Wave turbulence in inertial electron magnetohydrodynamics

A wave turbulence theory is developed for inertial electron magnetohydrodynamics (IEMHD) in the presence of a relatively strong and uniform external magnetic field B-0 = B-0(e) over cap parallel to. 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 Alfven waves. We show that for both invariants, energy and momentum, the transfer is anisotropic (axisymmetric) with a direct cascade mainly in the direction perpendicular (perpendicular to) to 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 similar or equal to 8.474. In the simplest case, the study reveals an energy spectrum in k(perpendicular to)(-5/2) k(parallel to)(-1/2) (with k the wavenumber) and a momentum spectrum enslaved to the energy dynamics in k(perpendicular to)(-3/2) k(parallel to)(-1/2). These solutions correspond to a magnetic energy spectrum similar to k(perpendicular to)(-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.

Automated summary

A wave turbulence theory is developed for inertial electron magnetohydrodynamics (IEMHD) in the presence of a relatively strong and uniform external magnetic field. The study shows that the transfer of energy and momentum in this regime is anisotropic with a direct cascade mainly in the direction perpendicular to the external magnetic field. The exact stationary solutions and the Kolmogorov constant are obtained, and the application of the theory to space plasmas is discussed.