Type II superconducting disk in a spatially inhomogeneous applied magnetic field

Abstract

The problem of a type II superconducting disk in a spatially inhomogeneous magnetic field is considered. The aim of the investigations undertaken here is to evaluate the effects of the spatial inhomogeneity of the parallel component of the applied magnetic field on the nature of the superconducting nucleation of a short cylinder. Full numerical solutions of the linearized Ginzburg-Landau equation for the order parameter, taking into account only the parallel component of the field, are presented in the case of a solid disk;free-standing and in a metallic matrix. In the case of a mesoscopic system, only the limiting form of the critical temperature is obtained. The temperature-field (e-f) curves are characterized by flux-entry points at each of which the azimuthal quantum number decreases by unity. The quasi-period of the flux-entry points increases in f with the increasing strength of the spatial inhomogeneity of the applied field. The increased effect of coating the superconductor with a suitable normal metal leads to the well known suppression of the critical temperature as well as smoothing out of flux entries. It is predicted that the wiping out of surface nucleation is effected with relative ease when the applied magnetic field is uniform than when it posseses a degree of spatial inhomogeneity.