The Angular Response of Spherical Plate Electrostatic Analyzers

Abstract

We examine the transmission characteristics of spherical plate electrostatic analyzers, for external particle sources, as functions of angular coordinates α and β, and particle energy E. The angle α is in the plane of the particle's trajectory; β is in the plane containing the point of incidence and perpendicular to the radius vector from the center of electrostatic force. We express the total energy‐geometrical factor F, which is the ratio of transmitted particle flux (particles/sec) to directional intensity (particles/cm²·sec·sr·keV), in the functional form $${\mathrm{F\equiv G}}_{\mathrm{\alpha \beta E}}{\mathrm{A\beta }}_0\mathrm{\Delta \alpha \Delta E}$$ , where β_o, and Δα are angular parameters and ΔE the energy resolution, all appropriately defined. We give methods for determining the function G and present some specific examples. We show that G is of the order of unity. A surprising result is that β_o, which is a measure of the angular aperture in β space, may differ appreciably from the value expected intuitively on the basis of the angular dimensions of analyzer plates. The angles α and β are locally defined with respect to each arbitrary point of incidence within the entrance aperture. We also give a general method for finding the detailed angular response of spherical plate analyzers in a frame of reference fixed with respect to the analyzer plates.