Local electromagnetic properties and hysteresis losses in uniformly and non-uniformly wound superconducting racetrack coils

Abstract

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 magnetoangular anisotropy properties of the critical current density, J c (B, θ), across the superconducting tape. It has been found that for moderate to low applied currents I a ≤ 0.6 I 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% 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, what simultaneously has enabled an adequate resolution for determining the experimental conditions when turn-to-turn misalignments of the order of 20 µm-100 µm in a 20 turns 4 mm wide racetrack coil can lead not only to the increment of the AC losses but also to its reduction.In this sense, we shown that for transport current amplitudes I a > 0.7 I 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.

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

“…It is worth mentioning that a full analysis of the time dynamics of flux front profiles inside the HTS domains under the RM model (excluding the CM, KM1 and KM2 models) has already been presented elsewhere [27], where equivalent high meshing considerations were applied in order to obtain a realistic account of the local and global electromagnetic properties of racetrack coils, and where well-defined regions with clear patterns obeying the occurrence of magnetisation currents, transport currents, and flux-free cores can be envisaged for the whole hysteretic behaviour of the racetrack coil with applied transport currents Itr=Iaprefixsin(ωt), of amplitudes ranging between Ia=0.1Ic0 and the self-field threshold value Ia=Ic0. Thus, as the main physical features encountered in the evolution of the flux front profiles for the different material law models have been found to be essentially the same as those reported in [27], for the sake of simplicity, here we display the profiles of current density for only moderate and high applied currents, Itr=Iaprefixsin(ωt), with amplitudes Ia=0.5Ic0 and Ia…”

“…This means that the physical mechanism leading to the flux creep in the coil turns during the low-current regime is mainly the linear consumption of the magnetisation currents caused by the global condition of transport current, but that at the same time and from local dynamics, it shows that the amount of resulting magnetisation currents inside of each of the coil turns remains nearly the same for all of them. On the other hand, two different phenomena can be recognised for the so-called moderate-intensity regime (0.4Ic0≲Itr≲0.8Ic0) [27]. Firstly, the field By/BCM rapidly increases up to a maximum value, at which the relatively spatial balance between the magnetisation currents and the transport currents (per turn of the coil) cannot be maintained.…”

“…In this sense, the simulation of the electromagnetic behaviour of 2G-HTS coils presents serious challenges, especially in conditions where one needs to consider the in-field dependence of the critical current, Ic, this in terms of the direction and intensity of the magnetic field per coil-turn, as pointed out in early experiments measuring the magnetic field distribution and AC loss of HTS thin films in superconducting coils [25,26]. Nonetheless, regardless of the 2G-HTS tape being used, certain consensus has been reached in terms of describing the current-voltage characteristics of all type-II superconductors as a power law, V(I/Ic)n, with n≫1, which from the computational point of view renders the well-known form of the material law for the electric field, also called the E-J power law, boldE(J)=E0·boldJ/Jc·(|J|/Jc)n−1, which in a local but macroscopical approach allows solution of the Maxwell equations inside the superconducting domains within diverse mathematical formulations, for a large range of experimental measurements [16,23,27,28,29,30,31,32,33,34,35,36,37,38]. Here, Jc is the critical current density of the 2G-HTS tape defined within the standard electric field criterion E0 = 1 …”

“…Thus, for this Special Issue of MDPI’s Materials , we present a comprehensive study of the impact of the E-J material law selection on the electromagnetic properties of superconducting racetrack coils, using the H-formulation as a benchmark [27,28] for solving the partial differential equation (PDE) system of Maxwell equations and the four most popular material law models for type-II superconductors, namely: (i) a simplified critical state (CS)-like-model [23,39]; (ii) the classical Kim’s model [40,41]; (iii) an empirical Kim-like model with orthonormal field dependence for SuperPower Inc. [42] SCS4050 2G-HTS tapes [33]; and (iv) the generalised form of the critical current density with magneto angular anisotropy measured on the SCS4050 tapes [20]. The paper is organised as follows.…”

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

“…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].…”