Relativistic theory of the spherical electrostatic analyzer

Abstract

A general relativistic analysis of the properties of spherical electrostatic analyzers is presented, and applied to some special cases of interest. An important limitation on the allowable kinetic energies is shown to exist: for energies greater than a certain kinetic energy T_max, the spherical analyzer is not an effective focusing instrument. Expressions for the velocity and energy dispersions, and for the resolving power, are derived. A special case, in which the central angle of the analyzer is greater than $\text{3π}\text{2}$, and which has desirable focusing properties, is briefly discussed.