  I construct a complete asymptotic expansion of solutions to the problem of
linear stability of three-dimensional steady space-periodic magnetohydrodynamic
states to perturbations involving large periods. Eddy diffusivity tensor is
derived for parity-invariant steady states. I present numerical evidences that
if perturbations of the flow are permitted, then the effect of negative eddy
diffusivity emerges at much larger magnetic molecular diffusivities than in the
kinematic dynamo problem (where no perturbations of the flow are assumed).
