  Differential rotation induced by the r-mode instability can generate very
strong toroidal fields in the core of accreting, millisecond spinning neutron
stars. We introduce explicitly the magnetic damping term in the evolution
equations of the r-modes and solve them numerically in the Newtonian limit, to
follow the development and growth of the internal magnetic field. We show that
the strength of the latter can reach large values, $B \sim 10^{14} $ G, in the
core of the fastest accreting neutron stars. This is strong enough to induce a
significant quadrupole moment of the neutron star mass distribution,
corresponding to an ellipticity $|\epsilon_B}| \sim 10^{-8}$. If the symmetry
axis of the induced magnetic field is not aligned with the spin axis, the
neutron star radiates gravitational waves. We suggest that this mechanism may
explain the upper limit of the spin frequencies observed in accreting neutron
stars in Low Mass X-Ray Binaries. We discuss the relevance of our results for
the search of gravitational waves.
