Transport ac loss of a superconducting cylinder with field dependent critical current density

The transport ac loss per cycle per unit length of a hard superconducting cylinder is calculated from the critical state model assuming a Kim-type and an exponential field dependent critical current density. Without such dependence, the results are consistent with Norris’ equations for an ellipse bar, in which the critical current density is assumed not to depend on the flux density. Based on Norris’ equations, the expressions of the loss are derived for a finite length cylinder. It is shown that the field dependence decreases and increases the loss at low and high ac currents, respectively, and the effects of the parameter p on the loss are related to the magnetization process. Compared to Norris’ prediction, the results for the Kim and exponential model show the same trend with respect to the external transport current.