Bowstring effect as a trigger for flux instabilities in thin superconductors

TL;DR

This paper introduces the bowstring effect as a trigger for flux instabilities in thin superconductors, analyzing its geometry, threshold conditions, and impact on flux avalanches, with implications for understanding experimental observations.

Contribution

It provides a detailed description of the bowstring vortex mechanism, calculates the threshold field for different geometries, and explains the absence of instabilities in certain superconducting films.

Findings

Bowstring vortices are geometrically characterized in superconductors.

Threshold magnetic field for bowstring release is derived as a function of geometry.

Moderate anisotropy suppresses the bowstring effect, explaining experimental observations.

Abstract

Magnetic vortices resemble bowstrings stretched across a corner at the initial stage of their penetration into a flat superconducting sample of a rectangular cross-section. As the external magnetic field $H_e$ reaches the threshold level $H_{th}$, a bowstring is "released" and instantaneously contracted in length with a substantial heat generation. This heat can serve as a trigger for nucleation of a flux instability (avalanche). At $H_e \approx \sqrt{2}H_{th}$ a usual vortex penetration starts at flat edges, and the bowstring mechanism is no longer effective. We describe the geometry of bowstring-like vortices, find $H_{th}$ for disk and strip shaped superconductors as a function of their thickness to width ratio, and determine the heat effect related to a bowstring release. Our results enable a novel treatment of numerous experimental data on flux instabilities and avalanche type penetration in flat superconducting samples. A moderate anisotropy of a superconducting penetration depth ($\lambda_c > \lambda_{ab}$) diminishes or even completely removes the bowstring effect. This explains the absence of spontaneous instabilities in epitaxial $\mathrm{YBa}_{2}\mathrm{Cu}_{3}\mathrm{O}_{7-\delta }$ films at all temperatures and in $\mathrm{MgB_{2}}$ above 10 K.