Investigating the effect of the density of vortices at the first matching field on the critical current density

Molecular dynamic simulations were carried out to investigate the properties of the critical current density in high temperature superconductors at several vortex densities at the first matching field. The study was conducted on samples with periodic square arrays of vortices and pinning sites. The variables in the simulations were the vortex density, the pinning sites density, the temperature, the pinning strength, the size of pinning sites. At low temperatures and for all first-matching fields, the critical current density was found to increase linearly with increasing the pinning strength for any size of pinning sites. Also at low temperatures, the critical current density was found to increase linearly with increasing the size of pinning sites for any value of the pinning strength. As the temperature increases, the role of the size and strength of pinning sites on the critical current density diminishes.