  The configuration of the magnetic field in the interior of a neutron star is
mostly unknown from observations. Theoretical models of the interior magnetic
field geometry tend to be oversimplified to avoid mathematical complexity and
tend to be based on axisymmetric barotropic fluid systems. These static
magnetic equilibrium configurations have been shown to be unstable on a short
time scale against an infinitesimal perturbation. Given this instability, it is
relevant to consider how more realistic neutron star physics affects the
outcome. In particular, it makes sense to ask if elasticity, which provides an
additional restoring force on the perturbations, may stabilise the system. It
is well-known that the matter in the neutron star crust forms an ionic crystal.
The interactions between the crystallized nuclei can generate shear stress
against any applied strain. To incorporate the effect of the crust on the
dynamical evolution of the perturbed equilibrium structure, we study the effect
of elasticity on the instability of an axisymmetric magnetic star. In
particular we determine the critical shear modulus required to prevent magnetic
instability and consider the corresponding astrophysical consequences.
