  We study analytically and numerically the overdamped, deterministic dynamics
of a chain of {\it charged}, interacting particles driven by a longitudinal
alternating electric field and additionally interacting with a smooth ratchet
potential. We derive the equations of motion, analyze the general properties of
their solutions and find the drift criterion for chain motion. For ratchet
potentials of the form of a double-sine and a phase-modulated sine it is
demonstrated that both, a so-called integer and fractional transport of the
chain can occur. Explicit results for the directed chain transport for these
two classes of ratchet potentials are presented.
