  We have found an attractor for an axially symmetric magnetic field evolving
under the Hall effect and subdominant ohmic dissipation, resolving the question
of the long term fate of the magnetic field in neutron star crusts. The
electron fluid is in isorotation, analogous to Ferraro's law, with its angular
velocity being approximately proportional to the poloidal magnetic flux,
$\Omega \propto \Psi$. This equilibrium is the long term configuration of a
magnetic field evolving because of the Hall effect and ohmic dissipation. For
an initial dipole dominated field the attractor consists mainly of a dipole and
an octupole component accompanied by an energetically negligible quadrupole
toroidal field. The field dissipates in a self-similar way: although higher
multipoles should have been decaying faster, the toroidal field mediates
transfer of energy into them from the lower ones, leading to an advection
diffusion equilibrium and keeping the ratio of the poloidal multipoles almost
constant. This has implications for the structure of the intermediate age
neutron stars, suggesting that their poloidal field should consist of a dipole
and a octupole component accompanied by a very weak toroidal quadrupole. For
initial conditions that have a higher multipole $\ell$ structure the attractor
consists mainly of $\ell$ and $\ell+2$ poloidal components.
