Development of an Analytical-Oriented Extensive Model for AC Coupling Losses in Multilayer Superconducting Composites

Previous analytical models of ac coupling losses in multifilamentary composites under a time-varying external magnetic field were developed for specific strand geometries. Therefore, no global expression of coupling losses was established for any circular geometry. The purpose of this paper is, thus, to present the general analytical strategy and the assumptions of the model developed at CEA. Furthermore, coupling losses are generally characterized by a global time constant nτ.In this paper, effective coefficients (analogous to time constants) are developed to reflect the coupling between the different layers. A global linear equation system linking the amplitudes of the electric field in each layer and their time variation and that of the external magnetic field is deduced, establishing a coupling matrix built with time constant coefficients. In addition to the physical interpretation of the quantities defined, the global equation is numerically solved. Local fields are quantified, as well as currents and ac coupling losses in different types of composites. A better physical understanding of the composite is tentatively achieved by the use of this analytical model.