Using recent results for the surface current density on cylindrical surfaces of arbitrary cross-section producing uniform interior magnetic field and an assumed set of flux-fronts, solutions of Bean’s critical state model for cylindrical samples with non-elliptic cross-section are presented. Magnetization hysteresis loops for two cross-sections with different aspect ratios are obtained. A comparison with some exact results shows the limitations of this approach.

Using the recent results for the surface current density on cylindrical surfaces of arbitrary cross-section producing uniform interior magnetic field we propose a method for obtaining solutions of Bean’s critical state model for general cylindrical samples. The method uses the technique of conformal mapping to express the sample surface and the flux-fronts in terms of a set of coefficients that depend on a parameter. The flux-fronts are to be determined by solving a system of nonlinear ordinary differential equations for the coefficients. Retaining only a certain finite number of leading coefficients we get an approximate solution. The procedure is illustrated by considering two cyclindrical samples — 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.