  We explore the influence of geometry variations on the structure and the
time-dependence of the magnetic field that is induced by kinematic $\alpha^{2}$
dynamos in a finite cylinder. The dynamo action is due to an anisotropic
$\alpha$ effect which can be derived from an underlying columnar flow. The
investigated geometry variations concern, in particular, the aspect ratio of
height to radius of the cylinder, and the thickness of the annular space to
which the columnar flow is restricted. Motivated by the quest for laboratory
dynamos which exhibit Earth-like features, we start with modifications of the
Karlsruhe dynamo facility. Its dynamo action is reasonably described by an
$\alpha^{2}$ mechanism with anisotropic $\alpha$ tensor. We find a critical
aspect ratio below which the dominant magnetic field structure changes from an
equatorial dipole to an axial dipole. Similar results are found for
$\alpha^{2}$ dynamos working in an annular space when a radial dependence of
$\alpha$ is assumed. Finally, we study the effect of varying aspect ratios of
dynamos with an $\alpha$ tensor depending both on radial and axial coordinates.
In this case only dominant equatorial dipoles are found and most of the
solutions are oscillatory, contrary to all previous cases where the resulting
fields are steady.
