  Two different approaches to the Roberts dynamo problem are considered.
Firstly, the equations governing the magnetic field are specified to both
harmonic and subharmonic solutions and reduced to matrix eigenvalue problems,
which are solved numerically. Secondly, a mean magnetic field is defined by
averaging over proper areas, corresponding equations are derived, in which the
induction effect of the flow occurs essentially as an anisotropic alpha-effect,
and they are solved analytically. In order to check the reliability of the
statements on the Karlsruhe experiment which have been made on the basis of a
mean-field theory, analogous statements are derived for a rectangular dynamo
box containing 50 Roberts cells, and they are compared with the direct
solutions of the eigenvalue problem mentioned. Some shortcomings of the simple
mean-field theory are revealed.
