Magnetization curves for general cylindrical samples in a transverse ???eld

摘要

Using the recent results for the surface current density on cylindrical surfaces of arbitrary cross-section producing uniform interior magnetic ???eld we propose a method for obtaining solutions of Beana€?s critical state model for general cylindrical samples. The method uses the technique of conformal mapping to express the sample surface and the ???ux-fronts in terms of a set of coef???cients that depend on a parameter. The ???ux-fronts are to be determined by solving a system of nonlinear ordinary differential equations for the coef???cients. Retaining only a certain ???nite number of leading coef???cients we get an approximate solution. The procedure is illustrated by considering two cylindrical samples a€“ one with an elliptical cross-section and the other with a non-elliptical cross-section. The virgin curve and small and large magnetization hysteresis loops for the two samples are obtained.