Dynamical Quenching of the $α^2$ Dynamo

George B. Field; Eric G. Blackman

doi:10.1086/340233

paper

Dynamical Quenching of the $α^{2}$ Dynamo

arXiv:astro-ph/0111470 · doi:10.1086/340233

Abstract

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 (2001), 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 $1/ k_{1}$ . 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), $α$ is resistively limited in the form predicted for the steady-state case. However, for $t << R_{M, 2}$ , $α$ 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 $α$ predicts substantial "fast" growth of large-scale field despite being "slow" at large times.

significantly revised, 21 pages, 6 new figs (figs. 1-5 in text, fig. 6 is separate), submitted to ApJ

Dynamical Quenching of the $α^{2}$ Dynamo

Abstract

References in corpus (3)

Cited by in corpus (81)

Dynamical Quenching of the α2 Dynamo

Abstract

References in corpus (3)

Cited by in corpus (81)

Dynamical Quenching of the $α^{2}$ Dynamo