A simple quadrupole-octupole electromagnetic lens

Charged particle beam trajectories in a simple electromagnetic quadrupole-octupole lens are numerically calculated based on analytical expressions for the +potential distribution. Locations of the lens foci in the image space are determined over a wide range of initial conditions. Relationships between the electrostatic and magnetic lens components that provide correction for chromatic aberrations of off-axis beams, which are different from classical beams, are obtained. Phase contours at the lens exit are calculated for beams occupying the major part of the aperture, and conditions for transforming the phase contour with minimal distortions are found.