Model of corona discharge from a thin point in a space-charge-limited current regime

Exact self-similar solutions for the problem of electric field and charge density distribution in the external region of a unipolar corona discharge from a thin point emitter have been found. The obtained solutions are valid outside the framework of the traditional Deutsch approximation based on the small influence of a volume charge on the shape of equipotential surfaces. The value of a saturated discharge current is estimated assuming that the corona discharge is generated by a certain part of the point.