Staircase penetration of magnetic flux into a superconducting flat ring

TL;DR

This paper investigates how magnetic flux penetrates a superconducting ring through dendritic avalanches, revealing a universal staircase pattern in flux trapping and the effects of heat release and flux pinning.

Contribution

It provides a quantitative theoretical model describing the staircase flux penetration pattern in superconducting rings, aligning well with experimental observations.

Findings

Staircase dependence of trapped magnetic flux on external field.

Universal staircase slope related to ring geometry.

Linear growth of heat released with each dendrite penetration.

Abstract

We analyzed the distribution of the Meissner shielding currents in a flat superconducting ring and quantitatively described the penetration of magnetic avalanches (dendrites) inside it. Using a recurrent procedure, the external field $H_{ext}$, in which a perforating (rim crossing) avalanche appears, is calculated. A staircase dependence of the mean field trapped inside a ring, $\left\langle H\right\rangle$, vs. $H_{ext}$, is comprehensively described. A staircase slope appears to be a universal function of a ring shape (rim width to ring diameter ratio). The heat released by a penetrating dendrite grows linearly with each next perforation. Flux pinning, if present, modifies a staircase dependence and makes steps smaller. Our theoretical results are in a good accordance with the experimental data.