Model of a wedge-electrode corona discharge under saturation: Exact solutions

Analytical solutions for the distributions of the electric field potential and electric charge density are derived for the outer region of a steady-state unipolar corona discharge from an ideal wedge-shaped electrode under the conditions of space-charge-limited current. Two situations are considered: a corona is initiated only from the edge of the wedge and from the entire surface of the electrode. In the former case, general solutions are obtained by sewing together exact cylindrically symmetric solutions in the drift space and plane symmetric solutions in space-charge-free regions. In the latter case, the field distribution near the edge turns out to be self-similar, i.e., invariant under extensions in the cross-sectional plane of the wedge, with the center at the top of the wedge. For both models, the dependences of the saturation current per edge’s unit length on the apex angle and applied potential difference are obtained.