The attenuation of magnetic fields is crucial for various application fields, including health, space exploration, and fundamental physics, to name just a few. Superconductors are key materials for addressing this challenge. In this review, we mainly focus on the shielding and screening of quasi-static magnetic fields using superconductor-based passive layouts. After providing a brief overview of the principles of magnetic shielding and screening using superconductors, we outline commonly used procedures for measuring the field attenuation. Next, we give an insight into analytical and numerical models able to reproduce experimental results and predict the performances of new designs. Key challenges and achievements in employing low temperature or high temperature superconducting bulk and tape-based structures for reducing a given applied field are then discussed. Additionally, hybrid designs combining superconducting and ferromagnetic materials, aimed at enhancing the shielding ability or fabricating magnetic cloaks, are described. Finally, we highlight future challenges and potential advancements in this technology.

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 ⩾ 10⁴ occurs near the close extremity of the shield to over 1 T.

Superconductors are strategic materials for the fabrication of magnetic shields, and within this class, MgB${}_2$ has been proven to be a very promising option. However, a successful approach to produce devices with high shielding ability also requires the availability of suitable simulation tools guiding the optimization process. In this paper, we report on a 3D numerical model based on a vector potential (A)-formulation, exploited to investigate the properties of superconducting (SC) shielding structures with cylindrical symmetry and an aspect ratio of height to diameter approaching one. To this aim, we first explored the viability of this model by solving a benchmark problem and comparing the computation outputs with those obtained with the most used approach based on the H-formulation. This comparison evidenced the full agreement of the computation outcomes as well as the much better performance of the model based on the A-formulation in terms of computation time. Relying on this result, the latter model was exploited to predict the shielding properties of open and single capped MgB${}_2$ tubes with and without the superimposition of a ferromagnetic (FM) shield. This investigation highlighted that the addition of the FM shell is very efficient in increasing the shielding factors of the SC screen when the applied magnetic field is tilted with respect to the shield axis. This effect is already significant at low tilt angles and allows compensating the strong decrease in the shielding ability that affects the short tubular SC screens when the external field is applied out of their axis.

A microwave technique suitable for investigating the AC magnetic susceptibility of small samples in the GHz frequency range is presented. The method—which is based on the use of a coplanar waveguide resonator, within the resonator perturbation approach—allows one to obtain the absolute value of the complex susceptibility, from which the penetration depth and the superfluid density can be determined. We report on the characterization of several iron-based superconducting systems, belonging to the 11, 122, 1144, and 12442 families. In particular, we show the effect of different kinds of doping for the 122 family, and the effect of proton irradiation in a 122 compound. Finally, the paradigmatic case of the magnetic superconductor EuP-122 is discussed, since it shows the emergence of both superconducting and ferromagnetic transitions, marked by clear features in both the real and imaginary parts of the AC susceptibility.

MgB₂ is one of the most promising materials for superconducting bulk applications. However, thermomagnetic instabilities can arise in the material because of its low heat capacity and thermal conductivity as well as its high critical current density. Being able to predict these phenomena, can guide and optimize MgB₂-based devices for magnetic flux shielding or trapping applications. In this work, the flux-jump occurrence in an MgB₂ cup-shaped shield is numerically studied using the finite element method by means of the commercial software COMSOL 6.0 Multiphysics®. To this aim, we developed a 2D axial-symmetric model coupling the heat diffusion equation and the magnetic equations based on a magnetic vector-potential ( A ⃗ ) formulation. The comparison of the computed shielding curves with the experimental ones evidenced a good agreement between the two sets of data at different temperatures and positions along the shield’s axis. The as-validated model was then exploited to investigate possible optimization routes via the improvement of both the thermal conductivity of the material and the thermal exchange between the device and the cooling stage.