The time-dependent Ginzburg-Landau (TDGL) equations are a useful computational tool for characterizing the spatiotemporal variance of an order parameter that represents the phase transition in mesoscopic type-II superconductors. Especially, they are used to simulate the dynamics of magnetic vortex for designing superconducting materials with high critical current density.
Therefore, simulation of type-II superconductors using TDGL equations is essential for understanding magnetic vortex dynamics and studying superconducting critical characters such as critical current density and critical magnetic field. Numerical simulations for it are conducted by the finite difference method (FDM), the finite element method (FEM), the lattice Boltzmann method (LBM), etc.
Ryu Yu Gwang, a researcher at the Faculty of Physical Engineering, has investigated the influences of surface defects on the motion of magnetic vortices in a mesoscopic type-II superconductor with randomly distributed pinning centers through the simulations of TDGL equations by using COMSOL Multiphysics.
Two kinds of surface defects are located in the boundary: one is pinning centers and the other is geometric defects along with pinning centers.
In the simulation, he analyzed the magnetization curves, the vorticity and the density of superconducting electrons for both different contents of pinning centers and various geometric defects.
For the pinning centers as surface defects, the maximum magnetization values as a function of the contents exponentially decrease, and the field where the first vortex penetrates and the field where the complete transition from superconducting to a normal state in the system occurs are reduced.
For the geometric defects as surface defects, the density of superconducting electrons and the magnetization curves depend on their size and form. In addition, a threshold in the size of geometric defects in which the motion of vortices and vorticity change, exists.
You can find the details in his paper “The Influence of Surface Defects on Motion of Magnetic Vortices in Mesoscopic Type-II Superconductor with Randomly Distributed Pinning Centers” in “Journal of Superconductivity and Novel Magnetism” (SCI).
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