  We present a two-scale approximation for the dynamics of a nonlinear
$\alpha^2$ dynamo. Solutions of the resulting nonlinear equations agree with
the numerical simulations of Brandenburg (2001), and show that $\alpha$ is
quenched by the buildup of magnetic helicity at the forcing scale $1/k_2$ as
the $\alpha$ effect transfers it from the large scale $1/k_1$. For times $t >
(k_1/k_2)R_{M,2}$ in eddy turnover units (where $R_{M,2}$ is the magnetic
Reynolds number of the forcing scale), $\alpha$ is resistively limited in the
form predicted for the steady-state case. However, for $t << R_{M,2}$, $\alpha$
takes on its kinematic value, independent of $R_{M,2}$, allowing the production
of large-scale magnetic energy equal to $k_1/k_2$ times equipartition. Thus the
dynamic theory of $\alpha$ predicts substantial "fast" growth of large-scale
field despite being "slow" at large times.

Astrophysics