标题： 超导薄片和矩形棱柱中宏观无力效应的三维建模 显示英文标题

标题： 3D modelling of macroscopic force-free effects in superconducting thin films and rectangular prisms

摘要： 当磁场具有与电流密度${\bf J}$平行的分量时，由于通量切割和交叉会出现无力效应。 这导致各向异性${\bf E}({\bf J})$的关系，其中${\bf E}$是电场。 理解无力效应不仅对超导电力和磁体应用的设计感兴趣，也对材料表征感兴趣。 这项工作开发并应用了一种基于变分方法的快速且准确的计算机建模方法，可以处理无力各向异性${\bf E}({\bf J})$的关系，并进行完全三维（3D）计算。 我们系统地研究了在施加磁场以任意角度$\theta$与表面相交的情况下，矩形薄片和棱柱在几种有限厚度下的无力效应。 结果与各向同性${\bf E}({\bf J})$的情况进行了比较。 薄片情况显示临界电流密度逐渐渗透，并且磁化强度的大小随角度$\theta$增加，但在磁化回路的剩余状态有一个最小值。 棱柱模型为所有角度展示了具有3D弯曲的电流路径 $\theta$。 厚度上的平均电流密度与薄膜模型非常吻合，除了最高角度外。 棱柱磁滞回线在剩余状态后显示出一个峰值，这是由于自磁场的平行分量引起的，并且在薄膜中被隐式忽略。 所提出的数值方法显示了在具有大量自由度的一般3D情况下考虑无力情况的能力。 结果揭示了薄膜和棱柱中无力效应的新特性。 显示英文摘要

摘要： When the magnetic field has a parallel component to the current density ${\bf J}$ there appear force-free effects due to flux cutting and crossing. This results in an anisotropic ${\bf E}({\bf J})$ relation, being ${\bf E}$ the electric field. Understanding force-free effects is interesting not only for the design of superconducting power and magnet applications but also for material characterization. This work develops and applies a fast and accurate computer modeling method based on a variational approach that can handle force-free anisotropic ${\bf E}({\bf J})$ relations and perform fully three dimensional (3D) calculations. We present a systematic study of force-free effects in rectangular thin films and prisms with several finite thicknesses under applied magnetic fields with arbitrary angle $\theta$ with the surface. The results are compared with the same situation with isotropic ${\bf E}({\bf J})$ relation. The thin film situation shows gradual critical current density penetration and a general increase of the magnitude of the magnetization with the angle $\theta$ but a minimum at the remnant state of the magnetization loop. The prism model presents current paths with 3D bending for all angles $\theta$. The average current density over the thickness agrees very well with the thin film model except for the highest angles. The prism hysteresis loops reveal a peak after the remnant state, which is due to the parallel component of the self-magnetic-field and is implicitly neglected for thin films. The presented numerical method shows the capability to take force-free situations into account for general 3D situations with a high number of degrees of freedom. The results reveal new features of force-free effects in thin films and prisms.