A numerical study of vortex interactions for high- kappa superconductors

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Abstract
The repulsive Lorentz force between two vortices in high- kappa superconductors with the vortices aligned along the direction of axial symmetry was calculated by approximating the numerical integral by a set of polynomials to speed up the computations. Calculations were carried out to simulate formation of hexagonal vortex lattice from a population of 400 initially randomly distributed vortices. Small domains with different alignments of vortices were found at the early stages, and a single large domain with hexagonal order aligned with the edges emerged at the end. Also, the expansion of a vortex population was simulated and it kept its initial shape while it expanded isotopically outward into a larger area. The force exerted on a displaced vortex in an otherwise perfect lattice was calculated and it was found to be about the same order of magnitude as the force between two isolated vortices, and about ten times stronger than the force exerted on an extra interstitial vortex.