Magnetic fields generated by r-modes in accreting millisecond pulsars

In rotating neutron stars the existence of the Coriolis force allows the presence of the so-called Rossby oscillations (r-modes) which are known to be unstable to emission of gravitational waves. In the Thesis, for the first time, we introduce the magnetic damping rate in the evolution equations of r-modes. We show that r-modes can generate very strong toroidal fields in the core of accreting millisecond pulsars by inducing differential rotation. We shortly discuss the instabilities of the generated magnetic field and its long time-scale evolution in order to clarify how the generated magnetic field can stabilize the star. Finally we discuss the possible astrophysical scenarios.