On the generation of mean fields by small-scale electron magnetohydrodynamics turbulence

The problem of the generation of mean magnetic fields by small-scale turbulence within the framework of electron magnetohydrodynamics (EMHD) is considered. Two EMHD models are investigated, a two and one-half dimensional (2½D) model in which the magnetic field has all three spatial components but, due to a strong external field, depends only on two coordinates, and a fully three-dimensional (3D) model with an imposed stationary and homogeneous magnetic field. It is shown that in the case of 2½D turbulence two possible mechanisms are responsible for the generation of mean magnetic fields. The first one is similar to the a-effect in the MHD dynamo problem and is due to a nonzero helicity of the turbulence. The second one is related to the anisotropy of the turbulence, which can give rise to negative dissipation (resistivity, viscosity) of the mean field. The influence of electron inertia on the above effects is analyzed. Inertia results in a qualitative modification of the helicity effects and may lead to a change in sign of the turbulent viscosity. The criteria for the generation of mean magnetic fields are obtained. In the case of the 3D model, the generation of large-scale helicons by the small-scale helicon turbulence is studied within the framework of the adiabatic approximation. A closed set of equations for the evolution of both the magnetic field of the large-scale helicon and of the generalized action of the small-scale turbulence is obtained. The criterion for the resonant instability of a large-scale helicon due to its interaction with small-scale helicon turbulence is obtained