Robert Bright Chimezie, Fareed Muhammad Umar, Ruiz Harold Steven
Department of Engineering and Leicester, Institute for Space & Earth Observation Science, University of Leicester, Leicester LE17RH, UK.
Materials (Basel). 2019 Aug 22;12(17):2679. doi: 10.3390/ma12172679.
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.
为了揭示材料定律选择对超导线圈电磁特性数值建模与分析的影响，本文比较了四种最常用的E-J幂律方法，这些方法用作第二代高温超导（2G-HTS）带材电导率特性的建模工具。所考虑的材料定律有：（i）著名的类E-J临界态模型，具有恒定的临界电流密度且与磁场无关；（ii）经典的金氏模型，该模型引入了与环境磁场的各向同性依赖关系；（iii）一种具有正交场依赖关系Jc(B)的半经验类金氏模型，广泛用于高温超导薄膜的建模；（iv）SuperPower公司2G-HTS带材的实验测量E-J材料定律，该定律考虑了场中临界电流密度Jc(B;θ)的磁角各向异性，其推导函数类似于金氏模型，但考虑了一些微观结构参数，如超导层的电子质量各向异性比(γ)。对于那些在宏观方法中可以通过成熟实验装置测量的物理量，我们给予了特别关注，例如超导线圈各匝的临界电流密度测量、由此产生的磁场分布以及在自场条件下不同幅值的外加交流传输电流时的磁滞损耗曲线。我们证明，尽管从纯定性的角度来看，所有这些超导材料定律都是同样有效的，但类临界态模型无法预测超导线圈各匝临界电流密度的局部变化，也无法预测其沿超导带宽度的非均匀分布。然而，根据感兴趣的物理量以及数值预测与实验测量之间允许的误差容限，本文针对不同的外加电流范围建立了决策标准，无论超导带材的实际磁角各向异性特性是否已知，都可以确保一种或另一种模型的适用性。
