Two-fluid turbulence including electron inertia

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.

References in corpus (4)

• Universality of solar wind turbulent spectrum from MHD to electron scales
• Wave turbulence in incompressible Hall MHD
• Multi-scale Hall-MHD turbulence in the solar wind
• Effects of electron inertia in collisionless magnetic reconnection

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• Solar Wind Turbulence Around Mars: Relation Between The Energy Cascade Rate And The Proton Cyclotron Waves Activity
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• Exact scaling laws for helical three-dimensional two-fluid turbulent plasmas
• Influence of the Hall effect and electron inertia in collisionless magnetic reconnection
• Normal Modes in Magnetized Two-Fluid Spin Quantum Plasmas
• Incompressible Extended Magnetohydrodynamics Waves: Implications of Electron Inertia