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We consider crystal formation of particles with dipole-dipole interactionsthat are confined to move in a one-dimensional helical geometry with theirdipole moments oriented along the symmetry axis of the confining helix. Thestable classical lowest energy configurations are found to be chain structuresfor a large range of pitch-to-radius ratios for relatively low density ofdipoles and a moderate total number of particles. The classical normal modespectra support the chain interpretation both through structure and thedistinct degeneracies depending discretely on the number of dipoles perrevolution. A larger total number of dipoles leads to a clusterization wherethe dipolar chains move closer to each other. This implies a change in thelocal density and the emergence of two length scales, one for the cluster sizeand one for the inter-cluster distance along the helix. Starting from threedipoles per revolution, this implies a breaking of the initial periodicity toform a cluster of two chains close together and a third chain removed from thecluster. This is driven by the competition between in-chain and out-of-chaininteractions, or alternatively the side-by-side repulsion and the head-to-tailattraction in the system. The speed of sound propagates along the chains. It isindependent of the number of chains although depending on geometry.

Formation of classical crystals of dipolar particles in a helical geometry