Dust lattice waves in a plasma crystal

The dust lattice wave in dusty plasma crystals is reexamined, taking into a ccount the dependence of the dust grain charge on the grain potential. The Poisson equation for small grain potentials then assumes the form of the Sc hrodinger equation. The spatial distribution of the potential in the lattic e includes the effect of the whole system of dust particles. Such a self-co nsistent description gives the dispersion relation for the dust lattice wav e, which is different from the expression found earlier. The case of large grain charge is also considered. The frequency of the lattice oscillation i ncreases considerably for large grain charges. Furthermore, it is noted tha t an ideal lattice can only exist if the dusty plasma parameters satisfy a definite relation between the dusty plasma Debye radius, the intergrain sep aration, and the grain size. (C) 2000 American Institute of Physics. [S1070 -664X(00)02103-0].