THE HALL EFFECT AND THE DECAY OF MAGNETIC FIELDS

Abstract

We consider the influence of the Hall effect on the evolution of a strong magnetic eld which can magnetize plasma. The Hall current couples various multipole eld com- ponentsandprovidesapossibilityofanenergyexchangeamong modes. Due to this, the evolution of strong magnetic elds is substantially more complicated than the ohmic decay of weak magnetic elds. Non-linear effects can create a complex mag- netic conguration even from the simplest one corresponding originally to the pure dipole eld outside the star. The energy transfer among eld components leads to a non-monotonic be- haviour of individual modes. Variations of the large scale mag- netic eld 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 sufciently short for a strong magnetic eld. The non- linear phenomena may be important for the magnetic evolution of white dwarfs and neutron stars.