Thin superconducting disk with B-dependent Jc: Flux and current distributions

TL;DR

This paper analyzes the flux and current distributions in a thin superconducting disk with a magnetic field-dependent critical current, deriving coupled integral equations and solving them numerically to understand flux penetration.

Contribution

It introduces a numerical method to solve for flux and current profiles in a superconducting disk with B-dependent Jc, extending the understanding of flux penetration in such geometries.

Findings

Flux penetration depth can be described by an effective Bean model with renormalized Jc.

Results are qualitatively applicable to thin superconductors of any shape.

Contrasts behavior with parallel geometry where B-dependence of Jc can be ignored at small fields.

Abstract

The critical state in a superconducting thin circular disk with an arbitrary magnetic field dependence of the critical sheet current, Jc(B), is analyzed. With an applied field Ba perpendicular to the disk, a set of coupled integral equations for the flux and current distributions is derived. The equations are solved numerically, and flux and current profiles are presented graphically for several commonly used Jc(B) dependences. It is shown that for small Ba the flux penetration depth can be described by an effective Bean model with a renormalized Jc entering the leading term. We argue that these results are qualitatively correct for thin superconductors of any shape. The results contrast the parallel geometry behavior, where at small Ba the B-dependence of the critical current can be ignored.