Non-equilibrium Hydromagnetic Dynamos

Preface Acknowledgements Author biography Symbols 1 The equations of magnetohydrodynamics 1.1 The Navier–Stokes equation—momentum balance 1.2 The induction equation—magnetic field evolution References 2 The essentials of mean-field turbulent dynamo theory 2.1 The turbulent electromotive force (EMF) 2.1.1 Production of fluctuational helicities 2.2 Effects of non-equilibrium turbulence in formation of the EMF—simplified picture References 3 Weak turbulence: effect of beating waves 3.1 Lehnert waves 3.2 Waves forced at two distinct frequencies 3.2.1 Mean EMF induced by forced beating waves 3.2.2 Dynamo action from beating waves 3.3 The effect of long-time oscillations of the α-effect and the turbulent magnetic diffusivity on magnetic energy evolution 3.3.1 Simple kinematic theory for homogeneous turbulence 3-19 3.3.2 Dynamic theory 3.3.3 Discussion 3.3.4 Nonlinear effects of the Lorentz force 3.4 Non-equilibrium dynamo effects in low-resistivity plasma of interstellar medium (ISM) and active galactic nuclei (AGN) References 4 The effect of nonlinear dynamics—weakly nonlinear renormalization group analysis 4.1 Dynamical equations 4.2 The α-effect in weak turbulence with weak seed field 4.2.1 Energy time evolution in weak turbulence 4.3 Renormalization procedure of the MHD equations 4.3.1 The recursion differential equations 4.3.2 Role of diffusivities 4.4 Mean field dynamics 4.4.1 Force-free mode, J ∝ B 4.5 Summary of main results References 5 Non-equilibrium turbulent dynamo from joint action and evolutional history of cross- and kinetic helicities 5.1 Outline of the TSDIA approach 5.1.1 The Green’s response functions 5.1.2 Statistical properties of the homogeneous and isotropic background turbulence 5.2 The large-scale electromotive force and the α-effect 5.2.1 Physical features of the non-equilibrium αX neq-effect 5.2.2 Further calculation of the αX neq-effect; Taylor (1921) ansatz for correlation functions 5.3 Coexistence of the kinetic and cross-helicities in turbulence 5.4 Summary References 6 Potential applications in tokamak research References