c © SAIt 2007 Memorie della Turbulent magnetic field averages for the

Abstract. Stokes parameters measured in the Solar atmosphere are in general time or space averages over a magnetic field probability distribution function. Here we show how to write the Zeeman propagation matrix in a reference frame defined with respect to the direction of a mean magnetic field and how to average over a random magnetic field distribution. We concentrate on the case of a normal Zeeman triplet but indicate how to treat general Zeeman patterns. Numerical results are presented for Gaussian distributions having cylindrical sym-metry about a mean field. Different models of probability distribution functions (PDF), are compared. Key words. line: formation – polarization – magnetic fields – turbulence – radiative transfer – Sun: atmosphere Observations and numerical simulations of magneto-convection show that the magnetic field in the solar atmosphere is highly intermit-tent down to scales which are much below the resolving power of modern telescopes. Thu