How to Choose the Superconducting Material Law for the Modelling of 2G-HTS Coils

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, J c ( B ) , 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 ( B ; θ ) , with a derived function similar to Kim’s model but taking into account some microstructural parameters, such as the electron mass anisotropy ratio ( γ ) 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.

Electromagnetic properties of curved HTS trapped field stacks under high-frequency cross fields for high-speed rotating machines

“…Four different material law models have been systematically compared in [44], including (7) and (10). It is concluded that when at a low transport current (below 0.4 Ic0), the magnetization losses obtained by (7) and (10) are almost the same.…”

Computational Modelling of Russia's First 2G-HTS Triaxial Cable

“…In Figure 1, it is to be noted that the thickness of the superconducting layer within the SuperOx tape has been increased by a factor of 50. This allows to overcome the numerical difficulties that can be caused by the large aspect ratio of the 2G-HTS tapes, whilst maintaining the integrability of the physical quantities by renormalizing the critical current density J c as it is customarily done in the numerical modelling of 2G-HTS tapes [22,23,29]. Likewise, as none of the other layers composing the SuperOx tapes are known to be magnetic nor carry any of the transport current which is to flow only on the superconducting layer, these can be assumed to have the same electrically insulating and non-magnetic properties of the so-called "air" domain, what allows to neglect also the occurrence of eddy currents.…”

“…Thus, in this paper we present the numerical estimation of the AC-losses produced by the first Russian triaxial 4 m ReBCO cable prototype, by the means of a detailed 2D model based on the so-called H-formulation previously used by our group and other researchers in other geometries [20][21][22][23][24][25][26]. The triaxial cable contains 87 SuperOx 4 mm width tapes with all their physical properties and dimensions being reported in [27,28].…”

Critical State Theory for the Magnetic Coupling between Soft Ferromagnetic Materials and Type-II Superconductors

“…However, it is precisely for this geometry where a certain amount of magnetic field has been observed in regions where no transport current is expected to flow, at least under the classical conception of the CST regime for a bare SC at self-field conditions. A significant rise and drop of the local magnetic field within the SC core near the surface of the SFM sheath has also been observed [ 41 ], both of these features being in apparent disagreement with the CST, despite its largely recognized success for all known type-II superconductors [ 10 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 ].…”