The galactic dynamo effect due to Parker-shearing instability of magnetic flux tubes I. General formalism and the linear approximation

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 accountmore 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 Parkershearing 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 α-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 α-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)