A numerical method for solving Laplace's equation in spherical coordinates for an axially symmetric geometry has been developed. Dirichlet boundary conditions on a closed surface yield a set of difference equations. The method of successive overrelaxation has been employed to find solutions to those equations. Application of the method is illustrated by finding the field configuration in a new type of electron gun used in a spherical electron monochromator.
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Hoeper et al. (1970) studied this question.
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