FEM Simulations of Crossed-field Effects in Bulk Superconducting Trapped-field Permanent Magnets

Bulk (RE)BCO samples can be used as efficient permanent magnets achieving trapped flux densities of a few teslas at 77 K. However, their magnetization decays over time when subjected to crossed fields (with a direction perpendicular to the initially trapped flux density). Such parasitic field may be generated in synchronous motors as stray fields. In this talk, I summarize the recent work carried out in our group at the University of Liege to better understand the crossed-field effects. Under a magnetic field perturbation with a non-vanishing crossed field, the superconductor magnetization is modified due to a rearrangement of currents. We have developed finite-element models predicting the time evolution of the current distribution, on the basis of an A-V formulation implemented in the open-source software GetDP and Gmsh. The construction of the models is discussed, including the time-step scheme used, the choice for the mesh and convergence issues. It is demonstrated how the redistribution of currents under a transverse field can be studied with either 3D models or computationally simpler 2D models. The crossed-field effects are illustrated as a function of the amplitude of the perturbations, their waveform, and the variation of their direction over time (purely transverse vs rotation in space). Hybrid structures made of superconductors and soft ferromagnetic materials are also investigated. For the case of a soft ferromagnetic disk put on top of a superconducting pellet, it is demonstrated that the ferromagnetic material helps in both increasing the initial trapped field and in reducing the crossed-field effects. Different hybrid structures are discussed in order to find a compromise between the maximum level of induction which can be reached and the improved protection against crossed-field effects. Potential extensions of the numerical models are also discussed.