we could not recover magnetic helicity conservation as above. This provides another check that we have indeed got the relative sign of these terms right. Also from the same argument, we note that one cannot have non-zero additions to the alpha term in the $r\to 0$ limit (the $-4aH(0,t)$ term in $\alpha_N$) without a corresponding addition to the diffusion term (the $2aM_L(0,t)$ term in $\kappa_N$).

We now consider §me of the implications of these equations for the evolution of small-scale fields.

 Kinematic evolution of $M_L$ and the small-scale dynamo
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We begin by first studying the kinematic evolution of $M_L$, ignoring the effects of the nonlinear coupling terms due to ambipolar drift. In particular we consider the small-scale dynamo in galactic turbulence with a model Kolmogorov spectrum. The results obtained in this section will be used to set the framework for Paper I. It also extends the analysis of the small-scale dynamo, due to turbulence with a single scale (cf. Zeldovich [*et al.*]{} (1983), Kleeorin [*et al.*]{} (1986)) to the situation when a range of scales are present.

First we note that in many contexts the coupling term $\alpha_N H$, due to helicity fluctuations of the velocity, has negligible influence 