J. I. Vestgården

Dynamics and morphology of dendritic flux avalanches in superconducting films

We develop a fast numerical procedure for analysis of nonlinear and nonlocal electrodynamics of type-II superconducting films in transverse magnetic fields taking into account realistic boundary conditions. Using this procedure we explore stability of such films with respect to dendritic flux avalanches. The calculated flux patterns are very similar to experimental magneto-optical images of MgB2 and other superconductors, where the avalanche size and morphology change dramatically with temperature. We also find a threshold magnetic field, which agrees with both experiments and linear stability analysis. The simulations predict the temperature rise during an avalanche, where for a sub-microsecond time T ~ 1.5 Tc, and a precursor stage with large thermal fluctuations.

Lightning in superconductors

Crucially important for application of type-II superconductor films is the stability of the vortex matter – magnetic flux lines penetrating the material. If some vortices get detached from pinning centres, the energy dissipated by their motion will facilitate further depinning, and may trigger a massive electromagnetic breakdown. Up to now, the time-resolved behaviour of these ultra-fast events was essentially unknown. We report numerical simulation results revealing the detailed dynamics during breakdown as within nanoseconds it develops branching structures in the electromagnetic fields and temperature, with striking resemblance of atmospheric lightning. During a dendritic avalanche the superconductor is locally heated above its critical temperature, while electrical fields rise to several kV/m as the front propagates at instant speeds near up to 100 km/s. The numerical approach provides an efficient framework for understanding the ultra-fast coupled non-local dynamics of electromagnetic fields and dissipation in superconductor films.

Flux distribution in superconducting films with holes

Flux penetration into type-II superconducting films is simulated for transverse applied magnetic field and flux creep dynamics. The films contain macroscopic nonconducting holes, and we introduce the holes in the simulation formalism by reconstruction of the magnetic field change inside the holes. We find that the holes induce a region of reduced flux density extending toward the nearest sample edge, in addition to the parabolic

Nonlocal electrodynamics of normal and superconducting films

d

Magneto-optical imaging of magnetic flux patterns in superconducting films with antidots

lines. The region of reduced flux density is due to compression of current streamlines and is accompanied by a significantly enhanced flux traffic. The results are compared to and found to be in good agreement with experimental magneto-optical images of

Modeling non-local electrodynamics in superconducting films: the case of a right angle corner

\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{x}

The Thermomagnetic Instability in Superconducting Films with Adjacent Metal Layer

films including holes and slits.

Nanosecond voltage pulses from dendritic flux avalanches in superconducting NbN films

Electrically conducting films in a time-varying transverse applied magnetic field are considered. Their behavior is strongly influenced by the self-field of the induced currents, making the electrodynamics nonlocal, and consequently difficult to analyze both numerically and analytically. We present a formalism which allows many phenomena related to superconducting and Ohmic films to be modeled and analyzed. The formalism is based on the Maxwell equations and a material current–voltage characteristics, linear for normal metals and nonlinear for superconductors, plus a careful account of the boundary conditions. For Ohmic films, we consider the response to a delta function source-field turned on instantly. As one of few problems in nonlocal electrodynamics, this has an analytical solution, which we obtain in both Fourier and real space. Next, the dynamical behavior of a square superconductor film during ramping up of the field, and subsequently returning to zero, is treated numerically. Then, this remanent state is used as initial condition for triggering thermomagnetic avalanches. The avalanches tend to invade the central part where the density of trapped flux is largest, forming dendritic patterns in excellent agreement with magneto-optical images. Detailed profiles of current and flux density are presented and discussed. Finally, the formalism is extended to multiply connected samples, and numerical results for a patterned superconducting film, a ring with a square lattice of antidots, are presented and discussed.

Flux penetration in a superconducting strip with an edge indentation

We present the results of experiments on visualization of magnetic flux distribution and its dynamics in high-temperature superconductors with artificial defects. High-Tc superconductor thin films were equipped with a special arrangement of antidots in order to separate the streams of magnetic flux moving in (or out of) the sample. A possibility to alter the direction and depth of flux penetration is clearly demonstrated by means of magneto-optical imaging. The resolution was sufficient for observation of flux in particular antidots, which allows more detailed dynamic analysis of such systems. 2006 Elsevier B.V. All rights reserved.

Limiting thermomagnetic avalanches in superconducting films by stop-holes

We consider magnetic flux penetration in a superconducting film with a concave corner. Unlike convex corners, where the current flow pattern is easily constructed from Bean’s critical state model, the current flow pattern at a concave corner is highly nontrivial. To address the problem, we do a numerical flux creep simulation, where particular attention is paid to efficient handling of the non-local electrodynamics, characteristic of superconducting films in the transverse geometry. We find that the current stream lines at the concave corner are close to circular, but the small deviation from exact circles ensures that the electric field is continuous inside the sample. Yet, the electric field is, as expected, very high at the concave corner. At low fields, the critical state penetration is deeper from the concave corner than from the straight edges, which is a consequence of the electrodynamic non-locality. A magneto-optical experiment on Y Ba2Cu3Ox displays an almost perfect match with the magnetic flux distribution from the simulation, hence verifying the necessity of including electrodynamic non-locality in the modeling of superconducting thin films.