Critical-state model with a secondary high-field peak

A critical-state model capable of describing the experimentally observed secondary or fishtail peak in magnetization data for bulk high-(Formula presented) superconductors is introduced. As suggested by a recent understanding of the fishtail effect, the field dependence of the critical current density is taken as a sum of two terms; one giving rise to a low-field magnetization peak and another being responsible for the fishtail peak. The model, which extends the Kim model by adding a Lorentzian term in (Formula presented) allows analytical treatment. Expressions for internal flux-density profiles as well as the various branches of the magnetization loop are presented. It is shown that measured magnetization loops of (Formula presented) samples showing a very pronounced fishtail peak are well fitted by this model. Using our procedure, (Formula presented) can be determined without invoking the Bean model (with a constant (Formula presented)), and thus avoiding an inconsistency in the analysis.