Large- and small-scale interactions and quenching in an α2-dynamo

The evolution of the large-scale magnetic field in a turbulent flow of conducting fluid is considered in the framework of a multiscale alpha(2)-dynamo model, which includes the poloidal and the toroidal components for the large-scale magnetic field and a shell model for the small-scale magnetohydrodynamical turbulence. The conjugation of the mean-field description for the large-scale field and the shell formalism for the small-scale turbulence is based on strict conformity to the conservation laws. The model displays a substantial magnetic contribution to the alpha effect. It was shown that a large-scale magnetic field can be generated by current helicity even solely. The alpha quenching and the role of the magnetic Prandtl number (P-m) are studied. We have determined the dynamic nature of the saturation mechanism of dynamo action. Any simultaneous cross correlation of alpha and large-scale magnetic field energy E-B is negligible, whereas coupling between alpha and E-B becomes substantial for moderate time lags. An unexpected result is the behavior of the large-scale magnetic energy with variation of the magnetic Prandtl number. Diminishing of P-m does not have an inevitable ill effect on the magnetic field generation. The most efficient large-scale dynamo operates under relatively low Prandtl numbers-then the small-scale dynamo is suppressed and the decrease of P-m can lead even to superequipartition of the large-scale magnetic field (i.e., E-B > E-u). In contrast, the growth of P-m does not promote the large-scale magnetic field generation. A growing counteraction of the magnetic alpha effect reduces the level of mean large-scale magnetic energy at the saturated state.