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

TL;DR

This paper models the magnetization and ac susceptibility of a superconducting thin disk considering a field-dependent critical current, improving agreement with experimental data and providing insights into flux behavior.

Contribution

It introduces a numerical analysis of a superconducting disk with a field-dependent critical current, extending the critical-state model to better match experimental observations.

Findings

Incorporating Jc(B) improves agreement with experimental susceptibility data.

Asymptotic behavior of susceptibility changes with field dependence of Jc.

Peak of Im(chi) shifts, aiding experimental discrimination of models.

Abstract

Magnetization hysteresis loops and the ac susceptibility 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 [PRB 60(17) p.13112 (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 relates directly to Jc(Ba) is determined. Comparing our results on susceptibility with experimental data for parametric plot Im(chi) vs. Re(chi) shows that by taking the B-dependence of Jc into account the agreement improves dramatically. We show that the asymptotic behavior for large ac-field amplitudes Bam changes from Re(chi) ~ 1/Bam^{3/2} and Im(chi) ~ 1/Bam for the Bean model, to Re(chi) ~ 1/Bam^3 and Im(chi) ~ 1/Bam^2 for Jc decreasing with |B| as 1/|B| 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 Im(chi) vs. Re(chi) plot the peak of Im(chi) increases in magnitude and shifts to lower |Re(chi)|. This allows an easy experimental discrimination between a Bean model behavior, one with Jc(B), and one where flux creep is an ingredient.