Dust lattice waves in a plasma crystal

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Abstract
The dust lattice wave in dusty plasma crystals is reexamined, taking into account the dependence of the dust grain charge on the grain potential. The Poisson equation for small grain potentials then assumes the form of the Schrödinger equation. The spatial distribution of the potential in the lattice includes the effect of the whole system of dust particles. Such a self-consistent description gives the dispersion relation for the dust lattice wave, which is different from the expression found earlier. The case of large grain charge is also considered. The frequency of the lattice oscillation increases considerably for large grain charges. Furthermore, it is noted that an ideal lattice can only exist if the dusty plasma parameters satisfy a definite relation between the dusty plasma Debye radius, the intergrain separation, and the grain size.