We apply time-dependent Ginzburg-Landau (TDGL) numerical simulations to study the finite frequency electrodynamics of superconductors subjected to an intense rf magnetic field. Much recent TDGL work has focused on spatially uniform external magnetic fields and largely ignores the Meissner state screening response of the superconductor. In this paper, we solve the TGDL equations for a spatially nonuniform magnetic field created by a point magnetic dipole in the vicinity of a semi-infinite superconductor. A two-domain simulation is performed to accurately capture the effect of the inhomogeneous applied fields and the resulting screening currents. The creation and dynamics of vortex semiloops penetrating deep into the superconductor domain are observed and studied, and the resulting third-harmonic nonlinear response of the sample is calculated. The effect of pointlike defects on vortex semi-loop behavior is also studied. This simulation method will assist our understanding of the limits of superconducting response to intense rf magnetic fields.

中文翻译：

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基于时间的Ginzburg-Landau超导体中rF磁涡旋的处理：空间非均匀磁场中的涡旋半环

我们应用时变的Ginzburg-Landau（TDGL）数值模拟来研究超导体在强射频磁场下的有限频率电动力学。TDGL最近的许多工作都集中在空间均匀的外部磁场上，并且很大程度上忽略了超导体的Meissner状态屏蔽响应。在本文中，我们求解了空间不均匀磁场的TGDL方程由半无限超导体附近的点磁偶极子产生。进行两域仿真以准确捕获不均匀施加场的影响以及产生的屏蔽电流。观察并研究了深入超导体域的涡旋半环的产生和动力学，并计算了所得样品的三次谐波非线性响应。还研究了点状缺陷对涡旋半环行为的影响。这种模拟方法将有助于我们了解对强射频磁场的超导响应的极限。