Model of a Wedge-Electrode Corona Discharge
under Saturation: Exact Solutions

G. Sh. Boltachev^a, N. M. Zubarev^{a, b}*, and O. V. Zubareva^a

^a Institute of Electrophysics, Ural Branch, Russian Academy of Sciences, ul. Amundsena 106, Yekaterinburg, 620016 Russia
^b Lebedev Physics Institute, Russian Academy of Sciences, Leninskii pr. 53, Moscow, 119991 Russia
*e-mail: nick@iep.uran.ru

Received June 20, 2013

Abstract—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 elec-
trode 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 solu-
tions are obtained by sewing together exact cylindrically symmetric solutions in the drift space and plane sym-
metric 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.

DOI: 10.1134/S1063784214030074

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