Magnetic field decay with Hall drift in neutron star crusts

The dynamics of magnetic field decay with Hall drift is investigated. Assuming that axisymmetric magnetic fields are located in a spherical crust with uniform conductivity and electron number density, the long-term evolution is calculated up to Ohmic dissipation. The non-linear coupling between poloidal and toroidal components is explored in terms of their energies and helicity. Non-linear oscillation of the drift in strongly magnetized regimes is clear only around equipartition between the two components. Significant energy is transferred to the poloidal component initially when the toroidal component dominates. However, the reverse is not true. Once the toroidal field is less dominant, it quickly decouples due to a larger damping rate. The polar field at the surface is highly distorted from the initial dipole during the Hall drift time-scale, but returns to the initial dipole over a longer dissipation time-scale, since it is the least damped form.