Time Domain Analysis on Magnetic Shielding Performance of YBCO Superconductor

在高温超导体（HTS）的工业应用中，磁悬浮和磁屏蔽是近年来最有前途的两个方面。由于屏蔽电流密度的定量评估对于磁悬浮系统和磁屏蔽设备的发展是必不可少的，因此迄今为止已经提出了各种方法来计算屏蔽电流密度的时间演变。然而，在所有的方法中，有限元法（FEM）一直被用于离散的控制方程，尽管相当方便，有限元法一直困扰着两个固有的困难。首先，在使用有限元程序之前，必须将区域划分为一组有限元单元。一般来说，单元生成甚至比有限元方程的装配和求解更耗时。其次，有限元法得到的解在光滑性方面有一定的局限性。即使解决方案是 ...更多信息 的连续性，其导数在单元边界上可能是不连续的。在屏蔽电流密度的数值模拟中，由于这种有限的正则性，导致了电场的不连续，为了解决上述问题，人们提出了几种无网格方法：DE法、EFG法和MLPG法。由于所有方法不再需要几何结构的有限元，因此数据准备工作大大简化，通过使用无单元Galerkin方法，我们开发了三维代码来集成HTS板中屏蔽电流密度的控制方程。利用该程序计算了屏蔽电流密度随时间的变化规律，并对磁场强度进行了频谱分析。结果表明：（1）在考虑流阻和临界电流密度的B依赖性的情况下，随着外加磁场幅值的增大，磁通密度的三次谐波被迅速激发;（2）在不考虑流阻和临界电流密度的B依赖性的情况下，外加磁场的增大会削弱三次谐波，由此可以得出结论：三次谐波的快速增长与流阻和临界电流密度的B依赖性密切相关。少

Among the industrial applications of the high-Tc superconductor (HTS), the magnetic levitation and the magnetic shielding have recently become promising. Since the quantitative evaluation of the shielding current density is indispensable for the development of the magnetic levitation system and the magnetic shielding apparatus, the various methods have been so far proposed for calculating the time evolution of the shielding current density. However, in all of the methods, the finite element method (FEM) has been employed for the discretization of the governing equations.In spite of the quite convenience, the FEM has been plagued by two inherent difficulties. First of all, the region has to be divided into a set of finite elements before using the FEM program. In general, the element generation is even more time-consuming than the assembly and the solution of the finite element equations. Second, the solution obtained by the FEM has a limitation in its smoothness. Even if the solution i … More s continuous, its derivative might be discontinuous across the element boundary. In the numerical simulation of the shielding current density, such a limited regularity of the solution leads to the discontinuous electric fields.In order to resolve the above difficulties, several meshless approaches have been proposed : the DE method, the EFG method and the MLPG method. Since the finite elements of a geometrical structure are no longer necessary for all of the methods, the data preparation is significantly simplified.By using the element-free Galerkin method, we have developed the 3D code to integrate the governing equations of the shielding current density in the HTS plate. After calculating the time evolution of the shielding current density by use of the code, we have performed the spectral analysis of the magnetic flux density. Conclusions obtained in the present study are summarized as follows :1) For the case where the B-dependence of the flow resistivity and the critical current density is taken into account, the third harmonics of the magnetic flux density are rapidly excited with an increase in the amplitude of the applied ac magnetic field.2) For the case where their B-dependence is neglected, an increase in the applied magnetic flux density will weaken the third harmonics.From the above results, we might conclude that the rapid growth of the third harmonics is closely related to the B-dependence of the flow resistivity and the critical current density. Less