Thin-film superconducting rings in the critical state: the mixed boundary value approach (Q2342148)

This paper deals with the study of circular currents (rings) in perfectly conducting and superconducting materials. In both cases there are the same field equations. The difference is that in a perfect conductor, the two points that divide the positive semi-axis are given by the two radii of the ring. In the case of superconductors, due to the partial penetration of the field, the two points fall inside the ring and mark the null field zone. They must be found with the requirement that the current density does not diverge to infinity, an imperative physical request. The main features of this paper are the following: (i) all the cases are treated in the same way; (ii) in the case of superconducting rings, the penetration of the magnetic field in the internal/external rims is a result of the method itself and does not have to be imposed; (iii) the method can be extended to investigate more complex cases. Numerical simulations support the abstract results of this paper.