Thin superconducting disk with field-dependent critical current: Magnetization and ac susceptibilities

Abstract

Magnetization hysteresis loops and the ac susceptibility χ=χ′+iχ″ of a superconducting thin disk are calculated in the critical-state model assuming a field-dependent critical current density Jc(B). The results are obtained by solving numerically the set of coupled integral equations for the flux and current distributions [Phys. Rev. B 60, 13 112 (1999)] for a disk placed in a perpendicular applied field Ba. From the magnetization curves the range of fields where the vertical width of the loop ΔM(Ba) relates directly to Jc(Ba) is determined. The susceptibility is analyzed in the limits of small and large ac-field amplitudes Bam, and also as a parametric relation χ″(χ′). Comparing our results with experimental data for χ″(χ′) shows that by taking the B dependence of Jc into account the agreement improves dramatically, in particular at small |χ′| (large field amplitudes). We show that the asymptotic behavior for large Bam changes from χ′∝Bam−3/2 and χ″∝Bam−1 for the Bean model, to χ′∝Bam−3 and χ″∝Bam−2 for Jc decreasing with |B| as |B|−1 or faster. For small Bam the behavior can always be described by an effective Bean model with a renormalized Jc. We also find that in the χ″(χ′) plot the peak of χ″ increases in magnitude and shifts towards χ′=0 when Jc decreases with |B|. This allows an easy experimental discrimination between a Bean model behavior, one with Jc(B), and one where flux creep is an ingredient.

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