Linear and nonlinear dust lattice waves in plasma crystals

Linear and nonlinear studies of dust lattice waves in a dusty plasma crysta l have been carried out on the basis of the Schrodinger equation which is d educed from Poisson's equation for small dust grain potentials. The spatial distribution of the potential in the dust-lattice includes the effect of t he whole system of the dust particles. Such a self-consistent analysis give s a dispersion relation for the dust lattice wave, which is different from the expression found earlier. The frequency of the lattice oscillation incr eases considerably for large grain charges. Furthermore, it is found that a n ideal lattice can only exist if the dusty plasma parameters satisfy a def inite relationship between the dusty plasma Debye radius, the inter-grain s eparation, and the grain size. Finally, accounting for the weak nonlinearit ies, we also derive a Korteweg-de Vries (KdV) equation for the nonlinear du st lattice waves in the long wavelength approximation (kd << 1), where k is the wave number and d the inter-grain spacing. (C) 1999 Published by Elsev ier Science B.V. All rights reserved.