Constraints on the Magnitude of α in Dynamo Theory

We consider the backreaction of the magnetic field on the magnetic dynamocoefficients and the role of boundary conditions in interpreting whethernumerical evidence for suppression is dynamical. If a uniform field in aperiodic box serves as the initial condition for modeling the backreaction onthe turbulent EMF, then the magnitude of the turbulent EMF and thus the dynamocoefficient $\a$, have a stringent upper limit that depends on the magneticReynolds number $R_M$ to a power of order -1. This is not a dynamic suppressionbut results just because of the imposed boundary conditions. In contrast, whenmean field gradients are allowed within the simulation region, or non-periodicboundary are used, the upper limit is independent of $R_M$ and takes itskinematic value. Thus only for simulations of the latter types could a measuredsuppression be the result of a dynamic backreaction. This is fundamental forunderstanding a long-standing controversy surrounding $\alpha$ suppression.Numerical simulations which do not allow any field gradients and invokeperiodic boundary conditions appear to show a strong $\alpha$ suppression (e.g.Cattaneo & Hughes 1996). Simulations of accretion discs which allow fieldgradients and allow free boundary conditions (Brandenburg & Donner 1997)suggest a dynamo $\alpha$ which is not suppressed by a power of $R_M$. Ourresults are consistent with both types of simulations.Comment: LaTex, version in press, Ap