Mode coupling of dust lattice wave propagation in an external magnetic field in 2D plasma crystal with wake effect

• Dust lattice waves with the effect of wake and magnetic field were studied.
• Some explicit dispersion relations of dust lattice waves were given.
• Hybrid phonon mode and hybrid optical mode are obtained.
• Mode coupling of the hybrid phonon mode and hybrid optical mode is investigated.

The effect of particle–wake interaction on the coupling between the longitudinal and transverse dust lattice waves in two-dimensional hexagonal lattice in an external magnetic field is investigated. Meanwhile the electrostatic interactions between a particle charge and all other particle charges together with the corresponding effective wake charges are taken into account. Explicit formulations of dispersion relations of dust lattice waves are given when both the primary wave vector and the external magnetic field are parallel to axes. The dispersion relations are calculated numerically and hybrid phonon mode and hybrid optical mode are obtained. Furthermore, the mode mixing rates of the hybrid phonon mode and the hybrid optical mode are calculated and the mode changing points are obtained. Finally, the mode coupling is very intense in the region where the dispersion curves are close together and the mode coupling intensity increases when the magnitude of the external magnetic field increases.