Abstract
Neutron stars contain the strongest magnetic fields known in the Universe. Using numerical simulations restricted to axially symmetric geometry, we study the long-term evolution of the magnetic field in the interior of an isolated neutron star under the effect of ambipolar diffusion, i.e. the drift of the magnetic field and the charged particles relative to the neutrons. We model the stellar interior as an electrically neutral fluid composed of neutrons, protons and electrons; these species can be converted into each other by weak interactions (beta decays), suffer binary collisions, and be affected by each other's macroscopic electromagnetic fields. We show that, in the restricted case of pure ambipolar diffusion, neglecting weak interactions, the magnetic fields evolves towards a stable MHD equilibria configuration, in the timescales analytically expected.
