  The spectrum of oscillation modes of a star provides information not only
about its material properties (e.g. mean density), but also its symmetries.
Spherical symmetry can be broken by rotation and/or magnetic fields. It has
been postulated that strong magnetic fields in the cores of some red giants are
responsible for their anomalously weak dipole mode amplitudes (the "dipole
dichotomy" problem), but a detailed understanding of how gravity waves interact
with strong fields is thus far lacking. In this work, we attack the problem
through a variety of analytical and numerical techniques, applied to a
localised region centred on a null line of a confined axisymmetric magnetic
field which is approximated as being cylindrically symmetric. We uncover a rich
variety of phenomena that manifest when the field strength exceeds a critical
value, beyond which the symmetry is drastically broken by the Lorentz force.
When this threshold is reached, the spatial structure of the g-modes becomes
heavily altered. The dynamics of wave packet propagation transitions from
regular to chaotic, which is expected to fundamentally change the organisation
of the mode spectrum. In addition, depending on their frequency and the
orientation of field lines with respect to the stratification, waves impinging
on different parts of the magnetised region are found to undergo either
reflection or trapping. Trapping regions provide an avenue for energy loss
through Alfven wave phase mixing. Our results may find application in various
astrophysical contexts, including the dipole dichotomy problem, the solar
interior, and compact star oscillations.
