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

The ac loss per cycle per unit length of a hard superconductivity cylinder is numerically calculated from the critical state model assuming a Kim-type and an exponential field dependent and a radius dependent critical-current density Jc. Without such a dependence, the results are consistent with Norris' formula for an elliptic bar (cylinder). It is shown that the field dependence decreases and increases the loss at low and high ac currents, respectively, and a quick decrease of Jc from the surface inwards is favourable to lower the loss at any value of ac current. The physical reasons for these phenomena are discussed in terms of the current density profile.