Magnetization loop modelling for superconducting/ferromagnetic tube of an ac magnetic cloak

Abstract

From the combination of superconducting (SC) and ferromagnetic (FM) materials, one can prepare composites with unusual magnetic properties, e.g. for the cloaking of a dc or low-frequency ac magnetic field by a shell from a SC/FM composite. In the design and optimisation of such SC/FM structures, numerical modelling is essential. Non-linear magnetic permeability, as well as the hysteresis of both kinds of materials, are to be incorporated in the calculations aimed at achieving reliable estimates. We present a technique that allows the prediction of the ac magnetization loops of SC/FM composites. The critical state model-based approach is used to describe the properties of the superconducting material. The ferromagnetic part is characterized by its (non-hysteretic) nonlinear permeability. With these ingredients, the distributions of the magnetic field are calculated in subsequent instants of the ac cycle and are used to evaluate the preliminary data for the magnetization loop, which is still missing the hysteresis of the FM part. Afterward, the latter component is added to the magnetization loop by an approximation deduced from the known dependence of the hysteresis loss in the FM material on the ac magnetic field. In spite of its approximate nature, this approach demonstrated very good predictability in experimental tests.