  Rotating deformed neutron stars are important potential sources for
groundbased gravitational-wave interferometers such as LIGO, GE0600 and VIRGO.
One mechanism that may lead to significant non-asymmetries is the internal
magnetic field. It is well known that a magnetic star will not be spherical
and, if the magnetic axis is not aligned with the spin axis, the deformation
will lead to the emission of gravitational waves. The aim of this paper is to
develop a formalism that would allow us to model magnetically deformed stars,
using both realistic equations of state and field configurations. As a first
step, we consider a set of simplified model problems. Focusing on dipolar
fields, we determine the internal magnetic field which is consistent with a
given neutron star model. We then calculate the associated deformation. We
conclude by discussing the relevance of our results for current
gravitational-wave detectors and future prospects.
