Finite-Element Simulations of Field and Current Distributions in Multifilament Superconducting Films
FE analysis provides more accurate information on separation of high-temperature superconducting tapes in filaments.
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.

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
conductors.
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 www.defensetechbriefs.com/tsp 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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Overview
The document titled "Finite-Element Simulations of Field and Current Distributions in Multifilamentary Superconducting Films" is a journal article published in the Superconductor Science and Technology. It presents a comprehensive study on the behavior of multifilamentary superconducting thin films when subjected to both alternating current (ac) and direct current (dc) magnetic fields. The research is conducted by a team of authors, including Timothy J. Haugan and Paul N. Barnes from the Air Force Research Laboratory, along with collaborators from various academic institutions.
The core of the study involves the development of a finite-element model implemented in the COMSOL Multiphysics software. This model is designed to solve Maxwell's equations, which govern electromagnetic fields, using a highly nonlinear resistivity to accurately represent the electrical characteristics of superconductors. The focus is on understanding how current and magnetic field distributions evolve in response to external influences, particularly the interplay between transport ac currents and perpendicularly applied dc fields.
Key findings from the research indicate that the distance between the filaments in the superconducting films significantly impacts the transport and screening current distributions. As the interfilamentary distance increases, both magnetic coupling and ac losses are reduced. This insight is crucial for optimizing the design of superconducting materials, as it suggests that careful consideration of filament spacing can enhance performance by minimizing energy losses.
The study also explores the time-dependent behavior of magnetic flux and current distributions, providing a detailed analysis of ac losses associated with different configurations. The results contribute to a deeper understanding of flux pinning and critical current density in superconductors, which are essential parameters for their practical applications in various technologies, including power transmission and magnetic resonance imaging.
Overall, this research not only advances the theoretical understanding of superconducting materials but also has practical implications for the development of more efficient superconducting wires and devices. The findings are expected to inform future designs and applications in the field of superconductivity, ultimately contributing to advancements in energy efficiency and technology. The document is unclassified and approved for public release, ensuring that the knowledge gained can be shared and utilized by the broader scientific community.
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