The magnetic flux dynamics of type-II superconductors within the critical state regime is posed in a generalized framework by using a variational theory supported by well-established physical principles. The equivalence between the variational statement and more conventional treatments based on the solution of the differential Maxwell equations together with appropriate conductivity laws is shown. Advantages of the variational method are emphasized, focusing on its numerical performance that allows us to explore a number of physical scenarios. In particular, we present the extension of the so-called double critical state model to three-dimensional (3D) configurations in which only flux transport ($T$ states), cutting ($C$ states), or both mechanisms ($CT$ states) occur. The theory is applied to several problems. First, we show the features of the transition from $T$ to $CT$ states. Second, we give a generalized expression for the flux cutting threshold in 3D and show its relevance in the slab geometry. In addition, several models that allow us to treat flux depinning and cutting mechanisms are compared. Finally, the longitudinal transport problem (current is applied parallel to the external magnetic field) is analyzed both under $T$ and $CT$ conditions. The complex interaction between shielding and transport is solved.

The crossed-magnetic-field effect on the demagnetization factor of stacked second generation (2G) high temperature superconducting tapes is presented. The superconducting sample was initially magnetized along the c-axis by the field cooling magnetization method and after achieving the magnetic relaxation of the sample, an extensive set of experimental measurements for different amplitudes of an applied ac magnetic field parallel to the ab-plane was performed. On the one hand, a striking reduction of the demagnetization factor compared with the reported values for superconducting bulks is reported. On the other hand, the demagnetization factor increases linearly with the amplitude of the ac transverse magnetic field confirming the universal linear behavior for the magnetic susceptibility predicted by Brandt [Phys. Rev. B 54, 4246 (1996)]. The study has been also pursued at different frequencies of the ac transverse magnetic field in order to determine the influence of this parameter on the demagnetization factor measurements. We report an even lower demagnetization factor as long as the frequency of the transverse magnetic field increases. Thus, the significant reduction on the demagnetization factor that we have found by using stacked 2G-superconducting tapes, with higher mechanical strength compared with the one of superconducting bulks, makes to this configuration a highly attractive candidate for the future development of more efficient high-power density rotating machines and strong magnet applications.

In recent years, major industrialized countries have begun to be concerned about the need for developing strategies on the integration and protection of the growing power capacity of renewable source energies, attracting back their interest on the development and understanding of superconducting fault current limiters (SFCLs). The reasons for this are simple: An SFCL may offer a rapid, reliable, and effective current limitation, with zero impedance during normal operation, and an automatic recovery after the fault. Nowadays, most of the R&D projects have turned toward the study of resistive-type SFCLs due to their potential to be small and the likely decrease in price of 2G coated conductors. Thus, in this paper, we provide an updated review on the state of the art of resistive-type SFCLs, emphasizing on the different approaches for the numerical modeling of their local physical properties, as well as on the already-tested experimental concepts. Comparison between the properties and characteristics of different resistive-type SFCLs using different superconducting materials is presented.

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.