  We consider the backreaction of the magnetic field on the magnetic dynamo
coefficients and the role of boundary conditions in interpreting whether
numerical evidence for suppression is dynamical. If a uniform field in a
periodic box serves as the initial condition for modeling the backreaction on
the turbulent EMF, then the magnitude of the turbulent EMF and thus the dynamo
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 suppression
but results just because of the imposed boundary conditions. In contrast, when
mean field gradients are allowed within the simulation region, or non-periodic
boundary are used, the upper limit is independent of $R_M$ and takes its
kinematic value. Thus only for simulations of the latter types could a measured
suppression be the result of a dynamic backreaction. This is fundamental for
understanding a long-standing controversy surrounding $\alpha$ suppression.
Numerical simulations which do not allow any field gradients and invoke
periodic boundary conditions appear to show a strong $\alpha$ suppression (e.g.
Cattaneo & Hughes 1996). Simulations of accretion discs which allow field
gradients and allow free boundary conditions (Brandenburg & Donner 1997)
suggest a dynamo $\alpha$ which is not suppressed by a power of $R_M$. Our
results are consistent with both types of simulations.
