Flux saturation number of superconducting rings

TL;DR

This paper calculates the flux saturation number in thin-film superconducting rings by solving the London equation, comparing it with bulk cases, and analyzing how it varies with hole size.

Contribution

It introduces a method to determine the fluxoid saturation number in thin-film rings considering depairing current limits, extending previous bulk analyses.

Findings

Flux saturation number depends on hole size and material properties.

For small holes, results match the Pearl vortex solution.

Large holes show a square root relationship between bulk and film saturation numbers.

Abstract

The distributions of electrical current and magnetic field in a thin-film superconductor ring is calculated by solving the London equation. The maximum amount of flux trapped by the hole, the fluxoid saturation number, is obtained by limiting the current density by the depairing current. The results are compare it with similar results derived for the bulk case of a long hollow cylinder [Nordborg & Vinokur, Phys. Rev. B 62, 12408 (2000)]. In the limit of small holes our result reduces to the Pearl solution for an isolated vortex in a thin film. For large hole radius, the ratio between saturation numbers in bulk and film superconductors is proportional to the square root of the hole size.