<title>Influence of the rod diameter of electrostatic quadrupole lenses on the axial field and on the minimum spot size in nonlinear microprobes</title>

Abstract

Different constructions of practical electrostatic lenses are numerically investigated. The electric field in electrostatic quadrupole lenses consisting of four copper rods depends, for a given lens aperture, on the value of the rod diameter. Furthermore, the aberration coefficients of electrostatic systems depend on the axial partial derivative of the electric field which, for example, influences the beam spot size, i.e., the microprobe resolution. We apply an integral formulation to the given set of polarized conductors in vacuum and in absence of space charge. These equations are numerically solved using an accurate version of the boundary element method in order to obtain the potential and the field distributions. The axial distributions of the electric field derivatives are found for different diameters of the rods. The developed Matrizant method is then applied to minimize the beam spot size -- for a fixed beam current -- in focusing systems consisting of electrostatic quadrupole lenses, using the computed axial distributions.