  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.
