Analysis of the 3-Tube Symmetrical Electrostatic Unipotential Lens

Abstract

The 3‐tube symmetrical electrostatic unipotential lens was analyzed in great detail. Starting from a mathematical expression for the axial potential distribution, the cardinal points and coefficients of spherical and chromatic aberration were obtained with the help of a digital computer. Values for S/R, the separation between the tubes, were taken equal to 0.25, 0.375, 0.5, 0.75, and 1.00 and the length of the central electrode, L/R, was varied from 0.25 to 2.00 in steps of 0.25. It was shown that the accelerating lens has a lower coefficient of spherical aberration than the decelerating lens. A comparison was made between the data obtained using the mathematical model and the relaxation technique. The agreement was excellent.