Small-scale turbulent dynamo

Kinematic dynamo theory is presented here for turbulent conductive fluids. We describe how inhomogeneous magnetic fluctuations are generated below the viscous scale of turbulence where the spatial smoothness of the velocity p ermits a systematic analysis of the Lagrangian path dynamics. We find analy tically the moments and multipoint correlation functions of the magnetic fi eld at small yet finite magnetic diffusivity. We show that the fil:ld is co ncentrated in long narrow strips and describe anomalous scalings and angula r singularities of the multipoint correlation functions which are manifesta tions of the field's intermittency. The growth rate of the magnetic field i n a typical realization is found to be half the difference of two Lyapunov exponents of the same sign.