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

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