The arbitrarily shaped field emitter mathematical modeling

This article is devoted to the field emitter of the arbitrary shape mathematical modeling. The axially symmetrical diode system with a field cathode on a plane substrate and a plane anode is under investigation. The effect of the field emitter is simulated using the charged circular lines to solve the boundary-value problem so that the zero electrostatic equipotential coincided with the cathode surface. The potentialal distribution as the Fourier-Bessel series is found an analytical form in the cylindrical coordinates.