  The principle of the Karlsruhe dynamo experiment is closely related to that
of the Roberts dynamo working with a simple fluid flow which is, with respect
to proper Cartesian co-ordinates x, y and z, periodic in x and y and
independent of z. A modified Roberts dynamo problem is considered with a flow
more similar to that in the experimental device. Solutions are calculated
numerically, and on this basis an estimate of the excitation condition of the
experimental dynamo is given. The modified Roberts dynamo problem is also
considered in the framework of the mean-field dynamo theory, in which the
crucial induction effect of the fluid motion is an anisotropic alpha-effect.
Numerical results are given for the dependence of the mean-field coefficients
on the fluid flow rates. The excitation condition of the dynamo is also
discussed within this framework. The behavior of the dynamo in the nonlinear
regime, i.e. with backreaction of the magnetic field on the fluid flow, depends
on the effect of the Lorentz force on the flow rates. The quantities
determining this effect are calculated numerically. The results for the
mean-field coefficients and the quantities describing the backreaction provide
corrections to earlier results, which were obtained under simplifying
assumptions.
