functions (see below). Kazantsev (1968) derived the equations for the longitudinal correlations in homogeneous, isotropic , Markovian turbulence, without mean helicity, using a diagrammatic approach. Vainshtein and Kitchatinov (1986) incorporated the effects of helicity, and derived equations for both helical and longitudinal correlations. They did not however give details of the algebra. We therefore first rederive these equations here, in a fairly transparent manner. Our work generalises the Kazantsev equations to helical turbulence, and corrects a sign error of Vainshtein and Kitchatinov (1986) in the helical terms, which could be important for understanding the back reaction of the small-scale field on the alpha effect (see below).

The above mentioned works on small-scale field dynamics were also purely kinematic. As the field grows one expects the back reaction due to the Lorentz force to become important. The full MHD problem, involving both the Euler and induction equation, presents a formidable challenge, which we do not take up here. However in order to get a first look at the effect of nonlinearities, we consider a simpler nonlinear modification to the velocity field due to the generated magnetic field, as would obtain for example in a partially ionised medium. Note that the gas 