Resolution of an ambiguity in dynamo theory and its consequences for back-reaction studies

An unsolved problem in turbulent dynamo theory is the "back-reaction" probl em: to what degree does the mean magnetic held suppress the turbulent dynam o coefficients that are needed to drive its growth? The answer will ultimat ely derive from a combination of numerical and analytical studies. Here we show that analytic approaches to the dynamo and back-reaction problems requ ire one to separate turbulent quantities into two components: those influen ced by the mean field (which are therefore anisotropic) and those independe nt of the mean held (and are therefore isotropic), no matter how weak the m ean field is. Upon revising the standard formalism to meet this requirement , we find the following: (1) The two types of components often appear in th e same equation, so that standard treatments, which do not distinguish betw een them, are ambiguous. (2) The usual first-order smoothing approximation that is necessary to make progress in the standard treatment is unnecessary when the distinction is made. (3) In contrast to previous suggestions, the current helicity correction to the dynamo alpha-coefficient is actually in dependent of the mean held and therefore cannot be interpreted as a quenchi ng.