Numerical Impact of Using Different E-J Relationships for 3-D Simulations of AC Losses in MgB₂ Superconducting Wires

AC losses in superconductors are generated every time a time-varying current/field is present. Engineers must be able to predict these losses as accurately as possible during the design phase of power applications. The electrodynamics of superconductors can be formulated as a nonlinear eddy current problem in which the resistivity of the superconducting region is a highly nonlinear function of the current density. In 3-D finite-element simulations, it leads to time-consuming simulations and convergence issues. In this paper, we compare two different E - J constitutive equations, namely: 1) power law model and 2) the percolation model (PM), programmed within both the H - \phi and T - \phi formulations. Based on the 3-D case of a three-filament twisted superconducting wire, the numerical performance of all these formulations/material models is compared in terms of accuracy, computation times, number of time steps, and number of Newton iterations for different relaxation methods. It is shown that the combination of the T - \phi formulation and the E - J PM works fine and should be further developed, as it seems to constitute the best modeling option from both a numerical and physical point of view.