  A numerical simulation utilizing a box_tree code is used to investigate the
structure and vertical mode spectrum of finite two-dimensional (2D) plasma
crystals. The overall structural symmetry of the system is examined for various
Debye lengths and a transition from a predominantly hexagonal structure to a
structure having concentric rings along the outer edge and hexagonal lattice
symmetry in the interior is shown to develop as the Debye length increases.
Both the vertical and horizontal oscillation modes for this type of system are
investigated where the horizontal mode spectra is shown to agree with published
results while the vertical mode spectra obtained is shown to agree with an
independent analytical method. The fundamental frequency for the vertical modes
decreases as the mode number l decreases and is shown to have a maximum
corresponding to that which would exist if the system acted in toto as a solid
plane. For low frequency vertical modes, the largest amplitude particle motion
is concentrated within a few inner rings with the outer rings remaining almost
motionless. Both of these are in direct contrast to the data obtained for the
horizontal modes where it is shown that at high frequencies the largest
amplitude particle motion is concentrated within the inner rings.
