  We consider the evolution of magnetic fields under the influence of Hall
drift and Ohmic decay. The governing equation is solved numerically, in a
spherical shell with r_i/r_o = 0.75. Starting with simple free decay modes as
initial conditions, we then consider the subsequent evolution. The Hall effect
induces so-called helicoidal oscillations, in which energy is redistributed
among the different modes. We find that the amplitude of these oscillations can
be quite substantial, with some of the higher harmonics becoming comparable to
the original field. Nevertheless, this transfer of energy to the higher
harmonics is not sufficient to significantly accelerate the decay of the
original field, at least not at the R_B = O(100) parameter values accessible to
us, where this Hall parameter R_B measures the ratio of the Ohmic timescale to
the Hall timescale. We do find clear evidence though of increasingly fine
structures developing for increasingly large R_B, suggesting that perhaps this
Hall-induced cascade to ever shorter lengthscales is eventually sufficiently
vigorous to enhance the decay of the original field. Finally, the implications
for the evolution of neutron star magnetic fields are discussed.
