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.

湍流的水磁发电机是通过导电流体（等离子，铁水等）的混沌流动而产生磁场的过程。它负责产生天体物体（例如行星，恒星，吸积盘，星系，星系团等）的大范围磁场。特别是大范围磁场的动力学过程是强非线性的，并且洛伦兹的力量至关重要。此处进行分析的目的是为快速旋转极限中的大型电动势（EMF）提供解析表达式，其中包括两种类型的非线性-洛伦兹力的影响（迄今很少考虑）和湍流波动的非线性演化。