  We consider the magnetophoresis problem within the Rubinstein-Duke model,
i.e. a reptating polymer pulled by a constant field applied to a single repton
at the edge of a chain. Extensive density matrix renormalization calculations
are presented of the drift velocity and the profile of the chain for various
strengths of the driving field and chain lengths. We show that the velocities
and the average densities of stored length are well described by simple
interpolating crossover formulae, derived under the assumption that the
difference between the drift and curvilinear velocities vanishes for
sufficiently long chains. The profiles, which describe the average shape of the
reptating chain, also show interesting features as some non-monotonic behavior
of the links densities for sufficiently strong pulling fields. We develop a
description in which a distinction is made between links entering at the pulled
head and at the unpulled tail. At weak fields the separation between the head
zone and the tail zone meanders through the whole chain, while the probability
of finding it close to the edges drops off. At strong fields the tail zone is
confined to a small region close to the unpulled edge of the polymer.
