The transverse critical-state susceptibility of rectangular bars

The complex ac susceptibility chi = chi' - jchi" of an infinitely long hard superconducting rectangular (2a x 2b) bar is calculated numerically with the uniform ac field applied along the 2b dimension, based on the critical-state model with a constant J(c). Normalized to the exact low-field limit of -chi', chi(0), -chi' and chi" as functions of the field amplitude H-m normalized to the exact full penetration field (H)p are given in figures and tables for 0.01 less than or equal to b/a less than or equal to 100. 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, chi" is proportional to and inversely proportional to H-m at H-m/H-p much less than 1 and much greater than 1, respectively. The maximum chi"/chi(0) at a certain intermediate H-m/H-p decreases and then increases with increasing b/a, showing a minimum value at b/a; 0.5. The low-field linear dependence of chi" 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 chi" varies as H-m(2).