Abstract
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, , 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 , with a derived function similar to Kim’s model but taking into account some microstructural parameters, such as the electron mass anisotropy ratio 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.
Highlights
In recent years, advances in the development of high-temperature superconducting coils with rare-earth barium-copper oxide (REBCO)-coated conductors have drawn significant attention by the community of researchers in applied superconductivity, thanks to the vast progress in the technology of thin films that has enabled the fabrication of the second generation of high-temperature superconducting (2G-HTS) tapes in the past decade
Multiple publications have already reported that the electrical properties of the large majority of 2G-HTS tapes can be strongly influenced by the intensity and direction of externally and self-induced applied magnetic fields [20,21,22], no strong agreement has been reached in terms of the material law that governs their critical current density properties, as widely different material laws can render similar results depending on the physical quantity being studied [22,23,24]
By assuming that the superconducting coil former lies on the zx −plane, the 2D axial symmetry commonly assumed for the modelling of long superconducting racetrack coils implies that, the components of the magnetic field inside each of the turns of the superconducting coil must lie on the “xy−plane”, [Hx, Hy ], orthonormal to the direction of the flux of current density, Jz, and with the vector of electric field pointing towards the same direction, with the E-J power law in Equation (1)
Summary
Advances in the development of high-temperature superconducting coils with rare-earth barium-copper oxide (REBCO)-coated conductors have drawn significant attention by the community of researchers in applied superconductivity, thanks to the vast progress in the technology of thin films that has enabled the fabrication of the second generation of high-temperature superconducting (2G-HTS) tapes in the past decade. Multiple publications have already reported that the electrical properties of the large majority of 2G-HTS tapes can be strongly influenced by the intensity and direction of externally and self-induced applied magnetic fields [20,21,22], no strong agreement has been reached in terms of the material law that governs their critical current density properties, as widely different material laws can render similar results depending on the physical quantity being studied [22,23,24]
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