Exponential critical-state model for magnetization of hard superconductors

We have calculated the initial magnetization curves and hysteresis loops for hard type-II superconductors based on the exponential-law model, J c(Hi) =k exp(-∥Hi∥/H0), where k and H0 are constants. After discussing the general behavior of penetrated supercurrents in an infinitely long column specimen, we define a general cross-sectional shape based on two equal circles of radius a, which can be rendered into a circle, a rectangle, or many other shapes. With increasing parameter p (=ka/H0), the computed M-H curves show obvious differences with those computed from Kim's model and approach the results of a simple infinitely narrow square pulse Jc(Hi). For high-Tc superconductors, our results can be applied to the study of the magnetic properties and the critical-current density of single crystals, as well as to the determination of the intergranular critical-current density from magnetic measurements.