Problems with kinematic mean field electrodynamics at high magnetic Reynolds numbers

Abstract

We discuss the applicability of the kinematic $\alpha$-effect formalism at high magnetic Reynolds numbers. In this regime the underlying flow is likely to be a small-scale dynamo, leading to the exponential growth of fluctuations. Difficulties arise with both the actual calculation of the $\alpha$ coefficients and with its interpretation. We argue that although the former may be circumvented -- and we outline several procedures by which the the $\alpha$ coefficients can be computed in principle -- the interpretation of these quantities in terms of the evolution of the large-scale field may be fundamentally flawed.

5 pages, LaTeX, no figures

References in corpus (2)

• Kinematic alpha effect in isotropic turbulence simulations
• Magnetic-field generation in helical turbulence

Cited by in corpus (28)

• Dynamo theories
• Shell Models of Magnetohydrodynamic Turbulence
• The Turbulent Dynamo
• Advances in mean-field dynamo theory and applications to astrophysical turbulence
• Zonal Flow Magnetic Field Interaction in the Semi-Conducting Region of Giant Planets
• Weak and Strong Field Dynamos: from the Earth to the stars
• Coarse-Grained Incompressible Magnetohydrodynamics: analyzing the turbulent cascades
• A Stochastically Forced Time Delay Solar Dynamo Model: Self-Consistent Recovery from a Maunder-like Grand Minimum Necessitates a Mean-Field Alpha Effect
• Magnetic field amplification in accretion discs around the first stars: implications for the primordial IMF
• Generation of large-scale magnetic fields by small-scale dynamo in shear flows
• A mean-field approach to the propagation of field patterns in stratified magneto rotational turbulence
• The alpha effect with imposed and dynamo-generated magnetic fields
• On Large-Scale Dynamo Action at High Magnetic Reynolds Number
• Self-consistent mean field MHD
• On the problem of large-scale magnetic field generation in rotating compressible convection
• The magnetic shear-current effect: generation of large-scale magnetic fields by the small-scale dynamo
• The kinetic helicity needed to drive large-scale dynamos
• The role of the Yoshizawa effect in the Archontis dynamo
• Modeling the Rise of Fibril Magnetic Fields in Fully Convective Stars
• Coherent nonhelical shear dynamos driven by magnetic fluctuations at low Reynolds numbers
• A Subgrid Turbulent Mean Field Dynamo Model for Cosmological Galaxy Formation Simulations
• The Turbulent Magnetic Diffusivity Tensor for Time-Dependent Mean Fields
• The alpha-effect in rotating convection: a comparison of numerical simulations
• A heuristic model for MRI turbulent stresses in Hall MHD
• The fate of alpha dynamos at large $Rm$
• Mean Field Electrodynamics: Triumphs and Tribulations
• Solar Magnetic Fields
• Saturation of turbulent helical dynamos