Toward Two-Dimensional Simulations of Hysteresis Losses in Partially Coupled Superconducting Wires

When designing superconducting magnets, it is of ample importance to be able to reliably simulate the electromagnetic behavior of the superconducting wires comprising the magnet. The filaments of the wires in the magnets are often twisted to minimize the coupling between the filaments in applied fields. In twisted superconductors, the filaments can be coupled, uncoupled or partially coupled. Typically, the partially coupled wires have been simulated using three-dimensional (3D) simulation tools. Even though they produce accurate results, the problems arising from 3D formulations can be computationally very heavy. In this paper, we present a two-dimensional (2D) approach to model coupled, partially coupled, and uncoupled superconducting wires using the
$H$
-formulation of the eddy current model. Furthermore, we use 3D simulations to benchmark our 2D simulations.