  Starting from the present version of the Riga dynamo experiment with its
rotating magnetic eigenfield dominated by a single frequency we ask for those
modifications of this set-up that would allow for a non-trivial magnetic field
behaviour in the saturation regime. Assuming an increased ratio of azimuthal to
axial flow velocity, we obtain energy oscillations with a frequency below the
eigenfrequency of the magnetic field. These new oscillations are identified as
magneto-inertial waves that result from a slight imbalance of Lorentz and
inertial forces. Increasing the azimuthal velocity further, or increasing the
total magnetic Reynolds number, we find transitions to a chaotic behaviour of
the dynamo.
