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Asymptotic solutions for mean-field slab dynamos

Lookup NU author(s): Yameng Ji, Laura Cole, Dr Paul Bushby, Professor Anvar Shukurov

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).


Abstract

We discuss asymptotic solutions of the kinematic alpha-omega dynamo in a thin disc (slab) surrounded by an electric insulator. Focussing upon the strong dynamo regime, in which the dynamo number D satisfies |D|>>1, we resolve uncertainties in the earlier treatments and conclude that some of the simplifications that have been made in previous studies are questionable. Having abandoned these simplifications, we show, by comparing numerical solutions with complementary asymptotic results obtained for |D|>>1 and |D|<<1, that the asymptotic solutions give a reasonably accurate description of the dynamo even far beyond their formal ranges of applicability. Indeed, our results suggest a simple analytical expression for the growth rate of the mean magnetic field that remains accurate across the wide range of values for D that are typical of spiral galaxies and accretion discs. Finally, we analyse the role of various terms in the governing equations to clarify the fine details of the dynamo process. In particular, in the case of the radial magnetic field equation we have shown that the alpha dB_phi/dz term (where B_phi is the azimuthal magnetic field, alpha is the mean-field dynamo coefficient, and z is measured across the slab), which is neglected in some of the earlier asymptotic studies, is essential for the dynamo as it drives a flux of magnetic energy away from the dynamo region, towards the surface of the slab.


Publication metadata

Author(s): Ji Y, Cole L, Bushby P, Shukurov A

Publication type: Article

Publication status: Published

Journal: Geophysical and Astrophysical Fluid Dynamics

Year: 2014

Volume: 108

Issue: 5

Pages: 568-583

Online publication date: 21/05/2014

Acceptance date: 19/01/2014

Date deposited: 01/10/2015

ISSN (print): 0309-1929

ISSN (electronic): 1029-0419

Publisher: Taylor & Francis

URL: http://dx.doi.org/10.1080/03091929.2014.898757

DOI: 10.1080/03091929.2014.898757


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