  We study the dynamics of a classical nonrelativistic charged particle moving
on a punctured plane under the influence of a homogeneous magnetic field and
driven by a periodically time-dependent singular flux tube through the hole. We
observe an effect of resonance of the flux and cyclotron frequencies. The
particle is accelerated to arbitrarily high energies even by a flux of small
field strength which is not necessarily encircled by the cyclotron orbit; the
cyclotron orbits blow up and the particle oscillates between the hole and
infinity. We support this observation by an analytic study of an approximation
for small amplitudes of the flux which is obtained with the aid of averaging
methods. This way we derive asymptotic formulas that are afterwards shown to
represent a good description of the accelerated motion even for fluxes which
are not necessarily small. More precisely, we argue that the leading asymptotic
terms may be regarded as approximate solutions of the original system in the
asymptotic domain as the time tends to infinity.
