Magnetic-field and current-density distributions in thin-film superconducting rings and disks

TL;DR

This paper presents methods to calculate magnetic-field and current distributions in thin-film superconducting rings and disks under various flux conditions, considering different penetration depths and screening lengths.

Contribution

It introduces a unified approach to analyze magnetic and current distributions in superconducting rings and disks with different flux trapping and penetration scenarios.

Findings

Derived formulas for magnetic-field and current distributions in rings and disks.

Analyzed flux focusing and trapping effects in superconducting geometries.

Provided insights into magnetization behavior under geometrical barriers.

Abstract

We show how to calculate the magnetic-field and sheet-current distributions for a thin-film superconducting annular ring (inner radius a, outer radius b, and thickness d<<a) when either the penetration depth obeys lambda < d/2 or, if lambda > d/2, the two-dimensional screening length obeys Lambda = 2 lambda^2/d << a for the following cases: (a) magnetic flux trapped in the hole in the absence of an applied magnetic field, (b) zero magnetic flux in the hole when the ring is subjected to an applied magnetic field, and (c) focusing of magnetic flux into the hole when a magnetic field is applied but no net current flows around the ring. We use a similar method to calculate the magnetic-field and sheet-current distributions and magnetization loops for a thin, bulk-pinning-free superconducting disk (radius b) containing a dome of magnetic flux of radius a when flux entry is impeded by a geometrical barrier.