### Abstract

Magnetic fields in astrophysics are generated by the inductive action of turbulence in the conducting fluid medium. This turbulence is usually generated by buoyancy forces and strongly influenced by coriolis effects, and in consequence 'lacks reflexional symmetry'; in particular, the mean helicity is nonzero, i.e. there is a correlation between velocity and vorticity fields. This property in general leads to an 'alpha-effect' in the fluid, whereby magnetic field grows on length-scales large compared with the dominant energy-containing scale of the turbulence. At the same time, the turbulent diffusivity controls the growth of the field. The primary problem of mean-field dynamo theory is to obtain reliable expressions for alpha and for the turbulent diffusivity in terms of the statistical properties and the magnetic Reynolds number of the turbulence. The first lecture will be concerned with this problem.

The second lecture will focus on dynamic back-reaction effects: as the magnetic field grows by turbulent dynamo action, the Lorentz force ultimately modifies the turbulence tending to reduce both alpha and turbulent diffusivity, until some kind of equilibrium is established, this equilibrium depending on the mechanism by which energy is supplied to the turbulence. Some aspects of this problem, which is the subject of much current debate, will be considered.