High-temperature superconducting (HTS) dynamos enable contact-free injection of large direct currents into superconducting circuits, and their multiphysics electromagnetic-thermal coupling and practical circuit interactions requiresmodels that are both accurate and computationally efficient. This work implements a hybrid J–A–φ formulation coupled to thermal model. It solves the scalar magnetic potential φ, the magnetic vector potential A, the current density J, and the temperature T. To consider the temperature dependence, the critical current density is a function of temperature that is computed by a thermal model. Two operating scenarios are examined: (i) an open-circuit case with zero-net transport current and (ii) a charging case in which the HTS tape is coupled to a series R–L circuit. Simulations at 10 Hz and 500 Hz evaluate global variables: instantaneous voltage between the terminal of tape Vsc, cumulative time-averaged voltage VDC, average temperature Tav, and charging current Isc using a segregated H-formulation as the reference and benchmarking against J-A, H-A and J-A-φ formulations. The J–A–φ formulation delivers substantial reductions in computational cost marked decreases the time footprint relative to H-A while preserving the accuracy of the reference solution. These results indicate that J–A–φ is a reliable and efficient tool for design-oriented studies of HTS dynamos.
Santos et al. (Tue,) studied this question.