How Fast Can Magnetic Fields Be Amplified By Turbulence?

Magnetic fields are observed very early in the evolution of structure of the universe. It is not known how or when these fields were created. I will discuss the various theories of the field origin. These theories challenge our present understanding of Magnetohydrodynamic turbulence. A central theoretical question is: how fast can magnetic field be amplified by dynamo action. This question is of interest in many astrophysical situations -- from the sun to galaxy clusters. Small scale fields of observable amplitudes may be created on short time-scales by turbulent flows or compact objects.
The central issue is the creation of the observed long scale coherence in the field. I will discuss how dissipation scale dynamics cannot be ignored. Indeed, it is still not clear which aspects of MHD turbulence are universal and which are problem specific.