  We consider kinematic dynamo action in rapidly rotating Boussinesq convection
just above onset. The velocity is constrained to have either a square or a
hexagonal pattern. For the square pattern, large-scale dynamo action is
observed at onset, with most of the magnetic energy being contained in the
horizontally-averaged component. As the magnetic Reynolds number increases,
small-scale dynamo action becomes possible, reducing the overall growth rate of
the dynamo. For the hexagonal pattern, the breaking of symmetry between up and
down flows results in an effective pumping velocity. For intermediate rotation
rates, this additional effect can prevent the growth of any mean-field dynamo,
so that only a small-scale dynamo is eventually possible at large enough
magnetic Reynolds number. For very large rotation rates, this pumping term
becomes negligible, and the dynamo properties of square and hexagonal patterns
are qualitatively similar. These results hold for both perfectly conducting and
infinite magnetic permeability boundary conditions.
