We model long term variations detected in the period residuals of pulsar PSR B1828-11 in terms of precession of an asymmetric rigid body. We consider two contributions: the geometric effect, due to variation of the pulsar beam orientation with respect to the observer with precession phase; and the spindown contribution, due to dependence of the spindown torque on the angle between the rotation and magnetic axes. We use the data to probe various properties of the star, most notably its shape. We find that a wide range of models are able to explain the variations in terms of precession. We offer an explanation for the observed variations in the pulse shape in terms of a compound beam structure.

Neutron stars will be deformed by their magnetic fields, which can explain long term variations in their period residuals. Magnetic stresses in normal conductors are insufficient (by a factor of about a thousand) to account for the deformation inferred for PSR B1828-11. However, magnetic stresses in type II superconductors (which form in neutron stars) can produce the necessary deformation.

We determine the form of axisymmetric toroidal magnetic fields in completely fluid, non-rotating, type II superconducting neutron stars, consistent with magnetohydrostatic equilibrium and boundary conditions. Using Lagrangian perturbation theory we determine stellar deformations for various models of neutron stars with type II superconducting and normal regions. We find that the star becomes prolate and can be sufficiently distorted to display precession with a period of the order of a few years.

We also study the stability of toroidal fields using an energy principle and a local analysis. We extend the stability criteria established by Tayler for normal conductors to include type II superconductors with magnetic free energy that depends on density and magnetic induction. We also derive the conditions and growth rate for a specific instability of type II superconductors, first discussed by Muzikar, Pethick and Roberts.

Finally, we consider the harder problem of poloidal fields in type II superconductors. In this case, the magnetic field direction, as well as strength, is unknown, and needs to be calculated numerically.