Three-dimensional modeling of the magnetization of superconducting rectangular-based bulks and tape stacks

Three-dimensional (3D) numerical models of the electromagnetic behavior of superconductors have been developed, but they are not routinely used yet. This work aims at providing a comparison and validation of three different approaches: The minimum electro-magnetic entropy production method, the H-formulation of Maxwell's equations, and the volume integral equation method for 3-D eddy currents computation. The investigated problem is that of a high-temperature superconductor (HTS) parallelepiped bulk with the magnetic field parallel to two of its faces and making an angle with the other one, without and with a further constraint on the possible directions of the current. The latter constraint allows simulating a stack of thin superconducting tapes, which are electrically insulated in one direction. The results in terms of current density profiles and energy dissipation are compared, and the differences in the two situations of unconstrained and constrained current flow are pointed out. This paper constitutes a concrete result of the collaborative effort taking place within the HTS numerical modeling community and will hopefully serve as a stepping stone for future joint investigations.