Hysteretic ac losses and susceptibility of thin superconducting disks

We calculate hysteretic magnetization curves and ac-susceptibility components χₙ^' and χₙ^'' 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 {χ}{'}=χ₁^' and {χ}{''}=χ₁^'' for both small and large values of the ac field amplitude, and we show how {χ}{''} 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.