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The principle of the Karlsruhe dynamo experiment is closely related to thatof the Roberts dynamo working with a simple fluid flow which is, with respectto proper Cartesian co-ordinates x, y and z, periodic in x and y andindependent of z. A modified Roberts dynamo problem is considered with a flowmore similar to that in the experimental device. Solutions are calculatednumerically, and on this basis an estimate of the excitation condition of theexperimental dynamo is given. The modified Roberts dynamo problem is alsoconsidered in the framework of the mean-field dynamo theory, in which thecrucial induction effect of the fluid motion is an anisotropic alpha-effect.Numerical results are given for the dependence of the mean-field coefficientson the fluid flow rates. The excitation condition of the dynamo is alsodiscussed within this framework. The behavior of the dynamo in the nonlinearregime, i.e. with backreaction of the magnetic field on the fluid flow, dependson the effect of the Lorentz force on the flow rates. The quantitiesdetermining this effect are calculated numerically. The results for themean-field coefficients and the quantities describing the backreaction providecorrections to earlier results, which were obtained under simplifyingassumptions.Comment: 12 pages, 9 figures, accepted for publication in Phys. Rev.

Contributions to the theory of a two-scale homogeneous dynamo experiment