Algorithm for calculating the emission current density in the beam-focussing problem

Abstract

AN ALGORITHM for determining the emission current density in a cylindrical vacuum waveguide is explained. The economy of the algorithm is demonstrated. This paper is devoted to the construction and justification of economical algorithms for calculating the emission current density and the singular function G 0( r, z; ξ, η), encountered when solving the problem of focussing relativistic electron beams in a vacuum waveguide [1]. The emission current density is calculated from the known particle trajectories, and the function G 0( r, z; ξ, η) at each of the points (r,z) and (ξ, η) of the waveguide. The need to construct economical algorithms to solve these problems is dictated by the fact that in a single solution of the problem of focussing relativistic electron beams (see [2]) each of them is solved repeatedly. The algorithms are so constructed that their accuracy is not lower than the accuracy with which other characteristics of the problem of focussing relativistic electron beams can be determined. The computer memory necessary for performing the calculations on realistic meshes (10–20 points per unit length of waveguide), amounts to 10–15 thousand words.