Screening of magnetic fields by superconducting and hybrid shields with a circular cross-section

The use of superconducting (SC) materials is crucial for shielding quasi-static magnetic fields. However, the need for space-saving solutions with high shielding performance requires the development of a three-dimensional (3D) modelling procedure capable of predicting the screening properties for different orientations of the applied field. In this paper, we use a 3D numerical model based on a vector potential formulation to investigate the shielding ability of SC screens with cylindrical symmetry and a height/diameter aspect ratio close to unity, without and with the superimposition of a ferromagnetic (FM) circular shell. The chosen materials were MgB2 and soft iron. First, the outcomes of the calculations were compared with the experimental data obtained with different shielding arrangements, achieving a notable agreement in both axial field (AF) and transverse field (TF) orientations. Then, we used this validated modelling approach to investigate how the magnetic mitigation properties of a cup-shaped SC bulk can be improved by the superimposition of a coaxial FM cup. Calculations highlighted that the FM addition is very efficient in enhancing the shielding factors (SFs) in the TF orientation. Assuming a working temperature of 30 K and using a layout with the FM cup protruding over the SC one, SFs up to eight times greater than those with a single SC cup were attained at applied field up to 0.15 T, reaching values equal to or higher than 102 in the inner half of the shield. In the AF orientation, the addition of the same FM cup incurs a modest worsening at low fields, but at the same time it widens the applied field range where SF ⩾ 10^4 occurs near the close extremity of the shield to over 1 T.