Entanglement of helicity and energy in kinetic Alfven wave/whistler turbulence

Abstract

The role of magnetic helicity is investigated in kinetic Alfvén wave and oblique whistler turbulence in presence of a relatively intense external magnetic field $b_0{\mathbf{e}}_{\parallel }$. In this situation, turbulence is strongly anisotropic and the fluid equations describing both regimes are the reduced electron magnetohydrodynamics (REMHD) whose derivation, originally made from the gyrokinetic theory, is also obtained here from compressible Hall MHD. We use the asymptotic equations derived by Galtier \& Bhattacharjee (2003) to study the REMHD dynamics in the weak turbulence regime. The analysis is focused on the magnetic helicity equation for which we obtain the exact solutions: they correspond to the entanglement relation, $n+\tilde{n}=-6$, where $n$ and $\tilde{n}$ are the power law indices of the perpendicular (to ${\mathbf{b}}_0$) wave number magnetic energy and helicity spectra respectively. Therefore, the spectra derived in the past from the energy equation only, namely $n=-2.5$ and $\tilde{n}=-3.5$, are not the unique solutions to this problem but rather characterize the direct energy cascade. The solution $\tilde{n}=-3$ is a limit imposed by the locality condition; it is also the constant helicity flux solution obtained heuristically. The results obtained offer a new paradigm to understand solar wind turbulence at sub-ion scales where it is often observed that $-3<n<-2.5$.

26 pages, submitted to the special issue of JPP "Present achievements and new frontiers in space plasmas"

References in corpus (8)

• Wave turbulence in incompressible Hall MHD
• Simulations of Electron Magnetohydrodynamic Turbulence
• Multi-scale Hall-MHD turbulence in the solar wind
• On the von Karman-Howarth equations for Hall MHD flows
• Nonlinear and Linear Timescales near Kinetic Scales in Solar Wind Turbulence
• Magnetic Helicity Conservation and Inverse Energy Cascade in Electron Magnetohydrodynamic Wave Packets
• Theory for helical turbulence under fast rotation
• Energy spectrum, dissipation and spatial structures in reduced Hall magnetohydrodynamic

Cited by in corpus (13)

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• Electron-scale reduced fluid models with gyroviscous effects
• Imbalanced kinetic Alfvén wave turbulence: from weak turbulence theory to nonlinear diffusion models for the strong regime
• MHD-kinetic transition in imbalanced Alfvénic turbulence
• Kinetic range spectral features of cross-helicity using MMS
• Exact scaling laws for helical three-dimensional two-fluid turbulent plasmas
• Fast magneto-acoustic wave turbulence and the Iroshnikov-Kraichnan spectrum
• -8/3 spectrum in kinetic Alfvén wave turbulence: implications for the solar wind
• Resistively controlled primordial magnetic turbulence decay
• Inverse cascade and magnetic vortices in kinetic Alfvén-wave turbulence
• Coexistence of weak and strong wave turbulence in incompressible Hall magnetohydrodynamics
• Wave Turbulence in Inertial Electron Magnetohydrodynamics