We derive general equations for axisymmetric Newtonian MHD and use these as the basis of a code for calculating equilibrium configurations of rotating magnetised neutron stars in a stationary state. We investigate the field configurations that result from our formalism, which include purely poloidal, purely toroidal and mixed fields. For the mixed-field formalism the toroidal component appears to be bounded at less than 7%. We calculate distortions induced both by magnetic fields and by rotation. From our non-linear work we are able to look at the realm of validity of perturbative work: we find for our results that perturbative-regime formulae for magnetic distortions agree to within 10% of the nonlinear results if the ellipticity is less than 0.15 or the average field strength is less than $10^{17}$ G. We also consider how magnetised equilibrium structures vary for different polytropic indices.Comment: 19 pages, 11 figures; typos removed, one paragraph of Discussion rewritte

The problem of the stability of magnetic fields in stars has a long history and has been investigated in detail in perturbation theory. Here we consider the nonlinear evolution of a nonrotating neutron star with a purely poloidal magnetic field, in general relativity. We find that an instability develops in the region of the closed magnetic field lines and over an Alfvén timescale, as predicted by perturbation theory. After the initial unstable growth, our evolutions show that a toroidal magnetic field component is generated, which increases until it is locally comparable in strength with the poloidal one. On longer timescales the system relaxes to a new non-axisymmetric configuration with a reorganization of the stellar structure and large-amplitude oscillations, mostly in the fundamental mode. We discuss the energies involved in the instability and the impact they may have on the phenomenology of magnetar flares and on their detectability through gravitational-wave emission.

Crustquake events may be connected with both rapid spin-up 'glitches' within the regular slowdown of neutron stars, and high-energy magnetar flares. We argue that magnetic field decay builds up stresses in a neutron star's crust, as the elastic shear force resists the Lorentz force's desire to rearrange the global magnetic-field equilibrium. We derive a criterion for crust-breaking induced by a changing magnetic-field configuration, and use this to investigate strain patterns in a neutron star's crust for a variety of different magnetic-field models. Universally, we find that the crust is most liable to break if the magnetic field has a strong toroidal component, in which case the epicentre of the crustquake is around the equator. We calculate the energy released in a crustquake as a function of the fracture depth, finding that it is independent of field strength. Crust-breaking is, however, associated with a characteristic local field strength of 2.4 × 10 14 G for a breaking strain of 0.001, or 2.4 × 10 15 G at a breaking strain of 0.1. We find that even the most luminous magnetar giant flare could have been powered by crustal energy release alone.