Multi-scale Hall-MHD turbulence in the solar wind

Solar wind magnetic fluctuation spectra exhibit a significant power law steepening at frequencies f>1Hz. The origin of this multi-scaling is investigated through dispersive Hall magnetohydrodynamics. We perform three-dimensional numerical simulations in the framework of a highly turbulent shell model and show that the large-scale magnetic fluctuations are characterized by a k^-5/3-type spectrum which steepens at scales smaller than the ion inertial length d_i, to k^-7/3 if the magnetic energy overtakes the kinetic energy, or to k^-11/3 in the opposite case. These results are in agreement both with a heuristic description a la Kolmogorov, and with the range of power law indices found in the solar wind.