Plasmas of Mg+ ions, containing more than 10(5) ions, have been observ
ed to reach well-ordered (crystalline) states by applying laser coolin
g. The crystals are highly elongated with up to ten concentric cylindr
ical shells surrounding a central string. Such large structures have n
ot previously been observed in a Paul trap. The amplitude of the micro
motion of the ions can be larger than the shell spacings. As the diame
ter changes along the crystals, sharp transitions are observed when ne
w shells form, in good agreement with molecular dynamics simulations.
The predictions from simulations of how ordering develops with decreas
ing temperature are also confirmed.