On the optical properties of magnetic lenses with fields of the form B(z) ∝ z − n, n = 2, 3, 4

Abstract

Summary The trajectories of electrons in magnetic lenses with field distributions in the form of an inverse power law can be expressed in terms of Bessel functions of fractional order. It is shown that the focal lengths and spherical and chromatic aberration coefficients can be evaluated explicitly. The results confirm and elucidate numerical results published by A. V. Crewe [1].