Spherical aberration correction with threefold symmetric line currents

It has been shown that N-fold symmetric line current (henceforth denoted as N-SYLC) produces 2N-pole magnetic fields. In this paper, a threefold symmetric line current (N3-SYLC in short) is proposed for correcting 3rd order spherical aberration of round lenses. N3-SYLC can be realized without using magnetic materials, which makes it free of the problems of hysteresis, inhomogeneity and saturation. We investigate theoretically the basic properties of an N3-SYLC configuration which can in principle be realized by simple wires. By optimizing the parameters of a system with beam energy of 5.5 keV, the required excitation current for correcting 3rd order spherical aberration coefficient of 400 mm is less than 1AT, and the residual higher order aberrations can be kept sufficiently small to obtain beam size of less than 1 nm for initial slopes up to 5 mrad.