K V BHAGWAT and DEBJANI KARMAKAR

Technical Physics and Prototype Engineering Division, Bhabha Atomic Research Centre, Trombay,
Mumbai 400 085, India

Abstract.

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 cylindrical 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.

Keywords:  Magnetization curves; Bean; critical state model; hysteresis curves.

Pacs Nos.  74.25.Ha