The dependence of bias current density through a junction on the velocity o
f a uniformly moving vortex carrying two magnetic flux quanta is establishe
d in the approximation of weakly nonlocal Josephson electrodynamics. It is
shown that the velocity quantization of free motion of the vortex, which is
induced by the Cherenkov interaction with Swihart waves, leads to the emer
gence of a discrete family of curves on the velocity-current plane. (C) 200
1 MAIK "Nauka/Interperiodica".