Hall-magnetohydrodynamic small-scale dynamos

Abstract

Magnetic field generation by dynamo action is often studied within the theoretical framework of magnetohydrodynamics (MHD). However, for sufficiently diffuse media, the Hall effect may become non-negligible. We present results from three-dimensional simulations of the Hall-MHD equations subjected to random nonhelical forcing. We study the role of the Hall effect in the dynamo efficiency for different values of the Hall parameter. For small values of the Hall parameter, the small-scale dynamo is more efficient, displaying faster growth and saturating at larger amplitudes of the magnetic field. For larger values of the Hall parameter, saturation of the magnetic field is reached at smaller amplitudes than in the MHD case. We also study energy transfer rates among spatial scales and show that the Hall effect produces a reduction of the direct energy cascade at scales larger than the Hall scale, therefore leading to smaller energy dissipation rates. Finally, we present results stemming from simulations at large magnetic Prandtl numbers, which is the relevant regime in the hot and diffuse interstellar medium. In the range of magnetic Prandtl numbers considered, the Hall effect moves the peak of the magnetic energy spectrum as well as other relevant magnetic length scales toward the Hall scale.