  In this research, formation of finite two-dimensional (2D) plasma crystals
was numerically simulated. The structure was investigated for systems with
various Debye length and it was found there is a transition from a complete
hexagonal structure to a structure with concentric rings on the outer edge and
hexagonal lattice in the interior as the Debye length increases. The vertical
as well as horizontal oscillation modes thermally excited in the 2D dust
coulomb clusters were investigated. The horizontal mode spectra is shown to
agree with published results while the vertical mode spectra obtained from
numerical simulation and analytical method agree with one another. The
frequency of the vertical modes is shown to have a maximum corresponding to the
whole system acting as a solid plane. For low frequency modes, the largest
amplitude particle motion is concentrated in a few inner rings with the outer
rings remaining almost motionless in contrast to the horizontal modes for which
the strongest motion of the particles is concentrated in the inner rings at
high frequencies.
