Matching fields of a long superconducting film

TL;DR

This paper uses London theory to analyze vortex configurations, matching fields, and magnetization in a finite cross-section superconducting film, extending previous models from infinitely long films.

Contribution

It introduces a model for finite cross-section superconducting films, providing new insights into vortex behavior and magnetic properties.

Findings

Calculated vortex configurations and matching fields.

Derived magnetization and magnetic induction profiles.

Extended previous infinite film models to finite geometries.

Abstract

We obtain the vortex configurations, the matching fields and the magnetization of a superconducting film with a finite cross section. The applied magnetic field is normal to this cross section, and we use London theory to calculate many of its properties, such as the local magnetic field, the free energy and the induction for the mixed state. Thus previous similar theoretical works, done for an infinitely long superconducting film, are recovered here, in the special limit of a very long cross section.