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Non-local effects in the mean-field disc dynamo: II - Numerical and asymptotic solutions

Lookup NU author(s): Ashley Willis, Professor Anvar Shukurov, Professor Andrew Soward, Professor Dmitry Sokoloff

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Abstract

The thin-disc global asymptotics are discussed for axisymmetric mean-field dynamos with vacuum boundary conditions allowing for non-local terms arising from a finite radial component of the mean magnetic field at the disc surface. This leads to an integro-differential operator in the equation for the radial distribution of the mean magnetic field strength, Q(r) in the disc plane at a distance r from its centre; an asymptotic form of its solution at large distances from the dynamo active region is obtained. Numerical solutions of the integro-differential equation confirm that the non-local effects act similarly to an enhanced magnetic diffusion. This leads to a wider radial distribution of the eigensolution and faster propagation of magnetic fronts, compared to solutions with the radial surface field neglected. Another result of non-local effects is a slowly decaying algebraic tail of the eigenfunctions outside the dynamo active region, Q(r) ∼ r-4, which is shown to persist in non-linear solutions where α-quenching is included. The non-local nature of the solutions can affect the radial profile of the regular magnetic field in spiral galaxies and accretion discs at large distances from the centre. © 2004 Taylor and Francis Ltd.


Publication metadata

Author(s): Willis AP, Shukurov A, Soward AM, Sokoloff D

Publication type: Article

Publication status: Published

Journal: Geophysical and Astrophysical Fluid Dynamics

Year: 2004

Volume: 98

Issue: 4

Pages: 345-363

Print publication date: 01/08/2004

ISSN (print): 0309-1929

ISSN (electronic): 1026-7506

Publisher: Taylor & Francis

URL: http://dx.doi.org/10.1080/03091920410001700797

DOI: 10.1080/03091920410001700797


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