Computer simulation of vortex pinning in type II superconductors. I. Two-dimensional simulation

Abstract

The summation of pinning forces to a volume force exerted on the vortex lattice in type II superconductors allowing it to carry a loss-free current is not fully understood. In order to clarify this question we have started computer simulations of flux pinning. It is shown that for many experimental situations bending of vortices may be neglected since the vortices are too short or pinning is too weak, and thus pinning is two-dimensional. As a first step, two-dimensional pinning simulations will thus be instructive with regard to, say, ribbons of amorphous metals. A general expression for the energy of a vortex-pin system in two and three dimensions is given. The simulation method is presented and illustrated for the isolated pin (with a detailed discussion of the “threshold effect” and of elastic instabilities) and for pin “walls” (grain boundaries) and “nozzles.” Random point pins acting on a perfect or defective vortex lattice are treated in an accompanying paper.