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After having used an analytical expression in the form of a power series expansion to calculate the interelectrode electrostatic field in the general case of a toroidal electrostatic analyzer, we derive approximate analytical expressions for the most interesting response functions (geometrical factor, angular aperture, energy resolution, etc.). Results of a study of the dependence of these quantities with respect to the geometrical parameters of the analyzers are given in the form of grids of curves. By using such grids one is able to determine the optimal parameters to obtain any particular solution. Examples of such a choise are given in the case of measurements of low energy particles in space (10 eV to 50 keV).
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Décréau et al. (1975) studied this question.
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