On the critical state in a non-uniform type II superconductor

We discuss the possibility of an exact solution of the critical state model for a superconductor in which the critical current density depends strongl y on coordinates. In the simplest case of a superconductor divided into per iodical layers with different critical current density values the magnetic hysteresis curve can be calculated analytically. The dependence of the magn etic moment M on the external magnetic field B-e essentially differs from t he standard dependence predicted by the Bean model for a homogeneous superc onductor. In particular, in the case of the virgin curve the standard quadr atic M(B-e) dependence becomes more complicated polynomial one with coeffic ients strongly dependent on the sample geometry and the ratio of the critic al current density in "weak" and "strong'' region. We also discuss the case of a smooth modulation of the critical current as a function of coordinate s, where an analytical solution can be constructed within the sample space quite far from its surface. (C) 1999 Elsevier Science B.V. All rights reser ved.