Analytical and numerical computation of AC loss in multifilament MgB₂ wires under arbitrarily time-varying transverse magnetic field

Abstract Multifilament MgB 2 wires can be used in electrical machines, in which the wires experience a time-varying transverse external magnetic field that is rotating (thus consists of two orthogonal components). Analytical formulae are available in the literature to calculate the instantaneous coupling loss, eddy current loss and hysteresis loss of a multifilament superconducting wire under the action of a time-varying external magnetic field in one direction. This paper extends those formulae to the situation when the wire is subject to a time-varying external magnetic field in two orthogonal directions transverse to the wire’s longitudinal axis, by deriving from first principles the instantaneous loss formulae. The coupling loss in the filament-matrix zone is derived using the anisotropic continuum model, which treats the filament-matrix zone as a continuum with anisotropic resistivity, and this removes the need to model filaments individually. The loss formulae derived are verified by numerical simulations done in the finite-element software COMSOL Multiphysics using an external magnetic field that is realistic in an electrical machine environment. Reasonable agreement can be seen between analytical and numerical calculations. In the numerical calculations, the anisotropic continuum model is implemented in 2D and 3D in COMSOL via the H -formulation, with almost identical results, but the 2D simulations are significantly faster than the 3D simulations.