  We show that r-mode oscillations distort the magnetic fields of neutron stars
and that their occurrence is likely to be limited by this interaction. If the
field is gtrsim 10^{16} (Omega/Omega_B) G, where Omega and Omega_B are the
angular velocities of the star and at which mass shedding occurs, r-mode
oscillations cannot occur. Much weaker fields will prevent gravitational
radiation from exciting r-mode oscillations or damp them on a relatively short
timescale by extracting energy from the modes faster than gravitational wave
emission can pump energy into them. For example, a 10^{10} G poloidal magnetic
field that threads the star's superconducting core is likely to prevent the
ell=2 mode from being excited unless Omega exceeds 0.35 Omega_B. If Omega is
larger than 0.35 Omega_B initially, the ell=2 mode may be excited but is likely
to decay rapidly once Omega falls below 0.35 Omega_B, which happens in lesssim
15^d if the saturation amplitude is gtrsim 0.1. The r-mode oscillations may
play an important role in determining the structure of neutron star magnetic
fields.
