Problems with kinematic mean field electrodynamics at high magnetic Reynolds numbers

We discuss the applicability of the kinematic $\alpha$-effect formalism at high magnetic Reynolds numbers. In this regime the underlying flow is likely to be a small-scale dynamo, leading to the exponential growth of fluctuations. Difficulties arise with both the actual calculation of the $\alpha$ coefficients and with its interpretation. We argue that although the former may be circumvented -- and we outline several procedures by which the the $\alpha$ coefficients can be computed in principle -- the interpretation of these quantities in terms of the evolution of the large-scale field may be fundamentally flawed.