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 their interpretation. We argue that although the former may be circumvented - and we outline several procedures by which 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.