Critical state model for general cylinders: unifying scheme for parallel and perpendicular geometries

Abstract

The critical state model (CSM) is examined for infinite cylindrical samples of a hard type-II superconductor subjected to a magnetic field in an arbitrary direction. The solution is based on a generalization of the result for the surface current density on a cylindrical surface that produces uniform interior magnetic field along an arbitrary direction. In contrast to the case of parallel or perpendicular geometry, in the present case, the direction of shielding current density is not in general perpendicular to the direction of the applied magnetic field. The general result pertaining to the current density has enabled us to get an unified scheme for the treatment of parallel and perpendicular geometries for infinite cylinders of arbitrary cross-section. The numerical scheme followed here is very similar to that followed in Refs. [Phys. Rev. B 65 (2002) 024518; J. Phys. 57 (2001) 763]. Flux contours in the plane transverse to the cylinder-axis are obtained and also hysteresis loops for both the parallel and perpendicular components of magnetization are presented for a typical orientation of the applied field. The variation of the orientations of components of magnetization with that of the applied field is studied.