Abstract
Abstract The ohmic decay of magnetic fields in the crusts of neutron stars is generally believed to be governed by Hall drift, which leads to what is known as a Hall cascade. Here we show that helical and fractionally helical magnetic fields undergo strong inverse cascading like in magnetohydrodynamics (MHD), but the magnetic energy decays more slowly with time t: instead of ∝t −2/3 in MHD. Even for a nonhelical magnetic field there is a certain degree of inverse cascading for sufficiently strong magnetic fields. The inertial range scaling with wavenumber k is compatible with earlier findings for the forced Hall cascade, i.e., proportional to k −7/3, but in the decaying cases, the subinertial range spectrum steepens to a novel k 5 slope instead of the k 4 slope in MHD. The energy of the large-scale magnetic field can increase quadratically in time through inverse cascading. For helical fields, the energy dissipation is found to be inversely proportional to the large-scale magnetic field and proportional to the fifth power of the rms magnetic field. For neutron star conditions with an rms magnetic field of a few times , the large-scale magnetic field might only be , while still producing magnetic dissipation of for thousands of years, which could manifest itself through X-ray emission. Finally, it is shown that the conclusions from local unstratified models agree rather well with those from stratified models with boundaries.
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