Role of galactic disc thickness in magnetic field generation

A large variety of galaxies have magnetic structures of lengthscales comparable with their radius. Theoretically, their existence is based on the dynamo mechanism. It is based on alpha-effect characterizing helicity of the turbulent motions and differential rotation which is connected with changing angular velocity. The field can be destroyed by turbulent diffusion, so the mechanism is threshold and can be realized only for the case when first and second effect are more intensive than the third one. Equations of magnetohydrodynamics that are used to describe the dynamo mechanism, are too difficult to be solved. So, usually different approximation taking into account details of astrophysical objects are used. As for galaxies, a thin disc approximation has been developed. It works properly for galactic objects with small half-thickness. However, as for thick discs we should take a model which uses more complicated structure of the field. Here we find the threshold for the field generation for thick astrophysical discs.