Dynamical Quenching of the α²Dynamo

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