Extended MHD turbulence and its applications to the solar wind

TL;DR

This paper develops a theoretical model of extended MHD turbulence incorporating electron inertia and Hall effects, deriving magnetic and kinetic spectra across different regimes, with implications for understanding solar wind observations.

Contribution

It introduces a comprehensive nonlinear Alfvénic wave solution framework within extended MHD, deriving spectra consistent with solar wind data, especially in the electron inertia regime.

Findings

Magnetic energy spectra with slopes of -11/3 and -13/3 are consistently recovered.

Results align with previous numerical and analytical studies of the solar wind.

The spectra suggest an extended inertial range beyond the standard dissipation range.

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 Alfv\'enic 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 $\left(k < 1/\lambda_i\right)$, Hall $\left(1/\lambda_i < k < 1/\lambda_e \right)$, and electron inertia $\left(k > 1/\lambda_e\right)$ regimes; $k$ is the wavenumber and $\lambda_s = c/\omega_{p s}$ 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.