Resolution improvements for hemispherical energy analyzers

An electron tracing code in spherical coordinates was used to treat irregul ar, nonspherical boundaries in the "Herzog regions" at the exit and entranc e planes of hemispherical energy analyzers. Some of the classical designs, i.e., the sudden cutoff "ideal field" approximation, real apertures in the 180 degrees plane, the Herzog correction, the Jost correction, and shortene d spheres were compared and checked for improvements. Ratios of gap to aver age radius from 0.2 to 0.55 are covered. Focusing, maximum trace width, bas e resolution, and the banana-shaped asymmetries from the circular reference path are investigated. Nearly ideal focusing and beam width can be restore d in all devices by simply rotating the entrance beams through a small nega tive angle. Design equations are provided. (C) 2000 American Institute of P hysics. [S0034-6748(00)01312-5].