Numerical synthesis of an optimal microprobe focusing system

An electrostatic microprobe focusing system including a separated Russian quadruplet and two slits (or diaphragms) is numerically synthesized, taking into consideration all geometrical aberrations of the third order. The matrizant method is applied to minimize the beam spot size for a fixed beam current. For quadrupoles consisting of four copper rods, the electric field inside of the quadruplet is computed using an accurate version of the boundary charge method. The minimum spot size, the appropriate radii of the diaphragms, the distance between them, the effective length and the polarisation for different diameters of the rods are found.