Multiscale Hall-magnetohydrodynamic turbulence in the solar wind

The spectra of solar wind magnetic fluctuations exhibit a significant power-law steepening at frequencies f > 1 Hz. The origin of this multiple 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 that 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.