An improved iteration method for calculating the axial potential distribution in slit-aperture electrostatic lenses

Abstract

Axial potential distributions in electrostatic slit-aperture lenses, consisting of plane and parallel electrodes, are derived using the method of conformal transformation. An improved iterative scheme is given which, for the first time, enables solutions to be obtained for multi-electrode configurations in which the aperture widths are larger than the electrode separations. No special conditions relating one aperture width to another, or relating one electrode spacing to another, were assumed. As an example, the axial potential distribution in the electron bombardment source used in AEI mass spectrometers was calculated; for this an analogue consisting of five apertured planes and an apertureless plane was used. Electrodes of finite thickness were each represented by two planes of infinitesimal thickness. The same problem required computer time greater by at least a factor of ten when solved by the method of numerical relaxation.