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从基本的角度和这些材料的实际应用，了解II型超级导管中涡流的动力学至关重要[1-6]。在II型超导体中，当我们应用大于临界场h C 1大的磁场时，量化通量线（涡旋）会穿透样品。在干净的超导体中，涡流之间的相互作用将它们排列在三角形晶格中，称为Abrikosov [7]涡旋晶格（VL）。ever，固体中不可避免地存在晶体缺陷作为涡旋的随机固定潜力。If these vortices are made to oscillate under the influence of an oscillatory cur- rent or magnetic field, their motion is governed by the follow- ing competing forces [ 8 ]: (a) Lorentz force due to the external current density driving the motion, (b) restoring force due to the combined effect of pinning by crystalline defects and repulsion from neighbouring vortices, and (c) the dissipative viscous drag of the vortices.此外，在有限温度下，热激活会导致涡流自发
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