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

Harmonic and subharmonic solutions of the Roberts dynamo problem. Application to the Karlsruhe experiment