Non-local effects in the mean-field disc dynamo I. An asymptotic expansion |
| |
Authors: | Vladimir Priklonsky Anvar Shukurov Dmitry Sokoloff Andrew Soward |
| |
Affiliation: | 1. Department of Physics , Moscow University , Moscow, 119899, Russia;2. Department of Mathematics , University of Newcastle , Newcastle, upon Tyne, NE1 7RU, UK;3. School of Mathematical Sciences, University of Exeter , Exeter, EX4 4QE, UK |
| |
Abstract: | 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: | Mean-field dynamos Thin-disc asymptotics Boundary conditions Galactic magnetic fields |
|
|