Dust grain oscillations in two-dimensional hexagonal dusty plasma crystals in the presence of a magnetic field

The influence of a constant magnetic field on the propagation of dust-lattice waves in a two-dimensional hexagonal strongly coupled dusty plasma crystal is considered. The expression for the wave dispersion relation clearly shows that high- and low-frequency dust lattice vibrations exist as a result of the coupling between the longitudinal and transverse dust lattice modes due to the Lorentz force acting on the charged dust particles. It is found that in an external magnetic field the damping rate of the high-frequency (low-frequency) dust lattice wave is increased (decreased). For special values of the wave number and the direction of the wave propagation, the imaginary part of low-frequency is zero and the imaginary part of high-frequency attains a maximum value. The present investigation indicates that the damping rates depend on direction of the external magnetic field. The polarization of dust lattice wave modes is found for different magnetic field strengths and for different directions.