Lens theory of non-paraxial rays for electron gun characterization

Abstract

It has been attempted to characterize the cathode rays inside electron guns by utilizing the optical concepts familiar in the paraxial lens theory. We have proposed the Canonical Mapping Transformation (CMT) theory to obtain the gun optical parameters. The method is based on the Lagrange differential invariant theorem known in analytical mechanics. It has been found that major electron source properties, such as the crossover position, crossover size, and the angular current intensity, are all deducible from the four CMT optical parameters ( zco , f , Csg , and Ccg ), which in turn can be estimated by calculating the normal electron rays, whose emanation vectors on the cathode surface are in the surface normal direction. Since the normal electron rays can in many cases be regarded as paraxial, a scheme has been proposed to calculate the relevant optical parameters by a modification of the conventional paraxial trajectory calculation. It is shown that the normal electron ray of the CMT theory corresponds to (1, 0) principal trajectory in the paraxial method, g(z) . The conventional perturbation characteristic function integral method can be employed for the evaluation of the CMT aberration coefficients. Two realistic electron gun models (a single-crystal LaB6 cathode gun and a Schottky emitter source) were analyzed by use of the CMT optical parameters. Both the ray tracing of the normal electrons and the modified paraxial calculation method were employed for the analyses. It has been found that the guns with quite different nature in the source properties can well be described by the CMT optical parameters proposed. The paraxial calculations have been shown to produce accurate enough results and the authors hope their use would help electron optical column designers both in reducing the work load and in having clear physical images of their gun characteristics. © 2008 Elsevier B.V. All rights