Dispersion properties of the out-of-plane transverse wave in a two-dimensional Coulomb crystal.

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(critical), and a positive dispersion when k>k(critical). The negative group velocity of the wave for k<k(critical) depends on the kappa 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>k(critical) depends on the propagation direction. The value of k(critical) depends on both kappa and propagation direction, but changes very little for all propagation directions and the range of kappa 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<k(critical) has a negative group velocity much larger than that of the 1D string, given the same particle parameters and operating environment. Again k(critical) for 1D string and 2D lattice are in the same range.