Vector potential theory of ac losses in superconductors

Abstract

A novel scheme for calculation of ac losses in superconductors is described. It is based on a formulation of the loses in terms of the vector potential. The method is a generalisation of ideas put forward by W.T. Norris in the 70s. In contrast to the widely used conformal mapping methods, the vector potential approach is not restricted to (infinitely) thin sheets, but allows for the analytical calculation of ac losses in conductors with arbitrary cross-section. It is restricted to situations where a so-called kernel or electric centre exists, i.e. a region or line inside the superconductor along which the electric field vanishes throughout the ac cycle. Fortunately many theoretically and practically important problems are of this type. Analytical expressions are derived for a series of problems involving rectangular superconductors, single conductors as well as assemblies of several conductors. Explicit solutions are obtained for the back- conduction for the reduction of ac losses and for gap losses occurring in transformer windings and cables. The formalism can be easily applied to other than rectangular, e.g. circular or more complicated cross-sections.