Potential and potential-gradient distributions for standard and practical electrode systems

An essential prerequisite of the so-called semiempirical method of estimating breakdown voltages for gas-insulated electrode systems is detailed information relating to potential gradients across the minimum-gap region. The paper provides formulas, and extensive tabulated potential and potential-gradient data, along the line or plane of minimum electrode separation, for several standard electrode systems for a wide range of gap/radius ratios. In addition, the paper presents various forward-, central-and backward-difference equations which, used in conjunction with digital numerical-field methods such as reported earlier by the authors, enable potential gradients (and consequently breakdown voltages) to be computed for many arbitrarily shaped practical electrode systems. Principal errors associated with these difference equations are discussed and illustrated by an example.