  We consider the Josephson vortex motion in a long one--dimensional Josephson
junction in a thin film. We show that this Josephson vortex is similar to a
mesoscopic capacitor. We demonstrate that a single Cooper pair tunneling
results in nonlinear Bloch--type oscillations of a Josephson vortex in a
current-biased Josephson junction. We find the frequency and the amplitude of
this motion.
