Dynamical Quenching of the $α^2$ Dynamo

Details Dynamical Quenching of the $α^2$ Dynamo Dynamical Quenching of the $α^2$ Dynamo

2001-11-25

arxiv.org/abs/astro-ph/0111470v2

Astrophys.J. 572 (2002) 685

Astronomy and Astrophysics

Astrophysics

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

Scientific paper

10.1086/340233

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.

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