In an attempt to unveil the impact of the material law selection on the numerical modelling and analysis of the electromagnetic properties of superconducting coils, in this paper we compare the four most common approaches to the E-J power laws that serve as a modelling tool for the conductivity properties of the second generation of high-temperature superconducting (2G-HTS) tapes. The material laws considered are: (i) the celebrated E-J critical-state like-model, with constant critical current density and no dependence with the magnetic field; (ii) the classical Kim’s model which introduces an isotropic dependence with the environment magnetic field; (iii) a semi-empirical Kim-like model with an orthonormal field dependence, $J_c\left(\mathbf{B}\right)$ , widely used for the modelling of HTS thin films; and (iv) the experimentally measured E–J material law for SuperPower Inc. 2G-HTS tapes, which account for the magneto-angular anisotropy of the in-field critical current density $J_c(\mathbf{B};\theta )$ , with a derived function similar to Kim’s model but taking into account some microstructural parameters, such as the electron mass anisotropy ratio $\left(\gamma \right)$ of the superconducting layer. Particular attention has been given to those physical quantities which within a macroscopic approach can be measured by well-established experimental setups, such as the measurement of the critical current density for each of the turns of the superconducting coil, the resulting distribution of magnetic field, and the curve of hysteretic losses for different amplitudes of an applied alternating transport current at self-field conditions. We demonstrate that although all these superconducting material laws are equally valid from a purely qualitative perspective, the critical state-like model is incapable of predicting the local variation of the critical current density across each of the turns of the superconducting coil, or its non-homogeneous distribution along the width of the superconducting tape. However, depending on the physical quantity of interest and the error tolerance allowed between the numerical predictions and the experimental measurements, in this paper decision criteria are established for different regimes of the applied current, where the suitability of one or another model could be ensured, regardless of whether the actual magneto angular anisotropy properties of the superconducting tape are known.

The Conductor on Rounded Core ( ${\mathrm CORC}$ ) cables manufactured by Advanced Conductor Technologies with current densities beyond 300 Amm $^{-2}$ at 4.2 K, and bending diameter of up to 3.5 cm, are considered as one of the strongest candidates for the next generation of high field power applications and magnets. In this paper, we present a full 3D FEM model for their monolayer and bilayer ${\mathrm CORC}$ cables made with up to three and six superconducting tapes respectively, disclosing the full curve of AC losses for the monolayer cable at magnetic fields beyond 60 mT, and the actual distribution of current density along and across the thickness of the superconducting tapes in both designs. The model is based on the so-called H-formulation, allowing to incorporate the true three-dimensionality of the tapes without recurring to 2D thin-film approaches where non-physical surface currents that do not follow the celebrated Bean’s model for type-II superconductors appear. Likewise, good agreement with the experimentally measured AC-losses for the monolayer and bilayer cable have been obtained, with all the details of the model disclosed in this paper.

The ac losses induced by an alternating transport current in type-II superconductors is a well-known phenomenon, which still attracts much attention because of its intrinsic relevance for the proper development of practical applications. In the case of single core superconducting cables of cylindrical cross-section, it is possible to find exact analytical solutions at self field conditions, and it has been believed for nearly two decades that the use of an ideal soft ferromagnetic sheath with negligible magnetization losses will not affect the electromagnetic properties of the superconducting wire, and on the contrary due to the shielding magnetic properties of the ferromagnet, the total ac losses of the SC wire have to be reduced or as maximum they must be equal to the one for the bare superconductor at self-field conditions, what contraries the experimental evidences that show a non-negligible increase on the ac losses. In this paper, we explain the physical nature of this mysterious increase in the ac losses for rounded superconducting/ferromagnetic heterostrutures, which for the sake of generality, has been solved within the critical state theory, and a magnetic multipolar expansion that enables the direct coupling of the magnetostatic properties of the superconductor and an ideal soft ferromagnet. A significant increase in the transient electric field during excitation period has been observed, which might have utter implications on the adequate selection of insulation materials for superconducting/ferromagnetic heterostructures.

Improving our understanding of the physical coupling between type-II superconductors (SC) and soft ferromagnetic materials (SFM) is the root for progressing to the application of SC-SFM metastructures in scenarios such as magnetic cloaking, magnetic shielding, and power transmission systems. However, in the latter, some intriguing and yet unexplained phenomena occurred, such as a noticeable rise in the SC energy losses, and a local but not isotropic deformation of its magnetic flux density. These phenomena, which are in apparent contradiction with the most fundamental theory of electromagnetism for superconductivity, that is, the critical state theory (CST), have remained unexplained for about 20 years, given the acceptance of the controversial and yet paradigmatic existence of the so-called overcritical current densities. Therefore, aiming to resolve these long-standing problems, we extended the CST by incorporating a semi-analytical model for cylindrical monocore SC-SFM heterostructures, setting the standards for its validation with a variational approach of multipole functionals for the magnetic coupling between Sc and SFM materials. It is accompanied by a comprehensive numerical study for SFM sheaths of arbitrary dimensions and magnetic relative permeabilities ${\mu }_r$, ranging from ${\mu }_r=5$ (NiZn ferrites) to ${\mu }_r$ = 350,000 (pure Iron), showing how the AC-losses of the SC-SFM metastructure radically changes as a function of the SC and the SFM radius for ${\mu }_r\ge 100$. Our numerical technique and simulations also revealed a good qualitative agreement with the magneto optical imaging observations that were questioning the CST validness, proving therefore that the reported phenomena for self-field SC-SFM heterostructures can be understood without including the ansatz of overcritical currents.

Conductor on a rounded core (CORC^®) cables with current densities beyond 300 A/mm^-2 at 4.2 K, and a capacity to retain around 90 % of critical current after bending to a diameter of 3.5 cm, make them a strong candidate for high field power applications and magnets. In this paper, we present a full 3D-FEM model based upon the so-called H-formulation for commercial CORC^® cables manufactured by Advanced Conductor Technologies LLC. The model presented consists of tapes ranging from 1 up to 3 SuperPower 4mm-width tapes in 1 single layer and at multiple pitch angles. By varying the twist pitch, local electromagnetic characteristics such as the current density distribution along the length and width are visualized. Measurements of macroscopical quantities such as AC-losses are disclosed in comparison with available experimental measurements. We particularly focused on the influence of the twist pitch by comparing the efficiency and performance of multiple cables, critically assessing the optimal twist pitch angle.

A noteworthy physical dependence of the hysteresis losses with the axial winding misalignment of superconducting racetrack coils made with commercial second generation high temperature superconducting (2G-HTS) tapes is reported. A comprehensive study on the influence of the turn-to-turn misalignment factor on the local electromagnetic properties of individual turns is presented by considering six different coil arrangements and ten amplitudes for the applied alternating transport current, $I_a$ , together with an experimentally determined function for the magneto-angular anisotropy properties of the critical current density, $J_c(B,\theta )$ , across the superconducting tape. It has been found that for moderate to low applied currents $I_a\le 0.6I_{c0}$ , with $I_{c0}$ the self-field critical current of individual tapes, the resulting hysteretic losses under extreme winding deformations can lead to an increase in the energy losses of up to $25\text{\%}$ the losses generated by a perfectly wound coil. High-level meshing considerations have been applied in order to get a realistic account of the local and global electromagnetic properties of racetrack coils, including a mapping of the flux front dynamics with well defined zones for the occurrence of magnetization currents, transport currents, and flux-free cores, which simultaneously has enabled an adequate resolution for determining the experimental conditions when turn-to-turn misalignments of the order of 20–100 $\mu \mathrm{m}$ in a 20 turns $4\mathrm{mm}$ wide racetrack coil can lead not only to the increment of the AC losses but also to its reduction. In this sense, we have shown that for transport current amplitudes $I_a>0.7I_{c0}$ , a slight reduction in the hysteresis losses can be achieved as a consequence of the winding displacement, which is at the same time connected with the size reduction of the flux-free core at the coil central turns. Our findings can be used as a practical benchmark to determine the relative losses for any 2G-HTS racetrack coil application, unveiling the physical fingerprints that possible coil winding misalignments could infer.