Generalized Analytical Solution and Study of Conductive Ellipsoidal Field Emitters

This paper presents new equations that describe ellipsoidal field emitters in both ellipsoidal and Cartesian coordinates. Expressions are found for the potential, electric field, and field enhancement at any point in space. For both ellipsoidal and spheroidal emitters, equations are given to determine field emission current density and total current. It is also shown that the field enhancement at the surface of a spheroidal emitter is purely dependent on the surface location and the emitter's height to radius aspect ratio. Furthermore, simplified equations are given to approximate the field enhancement and total current for prolate spheroidal emitters of height to radius ratios greater than 100.