INTRODUCTION

The nature of turbulent magnetic diffusion and the α-effect has been a puzzle for several decades. Until recently, virtually all the work in this subject has been based on analytical theory, but the advent of ready access to supercomputers now allows us to address the question of turbulent magnetic diffusion and the turbulent α-effect from the perspective of numerical experiments. In this paper, we shall describe numerical simulations of an idealized model of mean field dynamos.

In order to understand how fields are generated, the mean field theoretical approach is widely used (see Moffatt 1978). This two-scaled approach conveniently parametrizes the effects of small scale turbulence on large scale fields into two coefficients, α and β. The central problem of mean field electrodynamics is to calculate these transport coefficients from the statistical properties of the flow and the magnetic diffusivity, η. Explicit in these calculations is that the fluid flow is not affected by the presence of magnetic fields.

In typical magnetofluid circumstances, this is assumed to be the case, unless the magnetic energy of the large scale component is comparable to the energy in the flow. Recent two-dimensional simulations suggest that this is not the case and that turbulent diffusivity can be severely suppressed even when the mean field is less than the equipartition field value (see Cattaneo & Vainshtein 1991).