Mathematical modeling of two-dimentional periodic system of field emitters

The work is devoted to a two-dimensional periodic system of field emitters mathematical modeling. Field-emission electron-vacuum devices are actively used in many fields of science and technology. In this article the field cathode as a periodic system of emitters of infinite length and the same shape, located on a flat substrate and at the same distance from each other, is investigated. Anode is a plane parallel to the substrate. To calculate the electrostatic potential distribution the influence of each emitter is replaced by the influence of a charged filament. To solve the boundary value problem for the Poisson equation the variables separation method in Cartesian coordinates is used. The potential distribution was found in an analytical form in the entire area of the system. In accordance with the formulas obtained, numerical calculations were carried out and the effect of emitter packing density on the electrostatic potential distribution is shown.