The separation of high-temperature superconducting (HTS) tapes in filaments is a viable approach to reduce AC losses in HTS high-power applications, where AC currents and/or fields may be applied in addition to any DC field present. Methods such as mechanical, laser scribing, photolithography, or direct printing on buffered substrates using inkjet deposition have been used to create the filaments in the second-generation HTS coated conductors in order to reduce hysteretic losses. However, losses of the finely striated tapes can still be noticeably larger than predicted by analytical expressions, due to the addition of coupling currents or lack of field penetration, and such deviation tends to grow with increasing filament density. In order to reduce the magnetic coupling between filaments and the associated AC losses, an in-depth understanding of flux and current dynamics in the multifilamentary HTS, in realistic conditions, is required.

(a) Complete mesh and (b) detailed view near the edge of a Superconducting Filament. The red dashed line indicates the region of the simulated field profiles.
This is a complex nonlinear problem that necessitates a multiphysics approach since current and field distributions in superconductors depend strongly on the temperature and history of the applied field and transport current. The effects of different multifilamentary geometries on the current and field dynamics in an AC regime were analyzed. A model for computing the current and field distributions in multifilamentary superconducting thin films subjected to the simultaneous effects of a transport AC current and a perpendicularly applied DC field was created. In the finite-element simulations, the geometry and the value of the parameters were chosen to allow a direct comparison of the calculated magnetic flux and the current profiles with experimental data obtained by time-resolved magneto-optical imaging (TRMOI), scanning Hall probe, and Hall probe arrays. A comparison provides both a test for the model itself as well as new information on the complex behavior of these systems.

It was found that increasing the interfilamentary distance reduces the magnetic coupling between filaments. The screening and transport currents redistribute more evenly among all filaments. A reduction of magnetic coupling also affects field and current dynamics, and decreases the overall AC loss.

The superconductor is considered to be at a constant operating temperature below the critical temperature, and no quenching occurs. In addition, since the samples are long and straight, a 2D model considering only the superconducting cross-section was utilized. The model is implemented in COMSOL Multiphysics’ general PDE Module, and uses two magnetic field components as state variables. The use of edge elements of first order allows having the zero-divergence equation for the magnetic field automatically satisfied.

In the simulations, a system consisted of the air domain and six superconducting filaments connected at the ends. Since the substrate has very poor conductivity and is non-magnetic, it has been neglected in the simulated geometry. The model is not restricted to any number of filaments, dimensions, or aspect ratios. However, a high aspect ratio of the thin-film geometry introduces a large number of nodes that can severely affect the computation time, especially for systems with a large number of filaments. An example of the simulated geometry and corresponding mesh is illustrated in the figure (a). The density of nodes in the mesh increases near the filaments, as shown in the detailed view of (b) in the figure.

The field and current dynamics of a multifilamentary superconducting thin film by numerical simulation using a finite-element model to solve Maxwell’s equations were studied. A highly nonlinear resistivity was used to describe the electrical characteristics of the superconducting film. The model allows a direct comparison with measurements of local magnetic field variations performed by experimental techniques. It was observed that an increased interfilament distance alters the field and current dynamics due to reduced magnetic coupling between filaments. Screening and transport currents redistribute more evenly among all filaments, which respond more independently. The distance also significantly reduces the losses of the multifilamentary thin films. The model can be used to study low-loss geometries for manufacturing practical


This work was done by Timothy J. Haugan and Paul N. Barnes of the Air Force Research Laboratory, Andrea Lucarelli of the Laboratorium fur Festkörperphysik (Switzerland), Francesco Grilli of Ecole Polytechnique Montréal, and Gunter Lupke of The College of William and Mary. For more information, download the Technical Support Package (free white paper) at  under the Electronics/Computers category. AFRL-0174.

This Brief includes a Technical Support Package (TSP).
Finite-Element Simulations of Field and Current Distributions in Multifilament Superconducting Films

(reference AFRL-0174) is currently available for download from the TSP library.

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