  We consider the effect of Hall-drift on the evolution of magnetic fields in
neutorn star crusts using a finite difference code. Previously, most studies
have focused on the situation where the ohmic term dominates the evolution.
Here, we investigate the case where the ohmic term is small compared to the
Hall term. We show that the effect on the magnetic field energy decay rate is
up to 30 % different compared to pure ohmic decay, depending on the initial
conditions. In some cases the torroidal field act as an energy "reservoir" and
cause a slower decay rate than the ohmic case. We also investigate the
importance of high order vacuum multipoles and find that for situations where
the Hall term is a couple of orders of magnitude stronger than the ohmic term,
hexapoles and up are a significant part of the magnetic field at the surface of
the neutron star.
