Non-local effects in the mean-field disc dynamo. I. An asymptotic expansion
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.
Keywords
Cite
@article{arxiv.astro-ph/0309666,
title = {Non-local effects in the mean-field disc dynamo. I. An asymptotic expansion},
author = {Vladimir Priklonsky and Anvar Shukurov and Dmitry Sokoloff and Andrew Soward},
journal= {arXiv preprint arXiv:astro-ph/0309666},
year = {2015}
}