Three-dimensional electromagnetic modeling of practical superconductors for power applications

HTS are feasible for hight power applications because of the smaller consumption demand of the cooling system in comparison to the whole power device. Real industral devices contain superconductors with 2D and 3D geometry (coated conductors tapes represent an example of 2D geometry, since the superconducting layer is very thin). In order to know the feasibility and the optimum design of a certain device, there is a need of software tools. These Numerical tools have hight requirements like fast computation, a physical model for any E(J) relation of the superconductor and any complex geometry such as coils, motors and generators, where E is the electric field and J is the current density. In this work we present a 3D variational model based on a functional that restricts the problem in the superconductor volume. We show the magnetization process of a thin film and a 3D bulk sample. We compare our model of the thin film geometry with the thin film formula, reaching a good agreement. We also compare a striated tape, where the filaments are connected by linear material, with a FEM model. We present several results for a thin film with constant critical current density, Jc, magnetic-field dependent Jc, and an anisotropic E(J) relation. For the latter, E is not parallel to J when the magnetic flux density is not perpendicular to J (force free situation). The last studied situation is the 3D cubic sample. We find the time dependence of the current density and AC loss for each situation. In the cubic bulk sample, we found a non-negligible component of the current density in the direction of the applied field. The presented numerical method is very promising for 3D modeling of superconducting samples and power applications.