INTRODUCTION

An essential aspect of virtually all astrophysical magnetic dynamos is the role played by turbulent magnetic field diffusion. From the analytical perspective, discussions of turbulent diffusion have until recently been generally couched in the language of mean field theory, and in particular, within a kinematic context (cf. Moffatt 1978; Krause & Rädler 1980). Indeed, the great theoretical elegance of mean field electrodynamics, together with its attractive intuitiveness, have led to a situation where basic constructs of this theory, such as turbulent diffusion and the ‘α-effect’, have carried over into domains, such as numerical simulations, where their meaningfulness is not a priori obvious (cf. Glatzmaier 1985). In a recent series of papers, we have examined precisely the question of how such notions can be carried over into the nonlinear domain, and further have asked under what circumstances nonlinear effects are likely to matter (Vainshtein & Rosner 1991; Cattaneo & Vainshtein 1991; Vainshtein & Cattaneo 1992; Tao, Cattaneo & Vainshtein 1993).