Topological constraints associated with fast dynamo action

Author:

Moffatt H. K.,Proctor M. R. E.

Abstract

The conjecture of Vainshtein & Zel'dovich (1972) concerning the existence of a fast dynamo (i.e. one whose growth rate is independent of magnetic diffusivity η in the limit η → 0) is discussed with particular reference to (i) the stretch–twist–fold cycle which can double the strength of a magnetic flux tube, and (ii) the space-periodic Beltrami flow of maximal helicity, which has been shown to be capable of space-periodic dynamo action with the same period as the velocity field, by Arnold & Korkina (1983) and by Galloway & Frisch (1984). The topological constraint associated with conservation of magnetic helicity is shown to preclude fast dynamo action unless the scale of the magnetic field is almost everywhere of order η½ as η → 0; in this case, the field structure is severely singular in the limit. A steady incompressible velocity field, quadratic in the space variables, is shown to mimic the action of the stretch–twist–fold cycle, and is proposed as a plausible candidate for fast dynamo action.

Publisher

Cambridge University Press (CUP)

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Reference23 articles.

1. Parker, E. N. 1955 The formation of sunspots from the solar toroidal field.Astrophys. J. 121,491–507.

2. Zel'Dovich, Ya. B. , Ruzmaikin, A. A. & Sokoloff, D. D. 1983 Magnetic Fields in Astrophysics .Gordon & Breach.

3. Woltjer, L. 1958 A theorem on force-free magnetic fields.Proc. Natl Acad. Sci. 44,489–491.

4. Small-scale variation of convected quantities like temperature in turbulent fluid Part 1. General discussion and the case of small conductivity

5. Steenbeck, M. , Krause, F. & Rädler, K.-H. 1966 A calculation of the mean electromotive force in an electrically conducting fluid in turbulent motion under the influence of Coriolis forces (in German).Z. Naturforsch.21a,369–376.

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