Extended MHD turbulence and its applications to the solar wind

Abstract

Extended MHD is a one-fluid model that incorporates two-fluid effects such as electron inertia and the Hall drift. This model is used to construct fully nonlinear Alfvénic wave solutions, and thereby derive the kinetic and magnetic spectra by resorting to a Kolmogorov-like hypothesis based on the constant cascading rates of the energy and generalized helicities of this model. The magnetic and kinetic spectra are derived in the ideal $\left(k < 1/λ_i\right)$, Hall $\left(1/λ_i < k < 1/λ_e \right)$, and electron inertia $\left(k > 1/λ_e\right)$ regimes; $k$ is the wavenumber and $λ_s = c/ω_{p s}$ is the skin depth of species `$s$'. In the Hall regime, it is shown that the emergent results are fully consistent with previous numerical and analytical studies, especially in the context of the solar wind. The focus is primarily on the electron inertia regime, where magnetic energy spectra with power-law indexes of $-11/3$ and $-13/3$ are always recovered. The latter, in particular, is quite close to recent observational evidence from the solar wind with a potential slope of approximately $-4$ in this regime. It is thus plausible that these spectra may constitute a part of the (extended) inertial range, as opposed to the standard `dissipation' range paradigm.