A closed solution for the corona field and charge transfer phenomena and the transformation of the results into an arbitrary electrode system

Experimental and theoretical studies of corona discharges available in literature have concentrated on the classical configurations, namely plane to plane, cylindrical, pin-plane and filament-plane. A number of closed solutions have been published that cover much ground; in addition, the popularity of numerical methods has resulted in a number of programs being available for situations where a closed solution is not available, not accessible, or too complex to apply. However, most of the studies have concentrated on a given particular corona geometry. Less attention has been focused on the degree of validity, with which the theoretical and experimental results obtained in one particular corona configuration could be applied to other configurations. In the paper, a charge transfer equation valid for one type of corona discharge (plane-parallel) is formulated and its approximate closed solution found. Then transformations are proposed that apply the results to the other common electrode configurations, such as the filament-cylinder and point-sphere. The errors incurred in such transformations are discussed and the accuracy of the transformations justified by data obtained from experiments performed specifically for this purpose.