  The dipole-multipole transition in rapidly rotating dynamos is investigated
through the analysis of forced magnetohydrodynamic waves in an unstably
stratified fluid. The focus of this study is on the inertia-free limit
applicable to planetary cores, where the Rossby number is small not only on the
core depth but also on the length scale of columnar convection. By
progressively increasing the buoyant forcing in a linear magnetoconvection
model, the slow Magnetic-Archimedean-Coriolis (MAC) waves are significantly
attenuated so that their kinetic helicity decreases to zero; the fast MAC wave
helicity, on the other hand, is practically unaffected. In turn, polarity
reversals in low-inertia spherical dynamos are shown to occur when the slow MAC
waves disappear under strong forcing. Two dynamically similar regimes are
identified -- the suppression of slow waves in a strongly forced dynamo and the
excitation of slow waves in a moderately forced dynamo starting from a small
seed field. While the former regime results in polarity reversals, the latter
regime produces the axial dipole from a chaotic multipolar state. For either
polarity transition, a local Rayleigh number based on the mean wavenumber of
the energy-containing scales bears the same linear relationship with the square
of the peak magnetic field measured at the transition. The self-similarity of
the dipole-multipole transition can place a constraint on the Rayleigh number
for polarity reversals in the Earth.
