Accurate calculations of properties of the two-tube electrostatic lens. I. Improved digital methods for the precise calculation of electric fields and trajectories

Abstract

Digital methods of high precision have been developed for the calculation of electric fields and trajectories in electrostatic lenses and a computer program was written to apply these methods to the two-tube lens. The increased precision results from the use of nine-point formulas in the relaxation calculation of potentials in place of previously used five-point formulas and from the use of an improved predictor-corrector method for the calculation of trajectories. Trajectories obtained with these methods are sufficiently precise to determine third-order aberration coefficients.