Constraints on the magnitude of alpha in dynamo theory

We consider the back-reaction of the magnetic held on the magnetic dynamo c oefficients and the role of boundary conditions in interpreting whether num erical evidence for suppression is dynamical. If a uniform held in a period ic box serves as the initial condition for modeling the back-reaction on th e turbulent EMF, then the magnitude of the turbulent EMF, and thus the dyna mo coefficient a, have a stringent upper limit that depends on the magnetic Reynolds number R-M to a power of order -1. This is not a dynamic suppress ion but results just because of the imposed boundary conditions. In contras t, when mean held gradients are allowed within the simulation region, or no nperiodic boundary conditions are used, the upper limit is independent of R -M and takes its kinematic value. Thus only for simulations of the latter t ypes could a measured suppression be the result of a dynamic back-reaction. This is fundamental for understanding a long-standing controversy surround ing a suppression. Numerical simulations that do not allow any field gradie nts and invoke periodic boundary conditions appear to show a strong a suppr ession (e.g., Cattaneo & Hughes). Simulations of accretion disks that allow field gradients and allow free boundary conditions (Brandenburg & Donner) suggest a dynamo a that is not suppressed by a power of R-M Our results are consistent with both types of simulations.