Vortices confined to superconducting easy flow channels with periodic constrictions exhibit reversible oscillations in the critical current at which vortices begin moving as the external magnetic field is varied. This commensurability scales with the channel shape and arrangement, although screening effects play an important role. For large magnetic fields, some of the vortices become pinned outside of the channels, leading to magnetic hysteresis in the critical current. Some channel configurations also exhibit a dynamical hysteresis in the flux-flow regime near the matching fields.
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