An eddy current vector potential formulation for estimating hysteresis losses of superconductors with FEM

Abstract

Many people these days employ only commercial finite element method (FEM) software when solving for the hysteresis losses of superconductors. Thus, the knowledge of a modeller is in the capability of using the black boxes of software efficiently. This has led to a relatively superficial examination of different formulations while the discussion stays mainly on the usage of the user interfaces of these programs. Also, if we stay only at the mercy of commercial software producers, we end up having less and less knowledge on the details of solvers. Then, it becomes more and more difficult to conceptually solve new kinds of problem. This may prevent us finding new kinds of method to solve old problems more efficiently, or finding a solution for a problem that was considered almost impossible earlier. In our earlier research, we presented the background of a co-tree gauged T -ϕ FEM solver for computing the hysteresis losses of superconductors. In this paper, we examine the feasibility of FEM and eddy current vector potential formulation in the same problem.

Development of a three-dimensional finite-element model for high-temperature superconductors based on the H-formulation

“…For the case of helicoidal superconductors (Section 3.2), a comparison with a 2-D model utilizing the combination of translation and rotation symmetry is performed. This eddy current model is formed from the magnetostatic model of helicoidal conductors [16] coupled to Faraday's law, similarly to what has been done in [17]. In this example the mesh is refined near mid-length along the x-axis, because it is used to study the case of a localized defect there -see Section 3.3 for details.…”

3D simulation of AC loss in a twisted multi-filamentary superconducting wire

“…The analytical formula by Norris for the hysteresis loss over a cycle per unit length with an elliptical filament is [51] 2 0…”

An Optimization of a NbTi Wire Cross Section to Attain Low AC-Losses and High Critical Current

“…is a function space of -forms [11] and d, the exterior derivative, is [8] (4) Constitutive laws are (5) where is the resistivity, and (6) where is the permeability. is the Hodge operator [8] …”

“…There are several formulations and numerical techniques available for solving the eddy current problem [6], [9]- [11]. We review here shortly the eddy current model presented in [10] and introduce two extensions: applied field and exploitation of discrete symmetries.…”

“…Equation (11) holds for all and . and are the problem domain and the boundary operator [12], respectively.…”