Size effect of randomly distributed pinning centers on magnetic vortices motion in type-II superconductor

We consider the size effect of randomly distributed pinning centers on magnetic vortices motion in a mesoscopic type-II superconductor in the present of magnetic field using the time-dependent Ginzburg-Landau (TDGL) equations. The pinning centers distributed randomly in various contents in the system are characterized by a distribution function p(r) which fixes the size and positions of them. We investigate the magnetization curves and the magnetic induction as a function of the external magnetic field along the z-axis. In addition, the density of superconducting electrons and the maximum magnetization values for various sizes of the pinning centers is considered. The size of the pinning centers obviously affects the dynamics of the magnetic vortices in the superconductor. The numerical simulations show that Magnetization values and the stable vortex configuration depend on not only content but also size of the pinning centers. The smaller size R (or w) by which the shape of them is characterized results in an increase (or decrease) of both the lower critical magnetic field H1 and the maximum magnetization value. The present work will show good results into understanding and studying the size effect of pinning centers on dynamics of the magnetic vortices in a mesoscopic type-II superconductor.