  This paper presents a numerical study over a wide parameter space of the
likelihood of the dynamical bar-mode instability in differentially rotating
magnetized neutron stars. The innovative aspect of this study is the
incorporation of magnetic fields in such a context, which have thus far been
neglected in the purely hydrodynamical simulations available in the literature.
The investigation uses the Cosmos++ code which allows us to perform three
dimensional simulations on a cylindrical grid at high resolution. A sample of
Newtonian magneto-hydrodynamical simulations starting from a set of models
previously analyzed by other authors without magnetic fields has been
performed, providing estimates of the effects of magnetic fields on the
dynamical bar-mode deformation of rotating neutron stars. Overall, our results
suggest that the effect of magnetic fields are not likely to be very
significant in realistic configurations. Only in the most extreme cases are the
magnetic fields able to suppress growth of the bar mode.
