Power losses in hard superconductors: An analysis using the critical state model

In this paper, power losses in a superconductive wire, carrying a time-varying current and embedded in an external magnetic field, are evaluated on the basis of an analytical approach, previously developed by the authors, to the computation of magnetic fields. Computation is carried out for a hard superconductor rectilinear wire of circular cross section, in the presence of an external magnetic field orthogonal to the wire axis. The hard superconductor is modelled according to critical state theory, which leads to a non-linear hysteretic formulation. An approximate analytical solution is obtained for the losses, in the case of steady-state ac currents, as a function of the superconducting material parameters as well as of field and geometrical quantitites. On this basis, an attempt can be made to evaluate and discuss the influence of the various loss terms of different origin, though under the rather restrictive conditions required by the analytical solution.