  Strong magnetic fields play an important role in powering the emission of
neutron stars. Nevertheless a full understanding of the interior configuration
of the field remains elusive. In this work, we present General Relativistic
MagnetoHydroDynamics simulations of the magnetic field evolution in neutron
stars lasting 500 ms (5 Alfven crossing times) and up to resolutions of 0.231
km using Athena++. We explore two different initial conditions, one with purely
poloidal magnetic field and the other with a dominant toroidal component, and
study the poloidal and toroidal field energies, the growth times of the various
instability-driven oscillation modes and turbulence. We find that the purely
poloidal setup generates a toroidal field which later decays exponentially
reaching 1% of the total magnetic energy, showing no evidence of reaching
equilibrium. The initially stronger toroidal field setup, on the other hand,
loses up to 20% of toroidal energy and maintains this state till the end of our
simulation. We also explore the hypothesis, drawn from previous MHD
simulations, that turbulence plays an important role in the quasi equilibrium
state. An analysis of the spectra in our higher resolution setups reveal,
however, that in most cases we are not observing turbulence at small scales,
but rather a noisy velocity field inside the star. We also observe that the
majority of the magnetic energy gets dissipated as heat increasing the internal
energy of the star, while a small fraction gets radiated away as
electromagnetic radiation.
