Calculation of the electrostatic potential of the diode system based on a sharp-edged field cathode

A mathematical model of a diode system based on a sharp-edged field cathode is presented. The surface of the sharp-edged cathode is simulated by two infinitely thin spherical segments, while the anode is modeled by a single infinitely thin spherical segment. The region occupied by the cathode is a lens (lune-shaped region). The problem of the electrostatic potential distribution in the entire domain occupied by the system is solved.