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Non-local effects in the mean-field disc dynamo: I. An asymptotic expansion

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

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Abstract

We reconsider thin-disc global asymptotics for kinematic, axisymmetric mean-field dynamos with vacuum boundary conditions. Non-local terms arising from a small but finite radial field component at the disc surface are consistently taken into account for quadrupole modes. As in earlier approaches, the solution splits into a local part describing the field distribution along the vertical direction and a radial part describing the radial (global) variation of the eigenfunction. However, the radial part of the eigenfunction is now governed by an integro-differential equation whose kernel has a weak (logarithmic) singularity. The integral term arises from non-local interactions of magnetic fields at different radii through vacuum outside the disc. The non-local interaction can have a stronger effect on the solution than the local radial diffusion in a thin disc, however the effect of the integral term is still qualitatively similar to magnetic diffusion.


Publication metadata

Author(s): Priklonsky V, Shukurov A, Sokoloff D, Soward A

Publication type: Article

Publication status: Published

Journal: Geophysical and Astrophysical Fluid Dynamics

Year: 2000

Volume: 93

Issue: 1-2

Pages: 97-114

Print publication date: 01/01/2000

ISSN (print): 0309-1929

ISSN (electronic): 1026-7506

Publisher: Taylor & Francis

URL: http://dx.doi.org/10.1080/03091920008203723

DOI: 10.1080/03091920008203723


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