Finger patterns produced by thermomagnetic instability in superconductors

Abstract

A linear analysis of thermal diffusion and Maxwell equations is applied to study the thermomagnetic instability in a type-II superconducting slab. It is shown that the instability can lead to formation of spatially nonuniform distributions of magnetic field and temperature. The distributions acquire a finger structure with fingers perpendicular to the screening current direction. We derive the criterion for the instability, and estimate its build-up time and characteristic finger width. The fingering instability emerges when the background electric field is larger than a threshold field, $E>E_c$, and the applied magnetic field exceeds a value $H_{f}ing\propto 1/\sqrt{E}$. Numerical simulations support the analytical results, and allow to follow the development of the fingering instability beyond the linear regime. The fingering instability may be responsible for the nucleation of dendritic flux patterns observed in superconducting films using magneto-optical imaging.

8 pages, 6 figures, accepted to Phys. Rev. B; (new version: minor changes)

References in corpus (10)

• Experiments in vortex avalanches
• Dendritic magnetic instability in superconducting MgB2 films
• Suppression of Superconducting Critical Current Density by Small Flux Jumps in $Mg{B}_2$ Thin Films
• Dendritic flux patterns in MgB2 films
• Dendritic flux avalanches in superconducting Nb3Sn films
• Vortex avalanches and magnetic flux fragmentation in superconductors
• Local threshold field for dendritic instability in superconducting MgB2 films
• Current-induced dendritic magnetic instability in superconducting MgB2 films
• Growth-related profiles of remanent flux in bulk melt-textured YBaCuO crystal magnetized by pulsed fields
• Mesoscopic flux jumps in MgB2 films visualized by magneto-optical imaging

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