Printed in Great Britain The Role Function Theory of the Helicity Spectrum in Turbulent Dynamo

.I is shown that, for general homogeneous turbulence, the anti-symmetric part of the spectrum tensor can be expressed in terms of a single scalar function H(k,w) (the helicity spectrum function). Under the first-order smoothing approximation, the coefficients aij, Pi jk in the expansion of the mean electromotive force in terms of the mean magnetic field are determined; aij is a weighted integral of H(k,o), and j i j k contains a part which is likewise a weighted integral of H(k,o). When the turbulence is axisymmetric, p$l contains Radler’s (1969a) ‘‘Cl A J-effect”. It is shown that when the turbulence is statistically symmetric about a plane perpendicular to the axis of symmetry, then aij=O but the Radler effect is non-zero. Explicit expressions for aij and pi jk are given when the velocity field is generated by random forcing in a rotating medium. Finally, it is shown by means of a local analysis that the Radler effect, in conjunction with uniform mean shear, can give rise to non-oscillatory dynamo action, and it is argued that this effect may be significant in the well-mixed interior of a stellar convection zone, where by symmetry the a-effect may be weak. 1