  We consider crystal formation of particles with dipole-dipole interactions
that are confined to move in a one-dimensional helical geometry with their
dipole moments oriented along the symmetry axis of the confining helix. The
stable classical lowest energy configurations are found to be chain structures
for a large range of pitch-to-radius ratios for relatively low density of
dipoles and a moderate total number of particles. The classical normal mode
spectra support the chain interpretation both through structure and the
distinct degeneracies depending discretely on the number of dipoles per
revolution. A larger total number of dipoles leads to a clusterization where
the dipolar chains move closer to each other. This implies a change in the
local density and the emergence of two length scales, one for the cluster size
and one for the inter-cluster distance along the helix. Starting from three
dipoles per revolution, this implies a breaking of the initial periodicity to
form a cluster of two chains close together and a third chain removed from the
cluster. This is driven by the competition between in-chain and out-of-chain
interactions, or alternatively the side-by-side repulsion and the head-to-tail
attraction in the system. The speed of sound propagates along the chains. It is
independent of the number of chains although depending on geometry.
