X iv : a st ro - p h / 01 11 47 0 v 1 2 5 N ov 2 00 1 Quenching of the α - effect in Dynamo Theory
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چکیده
We use the formalism of Pouquet, Frisch and Léorat (hereafter PFL, 1976) to investigate time dependent quenching of α in mean field dynamo theory for a closed system. Quenching occurs as the result of an α induced flow of magnetic helicity from small to large scales. Our results agree reasonably well with with the numerical simulations of Brandenburg (2001ab). Gruzinov and Diamond (hereafter GD, 1994, 1995, 1996) and Bhattacharjee and Yuan (hereafter BY, 1995) also used the conservation of magnetic helicity to argue that α in a closed steady-state system is quenched for strongly subequipartition mean field strengths. Taken at face value, we find that the GD and BY results need to be reinterpreted when time dependence and turbulent diffusivity are included; then, quenching occurs only when the mean field reaches near equipartition. In the special case where the scale of the mean
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