Bessel-Fourier Series Solutions of Cylindrically Symmetrical Electrostatic Lens Potentials.

摘要

A method for expressing the electrostatic potential of a cylindrically symmetric electron lens using Bessel-Fourier series is presented. The method consists of partitioning the lens volume into cells and choosing appropriate series solutions made up from the set of functions comprising all possible solutions to Laplace's equation. The satisfying of boundary conditions and of continuity of the electric field at cell partitions leads to a set of linear equations for the series coefficients. Because the inherent error in these solutions is predictable, it is possible by this scheme to construct solutions which assure a specified accuracy. Moreover, this procedure affords a high degree of flexibility. Two lenses are analyzed by this method in detail.