Exponential critical-state model for magnetization of hard superconductors

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Abstract
We have calculated the initial magnetization curves and hysteresis loops for hard type‐II superconductors based on the exponential‐law model, Jc(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.