Rapid dissipation of magnetic fields due to the Hall current

We propose a mechanism for the fast dissipation of magnetic fields which is effective in a stratified medium where ion motions can be neglected. In such a medium, the field is frozen into the electrons, and Hall currents prevail. Although Hall currents conserve magnetic energy, in the presence of density gradients they are able to create current sheets which can be sites for efficient dissipation of magnetic fields. We recover the frequency ${\omega }_{\mathrm{MH}}$ for Hall oscillations modified by the presence of density gradients. We show that these oscillations can lead to an exchange of energy between different components of the field. We calculate the time evolution, and show that magnetic fields can dissipate on a time scale of order $1/{\omega }_{\mathrm{MH}}.$ This mechanism can play an important role in magnetic dissipation in systems with very steep density gradients, where the ions are static such as those found in the solid crust of neutron stars.