Comparison of the aperture and chromatic aberrations of magnetic round lenses with those of quadrupole doublets

The paraxial equation for rotationally symmetric magnetic lenses is integrated numerically by using the Numerov method. The normalized third-order aperture and second-order chromatic aberration coefficients (C3/sub N/ and C/sub c//sub N/) are calculated. A Fourier representation of the lens field is used, and a search for minimum C3/sub N/ is carried out by varying the Fourier coefficients. Comparisons with comparable quadrupole doublets, and calculations of C3/sub N/ and C/sub c//sub N/ for actual coil systems are presented. The main conclusion is that magnetic round lenses are about a factor of 2 better than comparable magnetic quadrupole doublets as far as the third-order aperture aberration is concerned, but the chromatic aberrations in both systems are comparable