Dependence of small-scale dynamo rates and scales on Kazantsev model parameters

Determine the quantitative dependence of the small-scale dynamo field amplification rate and the characteristic spatial scales of the generated magnetic field in the Kazantsev model on its key parameters, specifically the hydrodynamic Reynolds number Re, the magnetic Reynolds number Rm, and the magnetic Prandtl number Pm.

Background

The Kazantsev model describes kinematic small-scale dynamos through an equation for the magnetic-field correlation function with coefficients expressed via velocity correlation functions. Predicting growth rates and characteristic scales requires specifying these coefficients consistently with the full turbulence spectrum, which is nontrivial.

The paper notes that, in the broader literature, there remains uncertainty about how the field amplification rate and the characteristic scales of generated magnetic fields depend on key parameters such as the Reynolds numbers and magnetic Prandtl number. This uncertainty is linked to difficulties in specifying the Kazantsev equation’s coefficients from the turbulence spectrum and correlation functions.