Finite-element models for systems containing type II superconductors and ferromagnetic materials

Abstract

Superconductor and ferromagnetic materials have strongly different magnetic properties. While irreversible type-II superconductors restrict magnetic flux variations, ferromagnetic materials tend to channel magnetic flux lines by providing low reluctance paths. The physical modelling of the problem is strongly nonlinear. Different numerical methods for finding approximate solutions to the problem typically involve the nonlinearities in different manners and, as a result, exhibit very different numerical behaviors.

The first part of this work compares several existing finite element formulations (a magnetic field formulation and a vector potential formulation) for problems containing type-II superconductors and soft ferromagnetic materials. The proposed approach consists in starting from very simple problems with separate materials and increasing progressively their complexity until the modelling of two-dimensional problems with both materials together. The comparison brings antagonistic conclusions: in terms of accuracy and efficiency, none of the methods is found to be optimal for both materials at the same time.

The second part of this work investigates whether a new coupled formulation can improve the performances. The proposed coupled formulation demonstrates a good accuracy and a better efficiency than the existing formulations in all tested situations, without requiring any parameter tuning. It exploits the best method in each material (the magnetic field formulation in the superconductor and the vector potential formulation in the ferromagnetic material) and ensures coupling through surface terms.