On the mean-field theory of the Karlsruhe dynamo experiment I. Kinematic theory

K.-H. Rädler - M. Rheinhardt - E. Apstein - H. Fuchs

Astrophysical Institute Potsdam, An der Sternwarte 16, D-14482 Potsdam, Germany

Abstract
In the Forschungszentrum Karlsruhe an experiment has been constructed which demonstrates a homogeneous dynamo as to be expected in the Earth's interior. This experiment is discussed within the framework of mean-field dynamo theory. In this paper the mean-field concept is defined and elaborated for the relevant types of fluid flows, and mean-field dynamo models reflecting essential features of the experimental device are investigated. The crucial induction effect is an anisotropic α-effect, which is calculated in its dependence on the parameters of the fluid flow. On this basis the self-excitation condition of the dynamo and the structure of the magnetic field occurring in the kinematic limit are determined. These results are compared with the experimental results. In a following paper the back-reaction of the magnetic field on the fluid flow is taken into account and the saturation of the dynamo is considered. Tables 5, Figs 22, Refs 37.