  In this paper we investigate the idea of Hanasz & Lesch 1993 that the
galactic dynamo effect is due to the Parker instability of magnetic flux tubes.
In addition to the former approach, we take into account more general physical
conditions in this paper, by incorporating cosmic rays and differential forces
due to the axisymmetric differential rotation and the density waves as well. We
present the theory of slender magnetic flux tube dynamics in the thin flux tube
approximation and the Lagrange description. This is the application of the
formalism obtained for solar magnetic flux tubes by Spruit (1981), to the
galactic conditions. We perform a linear stability analysis for the
Parker-shearing instability of magnetic flux tubes in galactic discs and then
calculate the dynamo coefficients. We present a number of new effects which are
very essential for cosmological and contemporary evolution of galactic magnetic
fields. First of all we demonstrate that a very strong dynamo $\alpha$-effect
is possible in the limit of weak magnetic fields in presence of cosmic rays.
Second, we show that the differential force resulting from axisymmetric
differential rotation and the linear density waves causes that the
$\alpha$-effect is essentially magnified in galactic arms and switched off in
the interarm regions. Moreover, we predict a non-uniform magnetic field in
spiral arms and well aligned one in interarm regions. These properties are well
confirmed by recent observational results by Beck & Hoernes (1996)
