Mathematical modeling of a diode system with a spherical field cathode

Abstract

The rotationally symmetric diode system with a field cathode is under investigation. The shape of the field cathode is sphere-on-cone. The anode is a part of a sphere. In this paper two cases are considered, when the interior of system’s domain is filled with two and three different dielectrics. To calculate the electrostatic potential distribution the method of separation of variables is used. The solution of the boundary-value problem for the Laplace’s equation in the spherical coordinates is found an analytical form as the Legendre functions series.