High-$T_c$ superconductors have critical current densities $J_c$ that decay sharply with increasing magnetic fields. We solve Bean’s model for $J_c$ decaying exponentially with H and obtain virgin magnetization curves and hysteresis loops. We show that the shape of the hysteresis loop can be altered significantly if the maximum field applied is not large enough, and we explain discrepancies between various magnetization data reported in the literature.

• Received 25 January 1988

DOI:https://doi.org/10.1103/PhysRevB.39.4704