Computer analysis of electron gun characteristics by surface charge method

Abstract

Computer analysis of an electromagnetic field is indispensable when we come into design problems of electron optical devices. The difference method has been commonly applied where the potential of meshed space is solved using the successive over-relaxation (SOR), but it is fairly unfavorable in the electron optical application, since the potential derivatives necessary for the ray tracing must be evaluated numerically, open boundaries involve ambiguity in specifying their prerequisite potential values, and a large size of computer memories must be provided for mesh points, most of which are to cover the off-axis region where no electron paths take place. These problems become more serious for the case of an electron gun where the cathode has a very sharp curvature at the tip compared with the other configuration. It is for this reason that theoretical investigations could hardly present a quantitatively consistent interpretation over fundamental characteristics of the gun except for some papers which utilize analytical potential functions contrived under several approximations for simplified geometry such as a sphere cathode and an infinitely thin Wehnelt electrode.