Measured and modelled vectorial flux density generated by an eye-shaped magnet

Persistent current loops of arbitrary size can be built from second-generation high-Tc superconducting (2G-HTS) coated conductors. Such ‘eye-shaped’ loops are obtained by milling a slit along the central line of a tape section and extending both sides around a cylinder. These structures can serve as sizeable permanent magnets. Compared to cylindrical magnets, however, the flux density B is not axisymmetric and its main direction is deflected from the normal.
In order to improve the design of these eye-shaped magnets and to predict the flux density when several of them are combined and magnetized with different directions, we measure experimentally and model the three components of B generated by a 60 mm-diameter eye-shaped magnet made of 10 mm-wide 2G-HTS tapes (GdBa2Cu3O7) from Shanghai Superconductor.
The measurements are performed at 77 K using a bespoke, cryogenic 3-axis Hall sensor designed in a previous work. The first model is semi-analytical and based on Biot-Savart’s law applied to a superposition of eye-shaped wires. The other models are based on the finite element method in 3D. The structure is modelled either as a volume (H-phi-formulation) or a surface (T-A and thin-shell H-phi-formulation), in the magnetodynamic regime.
Both the experimental and modelling results show that, ~10.5 mm above the centre of the structure, B is deflected by ~4°. At the same height, the measured (resp. modelled) Br = √(B_x^2+B_y^2 ) appears to be constant above the upper branch of the structure and ~2 (resp. ~1.8) times larger than above the lower branch. The models can then be used to visualize B generated by a combination of eye-shaped magnets