  We present a theoretical and experimental study of Josephson vortex (fluxon)
moving in the presence of spatially homogeneous dc and ac bias currents. By
mapping this problem to the problem of calculating the current-voltage
characteristic of a small Josephson junction, we derive the dependence of the
average fluxon velocity on the dc bias current. In particular we find that the
low frequency ac bias current results in an additional nonlinear damping of
fluxon motion. Such ac induced damping crucially depends on the intrinsic
damping parameter and increases drastically as this parameter is reduced. We
find a good agreement of the analysis with both the direct numerical
simulations and the experimentally measured current-voltage characteristics of
a long annular Josephson junction with one trapped fluxon.
