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 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.

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.

Remarkable features on the magnetic moment of type-II superconducting (SC) wires of cylindrical shape, subjected to direct current conditions (DC) and transverse oscillating (AC) magnetic fields, are reported. We show how for relatively low amplitudes of the applied magnetic field, B _a , the superconducting wire rapidly develops a saturation state, ∣ M p ∣ , characterizing the limits of magnetization loops that exhibit a Boolean-like behaviour. Regardless of the premagnetization state of the SC wire, we show how after two cycles of magnetic relaxation, boolean-like ± M _p states can be measured during the entire period of time from which the external magnetic field B ₀ ranges from 0 to ± B _a , with the signs rule defined by the sign of the slope Δ B _{0 y} ( t ). In addition, for the practical implementation of SC DC wires sharing the right of way with AC lines, we report that for relatively low values of magnetic field, B a ≤ B P / 2 , being B _P the analytical value for the full penetration field in absence of transport current, I _tr , the use of semi-analytical approaches for the calculation of AC losses leads to a significant underestimation of the actual contribution of the induction losses. This phenomena is particularly relevant at dimensionless fields b a < 1 − i a 2 / 3 , being b _a = B _a / B _P and, i _a = I _a / I _c the amplitude of an AC or DC transport current, due to the local motion of flux front profiles being dominated by the occurrence of transport current. On the other hand, we have found that regardless of the nature of the transport current, either be DC or AC, when a transverse oscillating magnetic field greater than the classical limit b _a = (1 − i _a ) is applied to the SC wire, the difference between the obtained AC losses in both situations results to be negligible indistinctly of the approach used, semi-analytical or numerical. Thus, the actual limits from which the estimation of the AC losses can be used as an asset for the deployment of DC SC wires sharing the right of way with AC lines, against the sole use of SC wires for the transmission of AC transport current, are established.

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.

In this paper, a comprehensive analysis on the local electrodynamics at micron level for the second generation of magnetically anisotropic high temperature superconducting (2G-HTS) pancake coils is presented. Special attention has been paid to the influence of prospective winding misalignment factors onto macroscopical quantities such as the hysteresis losses and critical current density inside each one of the turns of a generic 2G-HTS coil, and their relation with the magneto-angular dependence of the infield critical current density $J_{c}(B,\theta)$ of the 2G-HTS tape. It has been shown that for low amplitudes of the applied transport current, $I_{a}~\leq~0.2~I_{c0}$, the flux-front profile for perfectly aligned pancake coils develops a well-shaped flux-free core with a complete absence of magnetization currents in $\sim~30\%$ the middle turns, that are enclosed by transport current profiles in similar fashion to what would be observed in superconducting bulks, but with the outer turns showing a clear dominance of magnetization currents. However, the misaligned pancake coils show a notorious deflection of the flux-front semi-elliptical vertices which induces a repositioning of the co-vertices, shaping then a ``worm-like'' flux-front profile that is caused by the breakdown in the ordinal symmetry of the mutual inductances. This phenomenon leads to an increment in the Lorentz force between the transport and magnetization currents, what causes an additional source of hysteretic losses which cannot be accounted by classical changes in the size of the flux-front profile. Thus, we have obtained that for relatively large deformations of the pancake coil, up to a $19\%$ increment in the AC losses can be achieved for moderate to low intensities of $I_{a}$, whilst for currents greater than $0.7~I_{c0}$, a striking although low reduction on the AC losses can be achieved, whose main physical signature has been connected to the actual disappearance of the flux-free core inside the superconducting coil.