超导薄膜和直角棱镜中宏观无力效应的三维模拟
3D modelling of macroscopic force-free effects in superconducting thin films and rectangular prisms
摘要：
当磁场具有平行于电流密度${\bf J}$的分量时，由于磁通切割和交叉，出现无力效应。这导致各向异性的${\bf E}({\bf J})$关系，即${\bf E}$是电场。理解无力效应不仅对于超导电力和磁体应用的设计，而且对于材料表征都是有趣的。这项工作开发和应用一种快速，准确的计算机建模方法的基础上的变分方法，可以处理力自由各向异性${\bf E}({\bf J})$关系，并进行全三维（3D）计算。本文系统地研究了磁场与表面成任意角度$θ$作用下，有限厚度矩形薄膜和棱镜中的无力效应。并与各向同性的${\bf E}({\bf J})$关系进行了比较。薄膜的情况表明，逐渐临界电流密度渗透和磁化强度的大小与角度$θ$的一般增加，但在剩余状态的磁化循环的最小值。棱镜模型呈现了对于所有角度$θ$具有3D弯曲的电流路径。除了最高角度之外，厚度上的平均电流密度与薄膜模型非常一致。棱镜磁滞回线揭示了一个峰值后的剩余状态，这是由于平行分量的自磁场和隐含的薄膜被忽略。所提出的数值方法显示出的能力，考虑到一般的3D情况下，具有高的自由度的力自由的情况。结果揭示了薄膜和棱镜中无力效应的新特征。
英文摘要：
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 $θ$ 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 $θ$ but a minimum at the remnant state of the magnetization loop. The prism model presents current paths with 3D bending for all angles $θ$. 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.
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