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Abstract
Numerous studies of magnetic fluctuations with a zero mean-field for small magnetic Prandtl numbers (Prm ≪ 1) show that magnetic fluctuations cannot be generated by turbulent fluid flow with the Kolmogorov energy spectrum. In addition, the generation of magnetic fluctuations with a zero mean-field for Prm ≪ 1 were not observed in numerical simulations. However, in astrophysical plasmas the magnetic Prandtl numbers are small and magnetic fluctuations are observed. Thus a mechanism of generation of magnetic fluctuations for Prm ≪ 1 still remains poorly understood. On the other hand, in astrophysical applications (e.g., solar and stellar convection zones, galaxies, accretion disks) the turbulent velocity field cannot be considered as a divergence-free.
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