Dendritic flux avalanches in superconductors
When a superconducting film is placed in a perpendicular magnetic field, the flux penetration sometimes occurs via abrupt avalanches that result in remarkable dendritic flux patterns that can be observed using magneto-optical imaging
Magneto-optical movie of flux penetration into a thin film of Mg2B. The movie is composed of 101 images taken at 3 K as the applied field increases from zero up to 35 mT and then decreases back to zero.
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Magneto-opitcal studies of a c-oriented MgB2 film show that below 10 K the global penetration of vortices is dominated by complex dendritic structures abruptly entering the film. This behavior contrasts the gradual uniform penetration usually found in superconducting films.
Figure shows magneto-optical images of flux penetration (image brightness represents flux density) into the virgin state at 5 K. The respective images were taken at applied fields (perpendicular to the film) of 3.4, 8.5, 17, 60, 21, and 0 mT.
This complex flux dynamics must be responsible for suppression and noisy behavior of magnetization:
Bulks: Phys. Rev. B 2004 PDF
Films: Phys. Rev. B 2006 PDF
A linear analysis of thermal diffusion and Maxwell equations shows that a thermo-magnetic instability can lead to formation of finger-like distributions of magnetic field and temperature. The fingering instability emerges when the background electric field is larger than a threshold field Ec, and the applied magnetic field exceeds a threshold value H(E), see the phase diagram.
We derive the criterion for the instability, and estimate its build-up time and characteristic finger width. Numerical simulations support the analytical results, and allow us to follow the development of the fingering instability beyond the linear regime.
Thin films are shown to be more unstable than bulk superconductors and have a stronger tendency to form fingering (dendritic) flux patterns.
Lower threshold field
Phys. Rev. Lett. 2006 PDF
The work presents a detailed comparison of experimental data and theoretical predictions for the dendritic flux instability. It is shown that a thermo-magnetic model published very recently [Phys. Rev. B 73, 014512 (2006)] gives an excellent quantitative description of key features like the instability onset (first dendrite appearance) magnetic field, and how the onset field depends on both temperature and sample size. The measurements were made using magneto-optical imaging on a series of different strip-shaped samples of MgB2. Excellent agreement is also obtained by reanalyzing data previously published for Nb.
Phys. Rev. B 2007 PDF
We propose a mechanism responsible for the abrupt vanishing of the dendritic flux instability when an increasing magnetic field is applied. The onset of flux avalanches and the subsequent reentrance of stability in NbN films was investigated using magneto-optical imaging, and the threshold fields were measured as functions of critical current density, jc. The results are explained with excellent quantitative agreement by a thermomagnetic model published in [Phys. Rev. B 73, 014512 (2006)], showing that the reentrant stability is a direct consequence of a monotonously decreasing jc versus field.
The flux pattern is strongly temperature dependent
Figures (a-c) show flux distribution at T = 3.3, 9.9 and 10.5 K at applied fields of 13, 17 and 19 mT, respectively.
We suggest that the observed behavior is due to a thermo-magnetic instability, which is supported by vortex dynamics simulations.
(d-f): Flux densities obtained by vortex dynamics simulations at T1 < T2 < T3, respectively, reproducing the morphology of the patterns in (a-c).
Phys. Rev. Lett. 2007 PDF
Anisotropic penetration of magnetic flux in MgB2 films grown on vicinal sapphire substrates is investigated using magneto-optical imaging. Regular penetration above 10 K proceeds more easily along the substrate surface steps, anisotropy of the critical current being 6%. At lower temperatures the penetration occurs via abrupt dendritic avalanches that preferentially propagate perpendicular to the surface steps. This inverse anisotropy in the penetration pattern becomes dramatic very close to 10 K where all flux avalanches propagate in the strongest-pinning direction. The observed behavior is fully explained using a thermomagnetic model of the dendritic instability.
Phys. Rev. B 2006 PDF
Flux dendrites with opposite polarities simultaneously penetrate superconducting, ring-shaped MgB2 films. By applying a perpendicular magnetic field, branching dendritic structures nucleate at the outer edge and abruptly propagate deep into the rings. When these structures reach close to the inner edge, where flux with opposite polarity has penetrated the superconductor, they occasionally trigger anti-flux dendrites. These anti-dendrites do not branch, but instead trace the triggering dendrite in the backward direction. Two trigger mechanisms, a non-local magnetic and a local thermal, are considered as possible explanations for this unexpected behaviour. Increasing the applied field further, the rings are perforated by dendrites which carry flux to the center hole. Repeated perforations lead to a reversed field profile and new features of dendrite activity when the applied field is subsequently reduced.