Kinematic and dynamic vortices in a thin film driven by an applied current and magnetic field

TL;DR

This paper develops a bifurcation theory for vortex behavior in a thin film superconductor under current and magnetic field, revealing vortex motion laws and coexistence phenomena.

Contribution

It introduces a rigorous bifurcation framework for vortex dynamics in thin films using a Ginzburg-Landau model, including vortex motion laws and coexistence analysis.

Findings

Derivation of vortex motion laws along the center line.

Identification of coexisting kinematic and magnetic vortices.

Numerical simulations showing periodic vortex evolution.

Abstract

Using a Ginzburg-Landau model, we study the vortex behavior of a rectangular thin film superconductor subjected to an applied current fed into a portion of the sides and an applied magnetic field directed orthogonal to the film. Through a center manifold reduction we develop a rigorous bifurcation theory for the appearance of periodic solutions in certain parameter regimes near the normal state. The leading order dynamics yield in particular a motion law for kinematic vortices moving up and down the center line of the sample. We also present computations that reveal the co-existence and periodic evolution of kinematic and magnetic vortices.