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" problem: to what degree does the mean magnetic field suppress the turbulent dynamo coefficients that are needed to drive its growth? The answer will ultimately derive from a combination of numerical and analytical studies. Here we show that analytic approaches to the dynamo and back-reaction problems require one to separate turbulent quantities into two components: those influenced by the mean field (which are therefore anisotropic) and those independent of the mean field (and are therefore isotropic), no matter how weak the mean field is. Upon revising the standard formalism to meet this requirement, we find the following: (1) The two types of components often appear in the same equation, so that standard treatments, which do not distinguish between 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 α-coefficient is actually independent of the mean field and therefore cannot be interpreted as a quenching.