  The exploration of mean-field galactic dynamos affected by a galactic spiral
pattern, begun in Chamandy et al. (2013, hereafter Paper I) with numerical
simulations, is continued here with an asymptotic solution. The mean-field
dynamo model used generalizes the standard theory to include the delayed
response of the mean electromotive force to variations of the mean magnetic
field and turbulence parameters (the temporal non-locality, or {\tau} effect).
The effect of the spiral pattern on the dynamo considered is the enhancement of
the {\alpha}-effect in spiral-shaped regions (which may overlap the gaseous
spiral arms or be located in the interarm regions). The axisymmetric and
enslaved non-axisymmetric modes of the mean magnetic field are studied
semi-analytically to clarify and strengthen the numerical results. Good
qualitative agreement is obtained between the asymptotic solution and numerical
solutions of Paper I for a global, rigidly rotating material spiral (density
wave). At all galactocentric distances except for the co-rotation radius, we
find magnetic arms displaced in azimuth from the {\alpha}-arms, so that the
ridges of magnetic field strength are more tightly wound than the
{\alpha}-arms. Moreover, the effect of a finite dynamo relaxation time {\tau}
(related to the turbulence correlation time) is to phase-shift the magnetic
arms in the direction opposite to the galactic rotation even at the co-rotation
radius. This mechanism can be used to explain the phase shifts between magnetic
and material arms observed in some spiral galaxies.
