Modeling Solar Wind Turbulence: The Kolmogorov-like Way

Abstract

The spectral energy distributions of the magnetohydrodynamic (MHD) fluctuations of the solar wind turbulence are derived using the dimensional arguments a la Kolmogorov within the framework of the Hall magnetohydrodynamics. While the velocity and the magnetic field fluctuations are dynamically related, the density fluctuations could behave as a passive scalar and be simply convected by the velocity or the magnetic field fluctuations. The Hall effect removes the degeneracy of the ideal Alfvénic spectra of the velocity and the magnetic fluctuations, at spatial scales shorter than or equal to the ion- inertial scale, adding steeper branches to the ideal MHD spectra. Which spectrum would the density fluctuations, behaving as a passive scalar, follow in such a case? The answer leads to the interesting consequence that the electron density fluctuations should follow the magnetic spectra since the electrons are frozen to the magnetic field and the ion density fluctuations should follow the kinetic energy spectra as ions carry the inertia. Thus the electron and the ion density would have different spectra at spatial scales equal to and smaller than the ion-inertial scale. However this raises the issue of the quasineutrality that must be maintained at each scale within the Hall-MHD. One way to accommodate both the quasineutrality as well as the electron- magnetic freezing in the Hall MHD is to discard the passive nature of the density fluctuations; they must be dynamically active in the turbulence. The quasineutrality could also be restored by a third species of particles providing a stationary background.