipative systems, which allows one to consider glow discharges or arc-cathode interaction within a single physically transparent framework without going into mathematical details and offers a possibility of systematic computation of the multiple solutions. Relevant computational aspects and experimental data are discussed.