Dendritic and uniform flux jumps in superconducting films

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, ${h}_{0}$, is small. Otherwise, the instability develops in a uniform manner. We find the threshold magnetic field, ${H}_{\mathrm{fing}}(E,{h}_{0})$, the characteristic finger width, and the instability buildup time. Thin films are found to be much more unstable than bulk superconductors, and have a stronger tendency for formation of fingering (dendritic) pattern.