  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.
