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

Generation of strong magnetic fields by r-modes in millisecond accreting neutron stars: induced deformations and gravitational wave emission