The inertial range of MHD turbulence and Hall MHD turbulence in solar wind

Turbulent fluctuations within solar wind spectrum follows nearly Kolmogorov's power law spectrum below the ion cyclotron frequency fci. Above this frequency, the observed steeper power law is believed to be a 'dissipative range' of the solar wind turbulence. The inertial range is studied here in terms of the pseudo-energy flux, which can be shown to have a linear scaling law in isotropic, homogeneous, fully developed turbulence. Such linear scaling has recently been observed in polar wind measured by Ulysses, and represent a strong evidence that a nonlinear, turbulent cascade is at work in the solar windplasma. Moreover, we analyze magnetic field fluctuations measured onboard Cluster, lasting two decades above fci. Well defined power law and a strong increase of intermittency with frequency in this range indicates that turbulence cannot be characterized by a 'dissipative range'. Rather we conjecture that the presence of dispersive effects is responsible for a steepening of the spectral energy density, simply because a cascade can be realized in a time that is shorter than the usual eddy- turnover time. In the Hall MHD formulation magnetic power depends on the degree of plasma compressibility. Such results are compared with numerical smulation of Hall MHD.