  We show that a very precise neutrino/anti-neutrino event separation is not
mandatory to cover the physics program of a low energy neutrino factory and
thus non-magnetized detectors like water Cerenkov or liquid Argon detectors can
be used. We point out, that oscillation itself strongly enhances the signal to
noise ratio of a wrong sign muon search, provided there is sufficiently
accurate neutrino energy reconstruction. Further, we argue that apart from a
magnetic field, other means to distinguish neutrino from anti-neutrino events
(at least statistically) can be explored. Combined with the fact that
non-magnetic detectors potentially can be made very big, we show that modest
neutrino/anti-neutrino separations at the level of 50% to 90% are sufficient to
obtain good sensitivity to CP violation and the neutrino mass hierarchy for
$\sin^22\theta_{13}>10^{-3}$. These non-magnetized detectors have a rich
physics program outside the context of a neutrino factory, including topics
like supernova neutrinos and proton decay. Hence, our observation opens the
possibility to use a multi-purpose detector also in a neutrino factory beam.
