We observed phase transitions and ordered structures of laser-cooled M
g+ ions stored in a radio-frequency quadrupole storage ring with a dia
meter of 115 mm. The ions are confined two dimensionally by a quadrupo
le field and can move freely along the ring circumference. By cooling
the ions with tangentially intersecting laser beams, we observed a lin
ear string of ions aligned along the center line of the quadrupole fie
ld. For higher ion densities the linear structure changes into a helic
al structure. The dynamics of the stored ions was studied.