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 > Ec, and the applied magnetic field exceeds a value H fing ∝ 1/ √ 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.

Limiting thermomagnetic avalanches in superconducting films by stop-holes

“…This can be understood from the fact that the magnitude of the electrical field is a key parameter deciding the onset of the thermomagnetic instability. 2 Since corners being concave with respect to the current flow pattern are indeed locations of largely enhanced electrical fields, 13 the superior stability of the circular hole is in full accordance with expectations.…”

“…In films, this instability leads to formation of finger-like flux structures, as found both theoretically, 2 and experimentally in many materials of technological importance. 3 Magnetooptical imaging (MOI) experiments have shown that the flux dendrites can grow during the runaway to lengths on the order of the sample size in approximately 100 ns.…”

Dendritic flux penetration in Pb films with a periodic array of antidots

“…It has been observed for many samples that in this configuration the field penetrates via highly branched expansions giving rise to a dendritic pattern of flux channels. 6,7 Theoretical studies as well as numerical simulations, [7][8][9] have reproduced the observed flux penetration patterns in thin films giving support to a thermomagnetic origin for these type of instabilities.…”

Controllable morphology of flux avalanches in microstructured superconductors

“…Besides, since high electric fields are known to trigger thermomagnetic avalanches [6,15,16], it is thus likely that thin superconductors with concave corners are far more susceptible to the occurrence of such dramatic events than specimens with convex corners or without corners at all. Notice that this concept applies equally to a superconductor with a square hole filled with flux: if the magnetic pressure pushes the flux trapped in the hole to invade the superconducting frame, it would thus have preferential directions, defined by the inner corners.…”