  Trapped singly-charged ions can crystallize as a result of laser cooling. The
emerging structure depends on the number of particles and on the geometry of
the trapping potential. In linear multipole radiofrequency traps, the geometry
of the radial potential can lead to the formation of single-ring structures. We
analyse the conditions and stability of single rings as a function of the
number of poles. For larger numbers of ions the rings form tubes in which the
arrangement of the ions corresponds to a triangular lattice folded onto a
cylinder. The stability of these tubular structures is numerically studied for
different lattice constants and their normal mode spectrum is determined.
