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

• Center manifold reduction yields periodic solutions.
• We obtain a motion law for kinematic vortices.
• Computational analysis yields anomalous vortex behavior.

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.