INTRODUCTION

The theory of linear, kinematic, mean field dynamos has been studied extensively since the pioneering paper by Parker (1955). In such dynamos, the mean magnetic field grows despite the action of resistivity through the combined action of small-scale, helical motions (α effect) and large-scale shear flows (ω effect). If the background state is time independent, the mean field evolves exponentially in time, and saturation of the field amplitude must occur through effects not included in the model.

Astrophysical systems typically have very low resistivities and correspondingly high magnetic Reynolds numbers Rm (of order 108–1010 in the Solar convection zone and 1018–1020 in the galactic disk). This raises a problem for dynamo theory: if the resistivity is assumed to be molecular, the fastest growing wavelengths are extremely short and it is difficult to see how large scale fields could be generated. Moreover, the resistivity plays a central role in the calculation of the a effect (e.g., Moffatt 1978). Most workers therefore assume that turbulent resistivity is present.