  The instability of r-mode oscillations in rapidly rotating neutron stars has
attracted attention as a potential mechanism for producing high frequency,
almost periodic gravitational waves. The analyses carried so far have shown the
existence of these modes and have considered damping by shear and bulk
viscosity. However, the magnetohydrodynamic coupling of the modes with a
stellar magnetic field and its role in the damping of the instability has not
been fully investigated yet. Following our introductory paper (Rezzolla, Lamb
and Shapiro 2000), we here discuss in more detail the existence of secular
higher-order kinematical effects which will produce toroidal fluid drifts. We
also define the sets of equations that account for the time evolution of the
magnetic fields produced by these secular velocity fields and show that the
magnetic fields produced can reach equipartition in less than a year. The full
numerical calculations as well as the evaluation of the impact of strong
magnetic fields on the onset and evolution of the r-mode instability will be
presented in a companion paper.
