The transverse critical-state susceptibility of rectangular bars

The complex ac susceptibility of an infinitely long hard superconducting rectangular (2 a × 2 b ) bar is calculated numerically with the uniform ac field applied along the 2 b dimension, based on the critical-state model with a constant J c . Normalized to the exact low-field limit of , χ 0 , and as functions of the field amplitude H m normalized to the exact full penetration field H p are given in figures and tables for . The numerical results are compared with existing exact and approximate analytical results. It is found for any value of b / a that with increasing H m / H p , is proportional to and inversely proportional to H m at and , respectively. The maximum at a certain intermediate H m / H p decreases and then increases with increasing b / a , showing a minimum value at . The low-field linear dependence of on H m at low b / a is qualitatively different from the prediction of a one-dimensional calculation for a thin strip, whose low-field varies as H m 2 .