3D computation of non-linear eddy currents: Variational method and superconducting cubic bulk

Abstract

Computing the electric eddy currents in non-linear materials, such as superconductors, is not straightforward. The design of superconducting magnets and power applications needs electromagnetic computer modeling, being in many cases a three-dimensional (3D) problem. Since 3D problems require high computing times, novel time-efficient modeling tools are highly desirable. This article presents a novel computing modeling method based on a variational principle. The self-programmed implementation uses an original minimization method, which divides the sample into sectors. This speeds-up the computations with no loss of accuracy, while enabling efficient parallelization. This method could also be applied to model transients in linear materials or networks of non-linear electrical elements. As example, we analyze the magnetization currents of a cubic superconductor. This 3D situation remains unknown, in spite of the fact that it is often met in material characterization and bulk applications. We found that below the penetration field and in part of the sample, current flux lines are not rectangular and significantly bend in the direction parallel to the applied field. In conclusion, the presented numerical method is able to time-efficiently solve fully 3D situations without loss of accuracy.

Modeling of airgap influence on DC voltage generation in a dynamo-type flux pump

“…It performs based on the calculation of current density J and scalar potential ϕ by minimizing a functional containing all the variables of the problem such as magnetic vector potential A, current density J, and scalar potential ϕ. It has been proved that the minimum of this functional in the quasimagnetostatic limit is the unique solution of Maxwell differential equations [62]. Since the current density is only inside the superconducting part, discretization of mesh in the domain around the superconducting part is not needed in this method.…”

“…This dissipation factor can include any E − J relations in superconductors including the critical state model [62].…”

Solution of 3D magnetization problems for superconducting film stacks

“…In such cases efficient solution of magnetization problems can be obtained using homogenization and transition to the anisotropic bulk model [14][15][16]. The stack of N films with the neighboring film distance d and the current-voltage relation (1) superconductor was simulated in [19,20] for the critical current density One of the methods, MEMEP [19], was based on a variational formulation for the effective magnetization; the algorithm, written in C++, was parallelized (see [26]) to accelerate time consuming computations. For a similar spatial resolution the problem was solved in [19] also using the popular h -formulation and COMSOL Multiphysics.…”

Time constant of the transverse-field demagnetization of superconducting stacks of tapes

“…Here, we compare the 2D model from this work and the 3D model from [28,35] for benchmarking purposes. The width used for the tape is 12 mm for both 3D and 2D model.…”