  We extend the standard two-scale theory of the turbulent dynamo coefficient
$\alpha$ to include the nonlinear back reaction of the mean field $\bar B$ on
the turbulence. We calculate the turbulent emf as a power series in $\bar B$,
assuming that the base state of the turbulence ($\bar B=0$) is isotropic, and,
for simplicity, that the magnetic diffusivity equals the kinematic viscosity.
The power series converges for all $\bar B$, and for the special case that the
spectrum of the turbulence is sharply peaked in $k$, our result is proportional
to a tabulated function of the magnetic Reynolds number $R_M$ and the ratio
$\beta$ of $\bar B$ (in velocity units) to the rms turbulent velocity $v_0$.
For $\beta\to 0$ (linear regime) we recover the results of Steenbeck et al.
(1966) as modified by Pouquet et al. (1976). For $R_M\gg 1$, the usual
astrophysical case, $\alpha$ starts to decrease at $\beta \sim 1$, dropping
like $\beta^{-2}$ as $\beta \to \infty$. Hence for large $R_M$, $\alpha$
saturates at $\bar B\sim v_0$, as estimated by Kraichnan (1979), rather than at
$\bar B\sim R^{-1/2}_Mv_0$, as inferred by Cattaneo and Hughes (1996) from
their numerical simulations at $R_M$=100. We plan to carry out simulations with
various values of $R_M$ to investigate the discrepency.
