It is well known that the magnetic and the velocity field fluctuations in the solar wind possess many features expected of fully developed magnetohydrodynamic (MHD) turbulence. However, for frequencies higher than 0.1 Hz the situation is different and clear discrepancies have been recently observed with, for example, a steepening of the magnetic fluctuation power law spectrum. In order to give a satisfactory description of the high frequency solar wind it is necessary to adopt a new description like the electron MHD approximation in which the dynamics is entirely governed by electrons. In that context, we review and discuss recent theoretical results obtained in anisotropic whistler wave turbulence for electron MHD 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 for the energy spectrum and for the magnetic helicity spectrum. A strong analogy is found with the problem of rotating turbulence for incompressible neutral flows which share almost all the same properties.
Anomalous resistivity and viscosity due to small-scale magnetic turbulence