Nonlinear interaction between a circularly (or elliptically) polarized electromagnetic field and the conduction electrons of a non-simply connected mesoscopic medium can lead to a photon-drag effect based on a net transfer of angular momentum from the field to the particles. In this work we establish a theory for the phenomenon in the case where a persistent current originating in the Aharonov-Bohm mechanism is present. Particular attention is devoted to a study of the magnetic-flux dependence of the induced steady-state current in thin circular metallic rings. Numerical results for the flux-periodic dc current are given for different values of the strength of the ac field so that the transition from the regime where the persistent current dominates to the regime where the photon-drag current gives the main contribution is seen. The fine structure in the flux dependence of the current, associated with photon-assisted excitations of electrons between states of neighbouring angular quantum numbers located on opposite sites of the Fermi level is investigated for different choices of the electronic relaxation time.
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