On relativistic space charge limited current in planar, cylindrical, and spherical diodes

Abstract

This paper revisits the relativistic limiting current in planar, cylindrical, and spherical diodes, with alternative analytic and numerical treatments which are easy to implement. Convenient, approximate expressions for the limited current are presented for gap voltages up to 10 MV. They are accurate to within 1% for planar diode, and to within 4% for both cylindrical and spherical diode in the range 10−5<rc/ra<500, where ra and rc are, respectively, the anode and cathode radius.