Wave turbulence in inertial electron magnetohydrodynamics - Laboratoire de Physique des Plasmas (LPP)
Journal Articles Journal of Plasma Physics Year : 2022

Wave turbulence in inertial electron magnetohydrodynamics

Abstract

A wave turbulence theory is developed for inertial electron magnetohydrodynamics (IEMHD) in the presence of a relatively strong and uniform external magnetic field $\boldsymbol {B_0} = B_0 \hat {\boldsymbol {e}}_\|$ . This regime is relevant for scales smaller than the electron inertial length $d_e$ . We derive the kinetic equations that describe the three-wave interactions between inertial whistler or kinetic Alfvén waves. We show that for both invariants, energy and momentum, the transfer is anisotropic (axisymmetric) with a direct cascade mainly in the direction perpendicular ( $\perp$ ) to $\boldsymbol {B_0}$ . The exact stationary solutions (Kolmogorov–Zakharov spectra) are obtained for which we prove the locality. We also found the Kolmogorov constant $C_K \simeq 8.474$ . In the simplest case, the study reveals an energy spectrum in $k_\perp ^{-5/2} k_\|^{-1/2}$ (with k the wavenumber) and a momentum spectrum enslaved to the energy dynamics in $k_\perp ^{-3/2} k_\|^{-1/2}$ . These solutions correspond to a magnetic energy spectrum ${\sim }k_\perp ^{-9/2}$ , which is steeper than the EMHD prediction made for scales larger than $d_e$ . We conclude with a discussion on the application of the theory to space plasmas.
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Dates and versions

hal-03817432 , version 1 (10-07-2024)

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Vincent David, Sébastien Galtier. Wave turbulence in inertial electron magnetohydrodynamics. Journal of Plasma Physics, 2022, 88 (5), pp.905880509. ⟨10.1017/S0022377822000976⟩. ⟨hal-03817432⟩
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