Abstract
We formulate a solvable model that describes the generation and saturation of a mean magnetic field in a dynamo with kinetic helicity, in the limit of a 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 by balancing the viscous and Lorentz stresses in the MHD Navier-Stokes equation. The model provides an analytical explanation for previously obtained numerical results.
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