The formation of a two-dimensional (2D) Coulomb crystal in a typical experimental environment was simulated with a computer code called BOX_TREE. The dispersion properties of a novel dust lattice wave (DLW) mode, the out-of-plane transverse wave, were obtained. The dispersion relation was determined to be an opticlike inverse dispersion when wave number $k$ is lower than a critical value $k_{\mathrm{critical}},$ and a positive dispersion when $k>\mathrm{}{k}_{\mathrm{critical}}.$ The negative group velocity of the wave for $k<\mathrm{}{k}_{\mathrm{critical}}$ depends on the κ value (with $\kappa =a/{\lambda }_D,$ where $a$ is the interparticle spacing and ${\lambda }_D$ is the Debye length) and the positive group velocity for $k>\mathrm{}{k}_{\mathrm{critical}}$ depends on the propagation direction. The value of $k_{\mathrm{critical}}$ depends on both κ and propagation direction, but changes very little for all propagation directions and the range of κ investigated. An analytical method has also been used to derive the dispersion relations assuming a hexagonal 2D lattice and Yukawa interparticle potential. These dispersion relations compare favorably with the simulation results. The dispersion relation for a 1D string was also obtained via BOX_TREE simulation and shown to agree with the analytical result given by Vladimirov [Physica A 315, 222 (2002)]. Comparison shows that the out-of-plane transverse DLW in a 2D lattice when $k<\mathrm{}{k}_{\mathrm{critical}}$ has a negative group velocity much larger than that of the 1D string, given the same particle parameters and operating environment. Again $k_{\mathrm{critical}}$ for 1D string and 2D lattice are in the same range.

• Received 8 May 2003

DOI:https://doi.org/10.1103/PhysRevE.68.046403