A Self-Consistent Treatment of the Electromotive Force in Magnetohydrodynamics for Large Diffusivities

The coupled equations that describe the effect of large-scale magnetic and velocity fields on forced high-diffusivity magnetohydrodynamic flows are investigated through an extension of mean field electrodynamics. Our results generalise those of R"adler & Brandenburg (2010), who consider a similar situation but assume that the effect of the Lorentz force on the momentum equation can be neglected. New mean coupling terms are shown to appear, which can lead to large-scale growth of magnetic and velocity fields even when the usual $\alpha$-effects are absent.