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We consider a nonrelativistic quantum charged particle moving on a planeunder the influence of a uniform magnetic field and driven by a periodicallytime-dependent Aharonov-Bohm flux. We observe an acceleration effect in thecase when the Aharonov-Bohm flux depends on time as a sinusoidal function whosefrequency is in resonance with the cyclotron frequency. In particular, theenergy of the particle increases linearly for large times. An explicit formulafor the acceleration rate is derived with the aid of the quantum averagingmethod, and then it is checked against a numerical solution with a very goodagreement.

A charged particle in a homogeneous magnetic field accelerated by a time periodic Aharonov-Bohm flux