A Paraxial approximation of the problem of formation of nonparaxial conical and toroidal electron beams of an arbitrary cross section

Abstract

A paraxial solution is constructed for the problem of calculation of forming electrodes for non-paraxial cuts from converging and diverging flows in a spherical diode and a Meltzer flow with circular paths. The solution is expressed in elementary functions for the case of a cone. For example, computations for a square on a sphere (the first approximation of the approximation of a contour) and a toroid with a circular cross section are presented.