Consequence of space correlation foliation for electron magnetohydrodynamic turbulence

Homogeneous electron magnetohydrodynamic turbulence is investigated under the presence of an imposed magnetic field. It is shown that this situation is well described in physical space by a divergence relation, which expresses the statistical conservation of magnetic energy flux through the inertial range. The ansatz is made that the development of anisotropy implies a foliation of space correlation with an algebraic relation between the axial and radial components of the separation vector r. A direct consequence is the possibility to derive a new universal law for the third-order moments, which is parametrized by the intensity of anisotropy. The so-called critical balance condition is used to fix this parameter and find a unique vectorial expression.