On the Design of Axially Symmetric Electron Guns

In the design of high-perveance electron beam devices, it is necessary to evaluate the effects of the self-fields on the beam trajectories as well as the effects of any external electromagnetic fields that may be present. This paper describes a means whereby the self-consistent solution of Poisson´s equation, the relativistic equations of electron motion, and the equation of charge continuity, all subject to specified boundary conditions, are determined by means of a digital computer program. In particular the method is applied to the case of an axially symmetric, solid-beam electron gun where the electrons are emitted with zero initial velocity from a spacecharge-limited cathode.