Confirmation of the Modified Bean Model from Simulations of Superconducting Vortices

Abstract

From a very simple description of vortices and pinning centers and without using any electrodynamical assumptions, we obtain nonlinear density profiles of vortices in type-II dirty superconductors that result from raising or lowering an external magnetic field. The results confirm a modified Bean model description of these systems, and in particular, follow the Kim empirical form that relates the current inside the material to the local magnetic field. We also obtain realistic magnetization hysteresis loops and examine the discrete evolution of the density profiles in our systems. This evolution is not continuous, but takes place by the occurrence of avalanches of vortices promoted by the addition or extraction of vortices from the edges of the system.