Dynamical quenching of the α2 dynamo

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 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)(>1/k(2)). For times t>(k(1)/k(2))Re-M,Re-2 in eddy turnover units (where Re-M,Re-2 is the magnetic Reynolds number of the forcing scale), alpha is limited resistively in the form predicted for the steady state case. However, for tmuch less thanRe(M,2), alpha takes on its kinematic value independent of Re-M,Re-2, allowing the production of large-scale magnetic energy equal to k(1)/k(2) times equipartition. Thus, the dynamic theory of predicts substantial fast growth of a large-scale field despite being slow at large times.