Renormalization group analysis of the turbulent hydromagnetic dynamo: Effect of anisotropy

Abstract

The turbulent hydromagnetic dynamo is a process of magnetic field generation by chaotic flow of an electrically conducting fluid (plasma, liquid iron etc.). It is responsible for generation of large-scale magnetic fields of astrophysical objects such as planets, stars, accretion discs, galaxies, galaxy clusters etc. In particular, the dynamical process of induction of large-scale fields is strongly nonlinear and the effect of the Lorentz force is crucial. The aim of the analysis presented here is to provide analytic expressions for the large-scale electromotive force (EMF) in the limit of rapid rotation, with inclusion of both types of nonlinearities - the effect of the Lorentz force (hitherto scarcely considered) and the nonlinear evolution of turbulent fluctuations. The renormalization group technique is applied to extract the final expression for the mean EMF from the full nonlinear dynamical equations (Navier-Stokes, induction equation) and the mean-field equations are studied in order to demonstrate amplification and saturation of the mean magnetic field in two simplifying limits, that is the limit of a thin disc and a limit of a narrow spherical gap.