第二类超导材料力学变形下磁通与涡旋特性分析

发布时间：2018-04-05 02:01

本文选题：第二类超导材料　切入点：力学变形　出处：《兰州大学》2015年硕士论文

【摘要】：超导材料在临界磁场,临界温度与临界电流密度确定的四面体参数空间内表现出零电阻与迈斯纳效应这一优越特性,使其具有极其广泛而重要的工程应用与前景。然而,超导材料往往工作于低温与电磁场环境并伴随体积的变化与不可避免的力学变形。已有研究结果表明超导材料的力学变形会对其超导特性产生显著影响,诸如临界电流、临界温度的改变等。本文采用time-dependent Ginzburg-Landau (TDGL)理论研究了外加均匀磁场中第二类超导材料力学变形下的超导磁学性能,考察了超导材料内部的磁通与涡旋特性和行为。基于混合变分原理,以序参量Ψ(或共轭Ψ*)、磁矢势A与位移u为独立变量,获得了第二类超导材料考虑变形影响的基本控制方程与边界条件；进一步运用有限元数值计算模型分析了第二类超导材料的磁通与涡旋特性与行为。首先,针对半无限大超导结构运用有限元数值方法求解非线性耦合TDGL方程,讨论了线弹性变形与外加均匀磁场对序参量Ψ、总能量的影响。研究结果表明：预应变与外加磁场对可变形超导材料的超导特性与能量均有较为显著的影响。其次,针对磁场中受约束情形的可变形无限长超导材料开展了数值研究,考虑了TDGL方程与弹性变形场的耦合,详细讨论了不同磁场下超导能、磁能、弹性变形能、超导-磁场相互作用能、超导-弹性场相互作用能与总能量密度的变化规律,给出了耦合系数对序参量、磁矢势、应变与能量影响结果。研究表明：在可变形超导材料中,超导冷凝态与晶格变形之间的相互作用不可忽略；序参量随外加均匀磁场的增强而减小,应变随磁场的增强而增大；耦合效应对序参量、磁矢势和系统能量密度均有一定影响。最后,开展了带孔超导二维薄板结构磁通涡旋动力学研究,给出超导薄板变形与孔洞附近应力集中对超导特性与涡旋动力学行为影响。结果表明：预应力和超导材料内部的应力集中对涡旋分布、涡旋动态与序参量有非常重要的影响；椭圆孔长短半轴比的变化不仅影响涡旋数目而且影响涡旋的稳态构型。
[Abstract]:In the tetrahedron parameter space determined by critical magnetic field, critical temperature and critical current density, superconducting materials exhibit the excellent characteristics of zero resistance and Meissner effect, which make them have extremely wide and important engineering applications and prospects.However, superconducting materials often work in low temperature and electromagnetic field environment, accompanied by volume changes and inevitable mechanical deformation.The results show that the mechanical deformation of superconducting materials has a significant effect on their superconducting properties, such as the critical current, the change of critical temperature, and so on.In this paper, the superconducting magnetic properties of the second kind of superconducting materials under mechanical deformation in an applied uniform magnetic field are studied by using time-dependent Ginzburg-Landau theory. The flux and vortex characteristics and behavior of the superconducting materials are investigated.Based on the mixed variational principle, the basic governing equations and boundary conditions of superconducting materials of the second kind considering deformation are obtained by taking order parameter 蠄 (or conjugate 蠄), magnetic vector potential A and displacement u as independent variables.The magnetic flux and vortex characteristics and behavior of the second type superconducting materials are analyzed by using the finite element numerical model.Firstly, the nonlinear coupled TDGL equation is solved by finite element method for semi-infinite superconducting structures. The effects of linear elastic deformation and applied uniform magnetic field on the order parameter 蠄 and total energy are discussed.The results show that both prestrain and applied magnetic field have significant effects on the superconducting properties and energy of deformable superconducting materials.Secondly, the deformable infinitely long superconducting materials in the magnetic field are studied numerically. The coupling between the TDGL equation and the elastic deformation field is considered, and the superconducting energy, magnetic energy and elastic deformation energy under different magnetic fields are discussed in detail.The interaction energy of superconducting magnetic field, the interaction energy of superconducting and elastic field and the total energy density are changed. The effects of coupling coefficient on order parameter, magnetic vector potential, strain and energy are given.The results show that the interaction between superconducting condensate state and lattice deformation can not be ignored in deformable superconducting materials, the order parameter decreases with the increase of the applied uniform magnetic field, the strain increases with the increase of the magnetic field, and the coupling effect is related to the order parameter.Both the magnetic vector potential and the energy density of the system have certain effects.Finally, the magnetic flux vortex dynamics of two-dimensional thin plate with holes is studied, and the effects of deformation and stress concentration near the hole on the superconducting characteristics and vortex dynamics are given.The results show that the stress concentration in prestressing and superconducting materials has a very important effect on the vortex distribution, vortex dynamics and order parameters, and the variation of the ratio of long and long axis of elliptical holes not only affects the number of vortices, but also affects the steady configuration of vortices.
【学位授予单位】：兰州大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TM26

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