Magnetic field generation by non-Gaussian, non-random turbulent motion

It is well known that a turbulent velocity field generates perturbations of the electric current and magnetic field that, under certain conditions, may generate an average,large-scale magnetic field. Such generation process is of great importance to account for the generation of large-scale magnetic fields in stars, planetary and laboratory plasmas. Traditionally, one attacks this generation process theoretically by assuming a random velocity field with near-Gaussian fluctuations. This simplifying ansatz allows to express the effective electromotive force appearing in Faraday's law in terms of a piece that is proportional to the large-scale magnetic field itself (the so-called $\alpha$-term), and a second one that is proportional to its curl (the $\beta$ term), if certain conditions regarding the symmetry of the system are met. Physically, the $\alpha$-term represents a measure of the mean helicity of the turbulent flow. The $\beta$-term, an enhanced magnetic diffusivity. In this contribution, we depart form this traditional view and explore instead the consequences of considering Levy-distributed, Lagrangianly-correlated velocity fields, that have been currently identified as of relevance in regimes of near-marginal turbulence or in the presence of strong, stable sheared flows