Wave turbulence in incompressible Hall magnetohydrodynamics

By S. Galtier. Journal of Plasma Physics, 2006

162 citations recorded by the source corpus.

We investigate the steepening of the magnetic fluctuation power law spectra observed in the inner Solar wind for frequencies higher than 0.5 Hz. This high frequency part of the spectrum may be attributed to dispersive nonlinear processes. In that context, the long-time behavior of weakly interacting waves is examined in the framework of three-dimensional incompressible Hall magnetohydrodynamic (MHD) turbulence. The Hall term added to the standard MHD equations makes the Alfvén waves dispersive and circularly polarized. We introduce the generalized Elsässer variables and, using a complex helicity decomposition, we derive for three-wave interaction processes the general wave kinetic equations; they describe the nonlinear dynamics of Alfvén, whistler and ion cyclotron wave turbulence in the presence of a strong uniform magnetic field $B_0 \^{e}_{\Vert}$. Hall MHD turbulence is characterized by anisotropies of different strength: (i) for wavenumbers $\textit{kd}_{\rm i}\,{\gg}\,1$ ($d_{\rm i}$ is the ion inertial length) nonlinear transfers are essentially in the direction perpendicular ($\perp$) to ${\bf B}_0$; (ii) for $\textit{kd}_{\rm i}\,{\ll}\,1$ nonlinear transfers are exclusively in the perpendicular direction; (iii) for $\textit{kd}_{\rm i} \sim 1$, a moderate anisotropy is predicted. We show that electron and standard MHD turbulence can be seen as two frequency limits of the present theory but the standard MHD limit is singular; additionally, we analyze in detail the ion MHD turbulence limit. Exact power law solutions of the master wave kinetic equations are given in the small- and large-scale limits for which we have, respectively, the total energy spectra $E(k_{\perp},k_{\Vert}) \sim k_{\perp}^{-5/2} |k_{\Vert}|^{-1/2}$ and $E(k_{\perp},k_{\Vert}) \sim k_{\perp}^{-2}$. An anisotropic phenomenology is developed to describe continuously the different scaling laws of the energy spectrum; one predicts $E(k_{\perp},k_{\Vert}) \sim k_{\perp}^{-2} |k_{\Vert}|^{-1/2} (1+k_{\perp}^2d_{\rm i}^2)^{-1/4}$. Non-local interactions between Alfvén, whistler and ion cyclotron waves are investigated; a non-trivial dynamics exists only when a discrepancy from the equipartition between the large-scale kinetic and magnetic energies happens.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/7d1a86353a44f050738364dc40d15e6a9d5110dc

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Citations in the corpus

A Model of Turbulence in Magnetized Plasmas: Implications for the Dissipation Range in the Solar Wind (2007, background): “…[Coleman, 1968; Denskat et al., 1983; Goldstein et al., 1994; Leamon et al., 1998b; Gary , 1999], Landau damping of kinetic Alfvén waves [Leamon et al., 1998a, 1999; Leamon et al., 2000], or the dispersive nature of whistler waves [Stawicki et al., 2001; Krishan and Mahajan, 2004; Galtier , 2006].”
Small-Scale Energy Cascade of the Solar Wind Turbulence (2007, background): “Others suggest that after the spectral break another turbulent cascade takes place (Biskamp et al. 1996; Ghosh et al. 1996; Stawicki et al. 2001; Li et al. 2001; Galtier 2006).”
Solar Wind Turbulence and the Role of Ion Instabilities (2013, background): “2009; Boldyrev and Perez 2012) and the transition from MHD to Hall MHD occurs at the ion inertial length λi (Galtier 2006; Servidio et al. 2007; Matthaeus et al. 2008, 2010).”
Self-consistent Coronal Heating and Solar Wind Acceleration from Anisotropic Magnetohydrodynamic Turbulence (2007, background): “Two-fluid effects also may affect the phenomenological form of the MHD turbulent cascade assumed in the above models (e.g., Galtier 2006).”
ASTROPHYSICAL GYROKINETICS: KINETIC AND FLUID TURBULENT CASCADES IN MAGNETIZED WEAKLY COLLISIONAL PLASMAS (2007, methodology): “However, as we have already mentioned above, the dominance of the perpendicular energy transfer (k‖ ≪ k⊥) is supported both by weakturbulence theory for Hall MHD (Galtier 2006) and by 3D numerical simulations of the Electron MHD (Cho & Lazarian 2004).”