Two-dimensional model of plasma cathode with an open plasma boundary

The paper deals with the solution of two problems for which a two-dimensional distribution is found of the current density and of the electric field in the hollow-cathode plasma. In the first one of these problems, the anode surface of the cavity represents two concentric flat anodes separated by an insulator. This system is used to study the problem of switching the current over from the external to internal anode, with the anode drop being a nonlinear function of current density. The distribution of the current density and of the anode voltage drop on the surfaces of both anodes is calculated for different potentials of the external and internal anodes. In the second problem, the function of internal anode is served by the open boundary of plasma with zero anode drop. The shape of the plasma boundary is determined depending on the plasma cathode geometry and parameters. The singularities are discussed that characterize the extraction of current from the open plasma boundary for different forms of electric discharges.