Image aberrations in an imperfectly-shaped electrostatic analyser

Image aberrations caused by mechanical imperfections of the electrodes of an electrostatic energy analyser are calculated. Deviations of the electrodes from the ideal cylindrical shape may be of any type. In examples, the following cases are treated: mis-positioning (eccentricity and non-parallelism) and mis-shaping (conical, hyperbolic and elliptic) of the electrodes, as well as the general case. First, the electric field is calculated in the imperfect analyser, and then the deviations of the ion orbits in this distorted field from the corresponding orbits in the ideal electrostatic analyser. This new method permits the setting of exact values for the tolerances in the manufacture and adjustment of the electrodes. (Auth.)