Design of Einzel Electrostatic Lenses Using Inverse Schiske’s Model

Abstract

This paper examines the computational design of an electrostatic Einzel lens utilizing the inverse Schiske's model with certain magnification conditions. The electrostatic lens potential distribution has been characterized by an analytical function referred to as the inverse Schiske model. By solving the paraxial ray equation with the Runge-Kutta technique of fourth order, the charged particle beam trajectory and its derivatives via the lens have been determined. One can determine the proposed electrostatic lens optical properties, for instance, magnification, focal properties, and aberrations (spherical and chromatic), from knowing the axial potential distributions of the Einzel lens' and its first and second derivatives, as well as the beam trajectory and its derivatives. Based on our findings, we can infer that the constant k substantially affects the aberration values, with the best results happening at k = 0.1 for constants (V_o = 1V and a = 0.025) with a 10mm lens length. Also, the form of the suggested lens' electrodes is calculated.