Shell model of magnetic field evolution under the Hall effect

P. Frick - R. Stepanov - V. Nekrasov

Institute of Continuous Media Mechanics, Perm, 614061, Russia

Abstract
The Hall effect occurs in strongly magnetized conductive media and results in nondissipative currents directed normaly to the electric field. We consider the magnetic field dynamics driven by the Hall effect ignoring fluid motions. Electronic magnetohydrodynamic turbulence may result from a nonlinear evolution of the magnetic field. We introduce a shell model for the corresponding induction equation written for the poloidal and toroidal components. The model provides the conservation laws in dissipationless limit, where the energy and the magnetic helicity become integrals of motion. Numerical simulations confirm that the inertial range with the spectral law "−7/3" is established in the EMHD system provided the Hall parameter \RH is sufficiently large and the outflow of helicity at the left end of the inertial range is possible. Figs 5, Refs 10.