To this date, the characterization of Non-Insulated HTS coils for parameter estimation has been conducted using relatively slow current ramps. In the present work, a methodology based on AC signals is proposed to get additional parameters to refine the model of such coils and to improve on the existing lumed-parameter models for DC applications under dynamic responses. In that regard, two sets of sequential characterizations were conducted in liquid nitrogen at 77.3 K. First, a classical U(I) characterization in DC and different ramp tests were carried out to deduce the critical current ICC and the self-inductance of the NI coil. Second, AC measurements are performed at different frequencies and current magnitudes. From these last measurements, it was found that the lumped-parameter model best agreeing with experimental data is serial and not parallel as usually considered in DC. Thus, it further simplifies the equivalent electrical circuit of the NI HTS coils with a serial resistance RS connected in series with a serial inductance XS. Both electrical parameters can be directly obtained from voltage measurements and strongly depend on frequency but not the current amplitude in subcritical conditions. Ultimately, a lumped-parameter model is a useful approach to understand the behavior of NI HTS coils interacting with a more complex system or to study their response to transients in DC or DC+AC conditions.

The present paper deals with the development of a costumed-made system and techniques to address the challenges of the magnetization and characterization of bulk superconductors as large as 100 mm in diameter. The system is composed of a dry superconducting magnet capable of producing a field variation up to 18 T and a measurement setup relying on an advanced field mapping arrangement made of a 10 & times; 10 Hall sensor matrix for rapid magnetic field acquisition under 0.5 s. To achieve the desired accuracy, the experimental setup incorporates precise thermal management and calibration. Its purpose is to investigate strategies to enhance the stability, structural integrity, and overall performance of superconducting bulk materials magnetized in high magnetic fields. The goal is to promote scientific collaborations through a dedicated experimental facility for forthcoming magnetization and fast field-mapping studies, thereby supporting the development of bulk superconductors.

High-temperature superconductors, especially rare earth barium copper oxide (REBCO) bulks, are promising for superseding permanent magnets in power applications. However, being essentially ceramics, their practical use is limited by their brittleness that turns into mechanical failures during high-field magnetization. These failures often arise from defects that appear during the fabrication process, such as pores and cracks. This fragility may be mitigated by including artificial holes in the bulks. The number, size and distributions of these holes may not just improve cooling, but they may also reduce porosity, and enhance both mechanical strength and flux pinning. Modelling the impact of such holes on the trapping performance of the bulks and their thermo-mechanical response to magnetization, particularly the pulsed field magnetization (PFM) that is considered practical for actual applications, is challenging and requires a multiphysics approach. In that context, the present work introduces a 2D finite element model (FEM) that includes coupled electromagnetic, thermal and mechanical physics to simulate thin-wall REBCO bulks with ring reinforcement. The numerical results provide insight on how to maximize trapped magnetic fields while minimizing mechanical loads with thin-wall reinforced REBCO bulks.

Abstract In the present work, the objective is to quantify via modeling the impact of the variability of the critical parameters (critical current density and critical temperature) as well as the presence of midsize to large defects on the thermo-magnetic response of REBCO bulks under pulse field magnetization. A particular interest is given to the trapped magnetic field as a figure of merit of the strength of the trapping mechanism. For this study, a statistical methodology is proposed that can be extended by adding experimental data to numerical results. The statistics are generated using a Monte Carlo method running a thermo-electromagnetic 3D finite element model (TM-FEM). The TM-FEM solves the heat balance equation in conjunction with the H - ϕ mixed formulation of the Maxwell equations. The results are analyzed using cluster analysis and multivariate analysis of variance to identify dominant regimes of variability and statistically significant parameter interactions. In addition to the physical parameters, numerical parameters such as mesh quality and computation time are incorporated into the analysis to account for possible biases arising from modeling parameters. A response surface model is obtained providing a reduced-order predictive representation of trapped magnetic field. The results confirm that the variability of J c is the primary physical parameter that defines the magnitude of the trapped magnetic field. Nevertheless, defects introduce nonlinear interactions that can indirectly degrade the trapping. From response surfaces, nonlinear regression models are provided for the case at hand. The proposed statistical methodology yields a systematic approach for uncertainty quantification to help defining guidelines to improve the fabrication and optimal use of REBCO bulks as pseudo-magnets.

During pulsed-field magnetization (PFM) processes, high-temperature superconducting (HTS) bulks are subjected to significant mechanical stress due to rapid changes in magnetic flux (Lorentz force) and temperature (thermal stress), potentially leading to mechanical failures. This is particularly emphasized by the inherent fabrication-induced defects such as cracks, grain boundaries, and pores. These defects often result in non-uniform trapped magnetic fields across the bulk, which can strongly impact its trapping performance. The present study focuses on the impact of porosity on the trapped magnetic field, temperature, and mechanical stress of REBCO disk-shaped bulks through a 2D transient multiphysics finite element model using COMSOL Multiphysics (R). The results show that porosity causes significant losses by locally densifying the current, leading to high local temperatures, which in turn reduces the critical current density, infusing more local losses. As a result, lightning-like thermal pathways passing through the pores radiate from the edge of the bulk to its center as the applied magnetic field increases, therefore limiting the magnitude of the trapped field. Finally, porosity causes two distinct peaks in maximum tensile stress during PFM: one attributed to thermal effects and the other to electromagnetic forces. Higher porosity often results in the increase of both peaks of tensile stresses, potentially compromising the bulk's physical integrity. It highlights the importance of controlling porosity to improve the trapping performance of HTS bulks. One mitigating action is to fill the pores with silver, which is shown to remarkably reduce both the temperature rise and stress.

Superconducting devices are attractive technologies that could improve and increase the electrification of several industries. However, as superconductors have highly non-linear electromagnetic behavior, equipment based on such materials should be thoroughly investigated through experiments and simulations. For the latter, the finite element method is a common tool for simulation. However, this method often demands high computational resources, especially in transients. Moreover, the computation burden naturally increases with the number of degrees of freedom involved in the solution. To alleviate this load, the magnetic vector potential A can be swapped for the magnetic scalar potential Phi in the existing formulations T-A and J-A where there are no electrically conductive or ferromagnetic materials. To show the relevancy of the approach and to quantify the gain in computational resources, two case studies in 2D are considered: a single superconducting tape and a pancake coil; both based on (rare earth barium copper oxide) REBCO. The idea is to show the ease of implementation of the approach in COMSOL Multiphysics (R). The coupling between the scalar potential Phi and the vector potential A is detailed. An additional benefit of the proposed approach is the manual creation of a unique straightforward thin cut in the mesh, independently of the characteristics of the geometry. This method simplifies grandly the laborious generation of cuts in multiple connected domains. For both case studies, experimental data on AC losses are used to validate the models. The new formulations are also cross-checked with their respective older forms, showing a reduction of the computational time while keeping a fair accuracy.

The electric dipole moments~(EDM) of fundamental particles inherently violate parity~(P) and time-reversal~(T) symmetries. By virtue of the CPT theorem in quantum field theory, the latter also implies the violation of the combined charge-conjugation and parity~(CP) symmetry. We aim to measure the EDM of the muon using the frozen-spin technique within a compact storage trap. This method exploits the high effective electric field, \$E \approx 165\$ MV/m, experienced in the rest frame of the muon with a momentum of about 23 MeV/c when it passes through a solenoidal magnetic field of \$|\vec{B}|=2.5\$ T. In this paper, we outline the fundamental considerations for a muon EDM search and present a conceptual design for a demonstration experiment to be conducted at secondary muon beamlines of the Paul Scherrer Institute in Switzerland. In Phase~I, with an anticipated data acquisition period of 200 days, the expected sensitivity to a muon EDM is 4E-21 ecm. In a subsequent phase, Phase~II, we propose to improve the sensitivity to 6E-23 ecm using a dedicated instrument installed on a different beamline that produces muons of momentum 125 MeV/c}.

To improve the understanding of the behaviour of High Temperature Superconducting (HTS) devices in electrical systems, it is relevant to couple Finite Element (FE) Models (FEM) and Electrical Circuits (EC). This coupling should include enough physics to look justly at the impact of the devices on the electrical system. Since some devices require the full or partial transition of the superconductor to its normal-resistive state, such as fault-current limiters, for instance, their modelling must address the dynamic change that the superconductor experiences moving both ways between its superconducting state and its normal-resistive state. To tackle this challenge, a multiphysics FEM coupled to an EC has been built targeting overcurrent operations of 2G HTS coils, used in such devices. Here, the basis of the approach is the electromotive force to compute the magnetic induction in the coil. The FEM is composed of two coupled submodels, an Electromagnetic one (EFEM) implementing the T-A formulation and a Thermal one (TFEM). The resulting TEFEM is coupled to an Electrical Circuit Model (ECM) in the same FE solver yielding the TEFEM-ECM. To further improve the computation time, a reduction method is employed to skim the ECM, without sacrificing accuracy. The simulation results for the most reduced version of the model are compared with experimental data obtained in liquid nitrogen at 77 K for a current pulse discharge system connected to a 2G HTS coil, showing good agreement.

Superconducting devices offer innovative solutions for the energy transition, with superconducting machines showing promise in applications such as aircraft propulsion and power generation. In this context, the present work compares three configurations of flux-trapped machines that utilize second-generation (2G) high-temperature superconducting (HTS) tapes in the rotor. The prototypes include only one machine with three rotor configurations; one wound with 2 turns of a single 50 mm-wide tape, one with 6 turns of three 12 mm-wide tapes and one with 18 turns of three 12 mm-wide tapes as well. The objective is to assess the performance of each configuration when operating the machine as motor and generator. For the generator tests, the machine was magnetized using high-intensity (up to 100 A) and short-duration (100 ms) direct current pulses supplied to the stator. Following the magnetization, a propulsion motor was coupled to the shaft of the machine, and the induced voltage at the generator's output was measured. Results indicated that the prototype with the 50 mm-wide tape has higher efficiency than the other topologies. However, this configuration did not fully realize its potential due to the limited number of turns, restricted to only two, here. This study provides valuable insights into the impact of 2G HTS rotor configurations on the performance of flux-trapped superconducting hybrid machines (superconducting rotor and conventional stator), both as motors and generators, with a focus on their future applications.

The Gargantua test station is capable of delivering a direct current of 4800 A at a voltage of 10 V. It is designed for acquiring the DC voltage-current characteristic of high-temperature superconducting power cables operating at 77.3 K in liquid nitrogen. The goal is to estimate their critical current. The standardization of this DC characterization is a prerequisite for the adoption of this promising technology by power grid operators. This document reports on the experimental setup and the subsequent measurements carried out on a high-temperature superconducting power cable manufactured by Sumitomo and tested as part of the international round robin test for the IEC Technical Committee 90 Superconductivity.

High temperature superconductors (HTSs) are enablers of extensive electrification for aircraft propulsion. Indeed, if used in electrical machines, HTS materials can drastically improve their performance in terms of the power-to-weight ratio. Among the different topologies of superconducting electrical machines, a flux modulation machine based on HTS bulks is of interest for its compactness and light weight. Such a machine is proposed in the FROST (Flux-barrier Rotating Superconducting Topology) project led by Airbus to develop new technologies as part of their decarbonization goals driven by international policies. The rotor of the machine will house large ring-segment-shaped HTS bulks in order to increase the output power. However, the properties of those bulks are scarcely known and have barely been investigated in the literature. In this context, the present work aims to fill out partially this scarcity within the framework of FROST. Thus, a thorough characterisation of the performances and homogeneity of 11 large REBaCuO bulks was carried out. Ten of the bulks are to be utilized in the machine prototype, originally keeping the eleventh bulk as a spare. A first set of characterisation was conducted on the eleven bulks. For this set, the trapped field mapping and the critical current were estimated. Then, a series of in-depth characterisations on the eleventh bulk followed. It included critical current measurement, X-ray diffraction, and scanning electron microscopy on different millimetre-size samples cut out from the bulk at various locations. The X-ray diffraction and scanning electron microscopy showed weakly oxygenated regions inside the bulk explaining the local drop or loss in superconducting properties. The objective was to determine the causes of the inhomogeneities found in the trapped field measured on all the bulks, sacrificing one of them, here the spare one. To help obtain a clearer picture, a numerical model was then elaborated to reproduce the field map of the eleventh bulk using the experimental data obtained from the characterisation of its various small samples. It is concluded that further characterisations, including the statistics on various bulks, are still needed to understand the underlying reasons for inhomogeneity in the trapped field. Nonetheless, all the bulks presented enough current density to be usable in the construction of the proposed machine.

Nanosatellites have gained great relevance in the aerospace sector since they represent continuous and economic access to space. Therefore, this sector raises the need to guarantee the integrity of the payload through the structural subsystem. To achieve such a guarantee, studies are required through missions focused on the dynamic thermal and mechanical environment in which a nanosatellite operates since the materials from which the components of the various subsystems are manufactured must resist the vibration of the launch vehicles. and the thermal shocks to which it will be exposed in orbit. However, to avoid costly space missions while accessing an environment close to the one encountered by nanosatellites in space, it is attractive to carry out, in the first instance, cheaper tests with suborbital flights using stratospheric balloons. In this context, the present work deals with designing and developing a payload specifically designed for future suborbital tests of nanosatellites. This payload incorporates sensors and electronics to register accelerations, pressures, and temperatures during the suborbital flight. Here, the interest lies in the mechanical and thermal response of the payload structure and in particular the response to accelerations that can be experienced by a CubeSat-type structure during suborbital flight conditions. Hence, as part of the development of the payload, functionality tests under vibration on a shaker and at low temperatures in an ultra-freezer were carried out in the laboratory according to nanosatellite standards. These experiments reproduced the conditions that may occur in a suborbital flight, without considering conditions of a high atmosphere and gusts of wind. The obtained results are useful to determine if the payload meets the functionality requirements as an experimental platform, to be operated in suborbital flight, to test nanosatellites. Once the payload design is validated, it will be mounted on a gondola for an actual suborbital test. In the present work, only the laboratory tests are reported.

High-temperature superconducting coils are used in various large-scale applications, like rotating machines and high-field magnets. However, modeling these coils is a complicated and time-consuming process, especially due to the non-linearity of the current-voltage characteristics of the superconductors and the complex multiphysics involved. In this work, we used a fast homogenized method to model the coupled electromagnetic and electrothermal properties of racetrack and pancake coils for different applications. For this purpose, various formulations wielding homogenization methods are used and benchmarked with each other, as well as with models considering the detailed structure of the HTS tapes. We observe a very good agreement between different models (homogenized and detailed), and we discuss the pros and cons of the inclusion of insulating layers between the turns in homogenization. This work was performed under the collaboration of the COST action modeling teams and can be used as a review of the state-of-the-art superconductor modeling techniques, and a source for the development and benchmark of future numerical methods.

High-temperature superconductors (HTS) are greatly appealing for the development of high efficient, and high energy density power devices. They are particularly relevant for applications requiring light and compact machines such as wind power generation. In this context, to ensure the proper design of the superconducting machines and their reliable operation in power systems, it is then important to develop models that can accurately include their physics but also can describe properly their interaction with the system. To achieve such a goal, one approach is the co-simulation. This numerical technique can bring fine geometrical and physical details of the machines through a finite element model (FEM) meanwhile dealing with the operation of the whole system that incorporates the machine and a subset of the power grid represented by an external electrical circuit. The goal of the present work is to put to use this numerical technique when superconducting components are involved. Here, a case study is proposed involving a 15 MW hybrid superconducting synchronous generator (HTS rotor and conventional stator) coupled to a direct current network via a rectifier and its associated filter. The case study related to wind power application allows grasping the technical issues when employing co-simulation dealing with HTS machines. The FEM of the generator is done in the commercial software COMSOL Multiphysics, which interacts with the circuit simulator Simulink through the built-in Functional Mock-up Unit. For the present study, a new version of the latest J-A formulation combined with homogenization technique is introduced allowing an even faster computation time compared to the T-A formulation. Distributed variables and global variables such as current density, magnetic flux density, and local losses for the former and voltage, current, electromagnetic torque, and power quality for the latter are estimated and compared for both formulations. The idea is to find the best-suited combination FEM-circuit under criteria of computational speed, accuracy, and numerical stability. Thus, it is shown that all formulations generate an error of less than 5% on the machine parameters and that the J-A formulation with first order elements stands out with a significant 4-fold reduction in computational costs.

Ten institutes from six countries participated in an international round-robin test to evaluate the critical current of a superconducting power cable made of Bi-2223 tapes. The cable design featured a two-layer inner core conductor and a single-layer outer shield conductor. The shield layer measured approximately 40 mm in diameter, and the cable length was 2.0 m. To eliminate the influence of resistive voltage drops from current transfer, voltage taps for measurement were positioned at a sufficient distance from the current terminals. The critical current was determined using the resistive method with the electric field criterion of 1.0 mu V/cm}. In addition, the n-value, an optional parameter reflecting the current-voltage (I-V) characteristics, was extracted from the I-V curve within an electric field range of 0.1-1.0 mu V/cm. A detailed uncertainty analysis was conducted for both the critical current and the n-value. Finally, this article discusses the potential for standardization of the employed resistive measurement method.

The AC losses, the current density and the magnetic field are important variables to design devices made of High Temperature Superconductors (HTS). These variables are often computed using a transient finite element analysis even though the interest may lay in the steady-state regime of the device. In this context, the need for solving time-dependent variables has led to improve the computation time with efficient finite element models (FEM) relying on different formulations of the Maxwell equations. Still, due to the time dependence and the highly nonlinear behavior of the superconductor, these transient FEM are computationally slow and, in general, demanding in terms of resources. In the present work, an alternative path is taken with the development of a frequency-domain FEM using a phasor representation to alleviate the computational burden. However, this model does not have the versatility of the transient models; but, it can generate the initial steady-state conditions for a subsequent transient analysis. At least, it is perfectly adapted to investigate the steady-state regime of HTS devices operated in AC conditions. In this phasor modelling approach, the Root Mean Square resistivity of the superconductor is introduced. It is subsequently approximated by an exponential decreasing function depending on the transition index, thus, introducing a factor to ease its implementation in the commercial software COMSOL Multiphysics with the most recent and fastest formulations of the Maxwell equations to this date, i.e. T-A and J-A. The case studies encompass single BSCCO and REBCO tapes as well as a CORC (R) cable, or more specifically, a Conductor on Round Tube. The results of the time- and frequency-domain FEM simulations are cross-checked and compared against experimental data. The comparison of the models' results is carried out comparing the current density distributions as well as the AC losses. The comparison against experimental data is only conducted for the AC losses. In the present case, it is used to quantify thoroughly the accuracy of the numerical results compared to the measurements. A reasonable agreement between those results and the experimental data was found.