A Custom Finite-Element Method Framework for Designing Superconducting Solenoidal Magnets and Coils with True HTS Tape Geometry

Superconducting solenoidal magnets are employed in magnetic resonance imaging and superconducting magnetic energy storage systems. Numerical methods are mandatory to optimize their design and predict their performance. Implementing the finite-element method (FEM) on the actual geometry of a high-temperature superconductor (HTS) tape is challenging due to the large aspect ratio of the tape, which creates meshing difficulties. In this article, we address this challenge by developing a custom FEM framework tailored specifically for this application, with a focus on speed and easy integration into optimization algorithms. A novel approach is adopted, representing the geometry of a coil-turn of HTS tape using a single point on the 2D plane. Each point corresponds to a matrix, serving both as an algebraic storage medium and the geometrical representation of the tape. The matrix cells possess imaginary dimensions that form the geometry of the coil-turn, eliminating the need for traditional meshing. The code of the framework is optimized to increase efficiency and utilize multiple cores of the processor. Results are compared with those obtained from COMSOL, verifying the framework's accuracy. A large magnet is designed to assess the computation efficiency. The successful application of this custom FEM framework in optimization routines opens new pathways for designing and predicting the performance of superconducting solenoidal magnets.