As well known, the time dependent Ginzburg-Landau (G-L) equations are a powerful tool for study on popular characteristics in nonlinear dynamics, especially the dynamics of magnetic vortices in a superconductor close to a critical temperature in a magnetic field.
Constant efforts to improve the critical properties of materials in type-Ⅱ superconductors and apply it into a variety of areas by forming artificial pinning centers are being made. Hence, it is of great importance to study the magnetic vortices in a superconductor with artificial pinning centers using the G-L equations.
In recent years, many works on superconductors with pinning centers and defects distributed in a fixed quantity and different forms have been conducted. However, the dynamic study of the magnetic vortices in a superconductor with randomly distributed pinning centers in a normal state has rarely been reported.
Ryu Yu Gwang, a researcher at the Faculty of Physical Engineering, has reported the simulation results on the dynamic behaviors of the magnetic vortices in the above mentioned superconductor by using the time dependent G-L equations.
COMSOL and MATLAB were combined for the simulation. The time dependent G-L equations were solved numerically using the PDE model of the COMSOL program. The pinning centers were randomly distributed on the whole area of the superconductor. Then a distribution function p(r), which was used to determinate the size and sites of the pinning centers, was defined in a MATLAB and was directly called during the calculating process by the LiveLinkTM for MATLAB in the COMSOL program.
First of all, he analyzed the magnetization curves and the density of superconducting electrons as a function of the external magnetic field along the z-axis.
The simulation result showed that the vortices configurations and magnetization depend on the content of pinning centers and that the maximum magnetization values decrease exponentially as the content increases. The analytic expression of the maximum magnetization values as a function of the content was -4πMmax/HC2≈0.24+0.175exp(-6.14ω). Therefore, it can be defined that the higher content, the more decrease in the diamagnetism of a superconductor.
Next, he determined the content of pinning centers with the largest mixed state by modeling the number of the magnetic vortices trapped in the pinning centers. According to it, the suitable content for trapping more magnetic vortices in a type-Ⅱ superconductor with pinning centers was 20%.
This work will be useful for studying and understanding the dynamics of magnetic vortices in a type-Ⅱ superconductor with randomly distributed pinning centers in view of the circumstance that they are randomly distributed in the superconductor during its fabrication.
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