Dendritic and uniform flux jumps in superconducting films

TL;DR

This paper extends the analysis of thermomagnetic instability in superconductors to thin films, revealing conditions for nonuniform flux jumps and dendritic pattern formation due to nonlocal electrodynamics and thermal effects.

Contribution

It generalizes previous models to thin films, deriving thresholds and patterns for flux jumps considering nonlocal electrodynamics and substrate heat transfer.

Findings

Thin films are more unstable than bulk superconductors.

Dendritic flux patterns form at high electric fields and low heat transfer.

Threshold magnetic fields and finger widths are quantitatively determined.

Abstract

Recent theoretical analysis of spatially-nonuniform modes of the thermomagnetic instability in superconductors [Phys. Rev. B 70, 224502 (2004)] is generalized to the case of a thin film in a perpendicular applied field. We solve the thermal diffusion and Maxwell equations taking into account nonlocal electrodynamics in the film and its thermal coupling to the substrate. The instability is found to develop in a nonuniform, fingering pattern if the background electric field, E, is high and the heat transfer coefficient to the substrate, h0, is small. Otherwise, the instability develops in a uniform manner. We find the threshold magnetic field, H_fing(E,h0), the characteristic finger width, and the instability build-up time. Thin films are found to be much more unstable than bulk superconductors, and have a stronger tendency for formation of dendritic pattern.