Dynamical Quenching of the α2Dynamo

We present a two-scale approximation for the dynamics of a nonlinear$\alpha^2$ dynamo. Solutions of the resulting nonlinear equations agree withthe numerical simulations of Brandenburg (2001), and show that $\alpha$ isquenched by the buildup of magnetic helicity at the forcing scale $1/k_2$ asthe $\alpha$ 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 magneticReynolds number of the forcing scale), $\alpha$ is resistively limited in theform 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 productionof large-scale magnetic energy equal to $k_1/k_2$ times equipartition. Thus thedynamic theory of $\alpha$ predicts substantial "fast" growth of large-scalefield despite being "slow" at large times.Comment: significantly revised, 21 pages, 6 new figs (figs. 1-5 in text, fig. 6 is separate), submitted to Ap