Two-fluid turbulence including electron inertia

TL;DR

This paper develops a comprehensive two-fluid MHD model including electron inertia, investigates its impact on turbulence spectra, and finds distinct power-law regimes corresponding to different spatial scales, aligning with solar wind observations.

Contribution

It introduces a full two-fluid MHD framework with electron inertia, revealing new spectral regimes and scaling laws in plasma turbulence not captured by traditional models.

Findings

Reproduced Kolmogorov $k^{-5/3}$ inertial range at large scales.

Identified a $k^{-7/3}$ spectral regime at intermediate scales.

Discovered a $k^{-11/3}$ power law at electron inertial scales.

Abstract

We present a full two-fluid magnetohydrodynamic (MHD) description for a completely ionized hydrogen plasma, retaining the effects of the Hall current, electron pressure and electron inertia. According to this description, each plasma species introduces a new spatial scale: the ion inertial length $\lambda_{i}$ and the electron inertial length $\lambda_{e}$, which are not present in the traditional MHD description. In the present paper, we seek for possible changes in the energy power spectrum in fully developed turbulent regimes, using numerical simulations of the two-fluid equations in two-and-a-half dimensions (2.5D). We have been able to reproduce different scaling laws in different spectral ranges, as it has been observed in the solar wind for the magnetic energy spectrum. At the smallest wavenumbers where plain MHD is valid, we obtain an inertial range following a Kolmogorov $k^{-5/3}$ law. For intermediate wavenumbers such that $\lambda_{i}^{-1} << k << \lambda_{e}^{-1}$, the spectrum is modified to a $k^{-7/3}$ power-law, as has also been obtained for Hall-MHD (HMHD) neglecting electron inertia terms. When electron inertia is retained, a new spectral region given by $k > \lambda_{e}^{-1}$ arises. The power spectrum for magnetic energy in this region is given by a $k^{-11/3}$ power law. Finally, when the terms of electron inertia are retained, we study the self-consistent electric field. Our results are discussed and compared with those obtained in solar wind observations and previous simulations.