14 research outputs found
Non-local effects in the mean-field disc dynamo. II. Numerical and asymptotic solutions
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, in the disc plane at a
distance 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, , which is shown to persist in nonlinear
solutions where -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.Comment: Revised version, as accepted; Geophys. Astrophys. Fluid Dyna