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By using the full 3D generalized time dependent Ginzbug-Landau equation westudy a long superconducting film of finite width and thickness under anapplied transport current. We show that, for sufficiently large thickness, thevortices and the antivortices become curved before they annihilate each other.As they approach the center of the sample, their ends combine, producing asingle closed vortex. We also determine the critical values of the thicknessfor which the closed vortex sets in for different values of the Ginzburg-Ladauparameter. Finally, we propose a model of how to detect a closed vortexexperimentally.

Closed vortex state in 3D mesoscopic superconducting films under an applied transport current