Reasearch Of Wave Function In The Deformable Superconductors With Weak Magnetic Field

High-temperature superconductors will lead to superconductor deformable in magnetic field or in the case of prestrain, then result in superconductor macroscopic properties of the critical current density, the critical magnetic field, the critical temperature change. In engineering application, superconducting magnets can lead to changes of super current and so on in the influence of external electromagnetic environment factors, which will result in its function or safety operation problems. Therefore, research on superconductivity properties with respect to complex deformation has always been a basic subject which is focused on theory and engineering application in this area. Based on the linearly elastic theory, with the Ginzburg-Landau theory, the wave function of the deformable superconductors in weak magnetic filed is studied. In addition, analytical solutions of the effective wave function and magnetic potential are derived.Firstly, the volume deformation of superconductor is added and the effective free energy expression is amended, joined in the expression of two superconducting energy term for deformation, and a coupling term of the deformation field and the magnetic field.Secondly, using the modified free energy expression, and Lagrange variational principle, the Ginzburg-Landau equations with superconducting deformation are obtained. For simplicity, the effect of superconducting deformation on the order parameters and the electronic quality is neglected.Again, using the special nature of isotropic material, the one-dimensional problem is considered. In a semi-infinite plane of the superconductor, x=0 is the surface of superconductor and along the z direction applied a weak magnetic filed Reference to the relevant literature's methods, dimensionless parameters and markers are used, and further simplify the equations. As in the weak magnetic field, the effective gradient of the wave function relatively smoothly, in the text, approximate zero. Then, the effective wave function and magnetic potential are expanded around the weak magnetic field and take them into the original equations, comparison, combined with boundary conditions and the effective wave function and the magnetic potential are obtained.Finally, the effect of prestrain on the wave function is studied. The results show that, advanced in a weak magnetic field and under the influence of prestrain, the prestrain effects of superconductivity on the two kinds of superconductors are different. Therefore, the superconductivity is influenced not only by the external magnetic field, but also by the superconductor volume deformation.