Equivalent capacitance derivation of space-charge-limited current from a filamentary cathode

Dow has outlined a method of calculating the space-charge-limited current and obtained a formula that is valid for cathode diameter to anode-to-anode spacing ratio of less than 40 percent. A new formula has been derived that will extend the limit and give excellent result for as high a cathode diameter to anode-to-anode spacing ratio as 70 percent.