Pierre Bernstein

The field trapped in a stack of MgB ₂ superconducting rings after field cooling magnetization (FCM) is investigated in the perspective of Nuclear Magnetic Resonance applications. According to the magnetizing field and temperature, the trapped field is either a constant or decreases along time as the external field goes to zero. In the first case, corresponding to moderate magnetizing fields, the field trapped along the stack axis is uniform, while it is non-uniform after FCM with a higher field. Non-uniform trapped fields are supposed to result from the depinning of some vortices which do not extend to the whole sample. Otherwise, the behaviour of the trapped field, as the temperature is increased after FCM at different temperatures and magnetizing fields, is investigated.

The ability of MgB₂ polycrystalline samples to carry strong current densities even across high-angle grain boundaries has boosted the fabrication of large bulk superconductors. However, the occurrence of thermomagnetic instabilities, such as flux jumps, compromises the use of this compound at low working temperatures. Investigating and mitigating these phenomena are then crucial for future applications, as for instance permanent bulk magnets. In this paper, starting from the experimental evidence of flux-jump occurrence in a MgB₂ disc-shaped magnet prototype, we numerically investigated this phenomenon coupling the electromagnetic equations (formulated using the magnetic vector potential) to the heat diffusion equation. This numerical approach – validated via the comparison between computed and experimental results – provided us with the evolution of the local magnetic field and temperature in correspondence to a flux-jump. Based on this information, we finally investigated possible solutions to prevent flux-jump occurrence through the improvement of the thermal exchange between the sample and the cooling stage.

In 2023, researchers from the University of Cambridge and the Paul Scherrer Institute (PSI) successfully demonstrated the feasibility of employing second-generation high-temperature superconducting (HTS) RE-Ba-Cu-O(REBCO) materials for undulator applications, achieving a magnetic field of 2.1 T with a 10 mm period and a 4 mm magnetic gap. This remarkable performance is primarily attributed to the high critical current density (J_c) of REBCO. However, REBCO also presents several challenges, including high production cost, complex fabrication procedures, and limited machinability. In contrast, although MgB₂ exhibits a lower J_c, it offers advantages such as ease of synthesis and machining, making it a promising candidate for undulator development. This study presents the design, preparation fabrication, and assembly of short-period MgB₂ bulk undulators, utilizing spark plasma sintered (SPS) MgB₂ bulks with a 16 mm period and a 4 mm magnetic gap, after 2D size optimization and 3D simulation, it is estimated that an undulator magnetic field of 1.75 T will be generated.

This article demonstrates the concept proof to manufacture parts of MgB2 by Laser Powder Bed Fusion (L-PBF) coupled to Spark Plasma Sintering (SPS) by an optimization of the L-PBF and SPS conditions to limit the phase degradation and complete the sintering. Optimal L-PBF parameters were identified in order to obtain the material preforms with a minimal degradation of the MgB2 phase, and then these preforms were sintered by SPS using an inert powder as matrix with a purpose to receive a mechanically more reliable product. Sintered samples show superconductivity state inherent for the raw material and demonstrate superconducting transition around 38 K according to the magnetic moment measurements.

The critical current of superconducting materials, such as magnesium diboride (MgB₂) bulk superconductors, is a key parameter influencing their performance in various applications, including magnetic field shielding, MRI, and Maglev systems. Spark plasma sintering (SPS) is one of the most efficient methods to fabricate high-quality MgB₂, significantly saving fabrication time and controlling grain growth. The fabrication conditions, including temperature, pressure, and dwell time, can affect the critical current density. Traditional methods for estimating critical currents are time-consuming and costly. This study explores the use of advanced artificial intelligence (AI) techniques to develop accurate and efficient models for predicting the critical current in MgB₂ bulks with respect to 10 different influential fabrication properties and physical conditions. By using AI algorithms such as Gaussian process regression, extremely gradient boosting, and generalized regression neural network (GRNN) an extremely high accuracy in predictions against the actual experimental data was achieved. By defining and studying the extrapolation scenario, this study goes beyond of simple AI-based estimator model that performs well only within the training range of data. The developed AI models not only reduce the need for extensive experimental campaigns but also offer real-time prediction capabilities, paving the way for faster advancements in the research and development of superconducting technology. Overall, GRNN model demonstrated a good performance for both interpolation and extrapolation tasks with an R-squared of 0.999958 and 0.99521, respectively.

We report the levitation and guidance forces of two set-ups including a 120 mm diameter MgB₂ disc cooled down to 20 K. The first one included the disc and a 30 mm thick and 100 mm diameter NdFeB magnet and is labelled as PM100 set-up. The second one called PM70 set-up included a 70 mm diameter and 35 mm thick magnet. All the measurements were carried out after cooling down the superconductor with a 30 mm separation between the magnet and the superconductor. Some remarkable results were obtained. It was reported by Xing et al (2024 Supercond. Sci. Technol. 37 02LT01) that the levitation force measured with the PM100 set-up has reached the strong value of 678 N at 5 mm separation between the magnet and the superconductor. In this new report, in addition to a comparison of the levitation forces measured on both set-ups, we report guidance force measurements. We show that this force decreases for the PM100 set-up as the magnet-superconductor distance decreases, while the guidance force of the PM70 set-up increases, as was reported for set-ups including Halbach guideways sections. Reproducing the measured levitation forces with analytical models, we show, on the one hand, that the large levitation forces measured with the PM100 set-up are due to the non-homogeneity of the magnetic field above the PM100 magnet. On the other hand, we explain the behaviour of the PM70 set-up guidance force by the low modulation of the magnetic moment of the superconductor resulting from the magnet motion.

The advent of superconducting bulks, due to their compactness and performance, offers new perspectives and opportunities in many applications and sectors, such as magnetic field shielding, motors/generators, NMR/MRI, magnetic bearings, flywheel energy storage, Maglev trains, among others. The investigation and characterization of bulks typically relies on time-consuming and expensive experimental campaigns; hence the development of effective surrogate models would considerably speed up the research progress around them. In this study, we first produced an experimental dataset containing the levitation and lateral forces between different MgB₂ bulks and one permanent magnet under different operating conditions. Next, we have exploited the dataset to develop surrogate models based on Artificial Intelligence (AI) techniques, namely Extremely Gradient Boosting, Support Vector Regressor (SVR), and Kernel Ridge Regression. After the tuning of the hyperparameters of the AI models, the results demonstrated that SVR is the superior technique and can predict levitation and lateral forces with a worst-case accuracy scenario 99.86% in terms of goodness of fit to experimental data. Moreover, the response time of these models for the estimation of new datapoints is ultra-fast.

This rapid communication highlights a remarkable achievement obtained with a 120 mm diameter large cylindrical MgB₂ bulk: the measurement of magnetic levitation forces up to 700 N at 20 K, levitation being stable up to levitation forces exceeding 400 N. The investigated sample, which has one of the largest dimensions reported in the literature, was fabricated using the unconventional spark plasma sintering technique. This method is known as one of the most efficient methods for producing dense MgB₂ samples. This breakthrough holds significant potential for advancing high-performance levitation systems and superconducting applications, including high-speed transportation systems and magnetic bearings.

Superconducting magnetic levitation force measurements on large field cooled cylindrical MgB₂ bulks with different diameters and thicknesses are reported. For these experiments, a special set-up permitting one to measure forces up to 500 N was used. In contradiction to previous measurements, the obtained force hysteresis cycles could not be reproduced with the analytical mean field model proposed by Bernstein et al (2017 Supercond. Sci. Technol. 30 065007). The failure of the model has been attributed to surface barriers effects which were not taken into account in the model. This last one was accordingly modified in order that the measured force cycles could be reproduced. Contrary to most other models describing surface barriers effects, the modified model suggests that above a threshold field anti-vortices and not vortices enter the superconductor. This behaviour is related to the storage by the superconductor of the mechanical work done by the operator. In addition, it has turned out that the threshold field is a decreasing function of the critical surface current density of the samples. As a consequence, the surface barriers effects occur only if this quantity and the critical current density are large enough. Otherwise, the internal magnetic field of the superconductor could be computed and was seen to be a decreasing function of the thickness of the superconductors.