The Hall effect and oscillating decay of a magnetic field

The decay of a strong magnetic field in a conducting matter is considered. It is shown that nondissipative Hall currents can considerably change the behavior of the field when it decays. The nonlinear character of the Hall effect leads to the generation of fields of high multipolarity even for most simple initial magnetic configurations. In particular, the evolution of an initially dipole configuration may give rise not only to quadrupole or higher poloidal harmonics but also to a toroidal field that is other than zero only inside the conductor. The nonlinear Hall currents relate different harmonics to each other and, in a sufficiently strong field, may provide efficient energy exchange between them. Due to this redistribution of the magnetic energy, the evolution of different harmonics has an oscillating character. The oscillation period is determined by the characteristic time of Hall drift and may be fairly short in strong magnetic fields.