Search

International audience; A special kind of magnetic shield, called the “magnetic cloak” consists of two parts: superconducting insert and ferromagnetic shell. In the numerical modelling utilized e.g. for the design and optimization purposes, electromagnetic behaviour of both these materials should be properly included. A similar situation exists also in case of conventional superconducting power devices like transformers and motors. The implementation of A-formulation in COMSOL Multiphysics allows building a numerical model that considers in the same physics the superconducting material and the ferromagnetic one. An important feature is that the Jiles- Atherton model of magnetic hysteresis could be easily implemented. In this way, the interaction between superconductors and ferromagnetic material can be introduced directly in the computation. We present numerical and experimental results for the magnetic cloak, where the superconducting part is made from six layers of coated conductor (CC) tapes and the ferromagnetic one is from an epoxy/ferrite powder composite. The current distribution in superconducting tapes and the magnetization of the ferromagnetic shell are solved within the same physics using the A-formulation.

We present the numerical procedure suitable for computing the distribution of electrical currents in a superconductor with geometry extending in all three spatial dimensions when it is exposed to magnetic field changing in time. Its main advantage is that it solves the problem in terms of vector potential, A , of the magnetic field. Such A-formulation is usually the default option for magnetic field calculations in commercial finite element codes. We have used it in past when a two-dimensional (2D) approximation was found sufficient to predict AC losses of single wires, cables, and coils with circular turns. Incorporation of superconductor properties based on the critical state model is straightforward in 2D because the flow of current is restricted to one direction only. The main challenge in extending the method to three dimensions is to cope with the situation when currents could flow in any direction. We have found that by assuming that the local current density in superconductor is always parallel to the local electrical field, and that its modulus is limited by the critical current density, provides sufficient input for accomplishing new working equation, linking the vector of current density to the time derivative of the magnetic vector potential. Our method successfully passed testing on the benchmark problem of superconducting cube magnetization. It is also used to interpret the magnetization measured on two cylindrical superconducting objects in the transverse field: one was the tube from bulk BSCCO and other the REBCO coated conductor tape helically wound on the non-metallic tube. Computed magnetization loops in both cases show good agreement with experiments and confirm the validity of the method.

Contributed talk at the 24th International Conference on Magnet Technology, 18-23 October 2015, Seoul, Korea.