Current Helicity and the Turbulent Electromotive Force

In a magnetofluid, magnetic and velocity fluctuations B ' and ν ' can generate a mean electromotive force along the mean magnetic field, which has been termed the alpha-effect. In the present paper the mathematical relationship between the alpha-effect and the mean current helicity of the fluctuations, ⟨ B ' · curl B '⟩, hitherto proven for the case that i) either the magnetic or the velocity fluctuations are statistically homogeneous and stationary, ii) the first-order smoothing approximation (FOSA) is valid, and iii) the mean flow, ⟨ ν ⟩, vanishes, is rederived, assuming the magnetic fluctuations to be stationary and the coupled magnetic-electric fluctuations to be homogeneous, but without using FOSA and allowing for a non-vanishing mean flow.