Analytical Model for Magnetic Field and Inductance of Toroidal D-Shaped HTS Magnet

The electromagnetic calculations of large-size high-temperature superconducting (HTS) toroidal D-shaped magnets present structural complexity and modeling difficulties, resulting in high complexity in the evaluation of the energy storage, critical current and central magnetic field, which pose significant challenges to the electromagnetic design. This paper established an analytical calculation model for the inductance and magnetic field of the toroidal D-shaped HTS magnet under the assumptions of static magnetic field and current distribution, and developed the discrete method and accelerate calculation further through integral transformations. The discrete method was compared and validated against the finite element analysis (FEM) method and 3D T-A homogenization method. The results indicate that the discrepancies in inductance and parallel fields between the discrete analytical method and the 3D T-A are less than 3%, with errors in perpendicular fields within 20%, and exhibit a computational speed 4 to 6 orders of magnitude faster than FEM. The larger error in the perpendicular field is due to the non-uniform superconducting current distribution, which occurs mainly inside the magnet. This approach can be applied to the preliminary evaluation of performance parameters such as stored energy and critical current in toroidal HTS magnets, thereby enhancing the efficiency of electromagnetic design.