Published online by Cambridge University Press: 19 July 2016
A concept of mean-field models of galactic dynamos is explained in which α-effect and differential rotation act in an infinite slab of electrically conducting fluid surrounded by free space or by conducting matter at rest. Some results for α2 -dynamos are presented. In the limiting case in which the α-coefficient does not depend on the radius, axisymmetric and non-axisymmetric magnetic fields can be maintained with equal ease. For reasonable α-distributions a preference of axisymmetric fields is suggested as long as an isotropic α-effect is considered but it may disappear with anisotropic α-effect. The effect of differential rotation, which allows αω-dynamos, is briefly discussed.