A Time-Harmonic Approach to Numerically Model Losses in the Metal Matrix in Twisted Superconductors in External Magnetic Field

The first NbTi superconductor was developed in 1962 at Westinghouse. During 50 years, the manufacturing process of NbTi wires became highly optimized, and complex wire structures, which are needed in reducing ac losses, can be produced these days. Twisted multifilamentary structures generate many challenges from the modeler's point of view. Considering numerical modeling, NbTi wires are too complicated to model with filament-level details. This is due to the high number and very nonlinear resistivity of filaments. Consequently, simplified approaches are needed for wire modeling. In this paper, a time-harmonic approach to model losses in the metal matrix is introduced. It is based on the linear approximation of filaments. The method to determine the linear resistivity of filaments is based on the definition of the skin depth and the radius of filaments. This can be done in advance without solving a nonlinear problem in 3-D. The suitability of the time-harmonic approach is benchmarked against the H-formulated 3-D eddy current model (ECM) with power-law resistivity. According to simulations, the losses in the metal matrix predicted by the time-harmonic approach agreed well with the nonlinear ECM when the filaments were uncoupled. The results achieved with the proposed approach similarly followed the effects of geometrical changes in the wire structure on losses as the nonlinear ECM and predicted the circumstances where the filaments became partially coupled. The simulation times were considerably lower with the new approach. From the manufacturer's perspective, it is important to design conductors where the filaments stay uncoupled and have low ac losses in such a situation. Thus, the new approach can provide an effective design tool in developing new superconductors.