Molecular + Field Dynamics (MFD) Simulation on Vortex dynamics in a Superconductor

We have developed an extended molecular dynamics simulation method on vortex dynamics including current field and impurity potential. We call it molecular + field dynamics (M+FD). Using this method, we can investigate dynamics of several ten thousand of vortices. In the usual molecular dynamics (MD) method, we must calculate the vortex-vortex interactions between all pairs of vortices and also pinning forces between all of vortices and all of impurities. These calculations take much time, and therefore number of vortices that we can treat is limited. Vortex-vortex interaction comes from current around every vortex. So, if we can calculate current distribution from all of vortices including an external current, we can obtain vortex-vortex interaction for a single vortex from all other vortices locally. We also use the FEM for computation of pinning force form an impurity potential. In our M+FD method, we sue the finite element method (FEM) to treat the current distribution. Our method is useful for investigation of phenomena that include many vortices, such as bundle motion of vortices and avalanche behavior of vortices.

We show how vortex bundle motion appears, using this method.