ANGULAR RESPONSE OF SPHERICAL PLATE ELECTROSTATIC ANALYZERS

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 F≡GαβEAβ0δαδ E, where βo, 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 βo, 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. © 1969 The American Institute of Physics.