Coupled axial and transverse currents method for finite element modelling of periodic superconductors

In this paper, we propose the Coupled Axial and Transverse currents (I) (CATI) method, as an efficient and accurate finite element approach for modelling the electric and magnetic behavior of periodic composite superconducting conductors. The method consists of a pair of two-dimensional models coupled via circuit equations to account for the conductor geometrical periodicity. This allows to capture three-dimensional effects with two-dimensional models and leads to a significant reduction in computational time compared to conventional three-dimensional models. After presenting the method in detail, we verify it by comparison with reference finite element models, focussing on its application to twisted multifilamentary superconducting strands. In particular, we show that the CATI method captures the transition from uncoupled to coupled filaments, with accurate calculation of the interfilament coupling time constant. We then illustrate the capabilities of the method by generating detailed loss maps and magnetization curves of given strand types for a range of external transverse magnetic field excitations, with and without transport current.