Magnetic Field Conforming Formulations for Foil Windings
Abstract
We extend the foil winding homogenization method to magnetic field conforming formulations. We first propose a full magnetic field foil winding formulation by analogy with magnetic flux density conforming formulations. We then introduce the magnetic scalar potential in non-conducting regions to improve the efficiency of the model. This leads to a significant reduction in the number of degrees of freedom, particularly in 3-D applications. The proposed models are verified on two frequency-domain benchmark problems: a 2-D axisymmetric problem and a 3-D problem. They reproduce results obtained with magnetic flux density conforming formulations and with resolved conductor models that explicitly discretize all turns. Moreover, the models are applied in the transient simulation of a high-temperature superconducting coil. In all investigated configurations, the proposed models provide reliable results while considerably reducing the size of the numerical problem to be solved.
Cite
@article{arxiv.2504.11191,
title = {Magnetic Field Conforming Formulations for Foil Windings},
author = {Louis Denis and Elias Paakkunainen and Paavo Rasilo and Sebastian Schöps and Benoît Vanderheyden and Christophe Geuzaine},
journal= {arXiv preprint arXiv:2504.11191},
year = {2026}
}
Comments
This work has been submitted to the IEEE for possible publication