MAGNETIC FLUCTUATIONS FOR SMALL MAGNETIC PRANDTL NUMBERS

Numerous studies of magnetic fluctuations with a zero mean-field for s nail magnetic Prandtl numbers (Pr-m << 1) show that magnetic fluctuati ons cannot be generated by turbulent fluid pow with the Kolmogorov ene rgy spectrum. In addition, the generation of magnetic fluctuations wit h a zero mean-field for Pr-m << 1 were not observed in numerical simul ations. However, in astrophysical plasmas the magnetic Prandtl numbers are small and magnetic fluctuations are observed. Thus a mechanism of generation of magnetic fluctuations for Pr-m << 1 still remains poorl y understood. On the other hand, in astrophysical applications (e.g., solar and stellar convection zones, galaxies, accretion disks) the tur bulent velocity field cannot be considered as a divergence-free. The g eneration of magnetic fluctuations by turbulent pow of conducting flui d with a zero mean magnetic field for Pr-m << 1 is studied by means of linear and nonlinear analysis. The turbulent fluid velocity field is assumed to be homogeneous and isotropic with a power law energy spectr um (proportional to k(-p)) and with a very short scale-dependent corre lation time. It is found that magnetic fluctuations can be generated w hen the exponent p > 3/2. It is shown also that the growth rates of th e higher moments of the magnetic field are larger than those of the lo wer moments, i.e., the spatial distribution of the magnetic field is i ntermittent. In addition, the effect of compressibility (i.e., del . u not equal 0) of the low-Mach-number turbulent fluid flow u is studied . It is demonstrated that the threshold for the generation of magnetic fluctuations by turbulent fluid flow with del . u not equal 0 is high er than that for incompressible fluid. This implies that the compressi bility impairs the generation of magnetic fluctuations. Nonlinear effe cts result in saturation of growth Of the magnetic fluctuations. Asymp totic properties of the steady state solution for the second moment of the magnetic field in the case of the Hall nonlinearity, for the low- Mach-number compressible pow are studied.