Anisotropic weak whistler wave turbulence in electron magnetohydrodynamics

Abstract

A weak wave turbulence theory is given for electron magnetohydrodynamics in the presence of a strong and uniform external magnetic field. Using helicity decomposition, the wave kinetic equations for energy and magnetic helicity are derived at the level of three-wave interactions between whistler waves. It is shown that nonlinear interactions of whistler waves transfer energy and magnetic helicity mainly in the direction perpendicular to the external magnetic field. The anisotropic turbulence thus generated has exact stationary power law solutions which scale as k⊥−5/2k∥−1/2 for the energy spectrum and k⊥−7/2k∥−1/2 for the magnetic helicity spectrum.