Power-law characteristic for 3-D macroscopic modeling of superconductors via an integral formulation

In this paper, we solve the eddy-current problem in presence of superconductors in three-dimensional geometries, fed through electrodes and possibly carrying transport current. An integral formulation of the electromagnetic part of the problem is complemented by a variational form of the macroscopic constitutive relationship of a superconductor, obtained by the use of a suitable power-law characteristic. This formulation allows us to solve the problem as an unconstrained minimization of a functional that is convex under suitable assumptions.