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