A Solvable Model for Nonlinear Mean Field Dynamo

Abstract

We formulate a solvable model that describes generation and saturation of mean magnetic field in a dynamo with kinetic helicity, in the limit of large magnetic Prandtl number. This model is based on the assumption that the stochastic part of the velocity field is Gaussian and white in time (the Kazantsev-Kraichnan ensemble), while the regular part describing the back reaction of the magnetic field is chosen from balancing the viscous and Lorentz stresses in the MHD Navier-Stokes equation. The model provides an analytical explanation for previously obtained numerical results.

6 pages

Cited by in corpus (10)

• Simulations of small-scale turbulent dynamo
• Dynamo theories
• On magnetic field generation in Kolmogorov turbulence
• The Turbulent Dynamo
• Spectra and Growth Rates of Fluctuating Magnetic Fields in the Kinematic Dynamo Theory with Large Magnetic Prandtl Numbers
• The small-scale structure of magnetohydrodynamic turbulence with large magnetic Prandtl numbers
• Magnetic-field generation in helical turbulence
• Models of magnetic-field evolution and effective viscosity in weakly collisional extragalactic plasmas
• The turbulent dynamo as an instability in a noisy medium
• Kazantsev model in nonhelical 2.5D flows