Hysteretic ac losses and susceptibility of thin superconducting disks.

Abstract

We calculate hysteretic magnetization curves and ac-susceptibility components ${\mathrm{\ensuremath{\chi}}}_{\mathrm{n}}^{\ensuremath{'}}$ and ${\mathrm{\ensuremath{\chi}}}_{\mathrm{n}}^{\mathrm{\ensuremath{''}}}$ for n=1, 3, and 5 for a type-II superconducting thin circular disk subjected to a low-frequency oscillating applied field, extending previous approaches for calculating hysteretic current-density and magnetic flux-density profiles in the critical state. We also present limiting expressions for \ensuremath{\chi}\ensuremath{'}=${\mathrm{\ensuremath{\chi}}}_{1}^{\ensuremath{'}}$ and \ensuremath{\chi}\ensuremath{''}=${\mathrm{\ensuremath{\chi}}}_{1}^{\mathrm{\ensuremath{''}}}$ for both small and large values of the ac field amplitude, and we show how \ensuremath{\chi}\ensuremath{''} is simply related to the ac loss per cycle per unit volume. Finally, a comparison is made between our results and those obtained for slab and strip geometries.