Be+ ions trapped in a Penning trap are laser-cooled to about 10 mK. Th
e excitation spectra of ion clouds containing about 500 ions are obtai
ned by scanning the frequency of the cooling laser and discontinuities
in these spectra are observed because of phase transitions. When the
cooled ions are heated electrically by applying an rf voltage, no phas
e transition occurs and the spectra become continuous. Two-dimensional
measurement of the ion clouds is carried out and the abrupt change in
the shape of the ion cloud due to the phase transition is observed, W
hen many ions are trapped and cooled, the phase transition occurs part
ially and a transient state where two states are mixed can be observed
. The static properties of the ions are also measured by using an addi
tional probe laser and the results of experimental measurements are co
mpared with theoretical predictions.