The Hall effect and the decay of magnetic fields

We consider the influence of the Hall effect on the evolution of a strong magnetic field which can magnetize plasma. The Hall current couples various multipole field components and provides a possibility of an energy exchange among modes. Due to this, the evolution of strong magnetic fields is substantially more complicated than the ohmic decay of weak magnetic fields. Non-linear effects can create a complex magnetic configuration even from the simplest one corresponding originally to the pure dipole field outside the star. The energy transfer among field components leads to a non-monotonic behaviour of individual modes. Variations of the large scale magnetic field are of the same origin as the so called helicoidal oscillation of magnetized plasma. The period of variations is determined by the time scale associated with the Hall effect and may be sufficiently short for a strong magnetic field. The non-linear phenomena may be important for the magnetic evolution of white dwarfs and neutron stars.