Recent results of experiments on the magnetization and the internal flux line distribution of several low-w, type-11 superconductors obtained by the neutron depolarization method (1, 2) led to the conclusion that the maximum depolarization indicated the entrance of the entire sample into the critical state (3 to 5). Most of the theories involving the critical state have been developed to account for the hysteresis in high-w materials, where the influence of the Meissner effect and of the reversible magnetization on the apparent hysteretic behaviour may be neglected. Therefore, an attempt was made to adopt an existing model to include the properties of low-at superconductors.The theory of Irie and Yamafuji (6) seemed to be most suitable because of its convenience of comprising the models of Bean (3) (strong pinning), Silcox and and f: is the pinning force density (6).
PNeglecting the tensor character of the distribution of pinning centres, considering a cylindrical superconductor of radius R with its axis parallel to the external field Ho and using the reduced variable r/R, equation (1) may be rewritten in the form