Theory of dust crystal and its oscillations in plasmas

It is analytically shown that dust grains in a plasma can form regular periodic structures. In the dust crystal the charge of a given grain is not only determined by its own potential, but it also strongly depends on the potential of other dust grains that are participating in the dust crystallization. It means that although short range interaction is provided by the Debye-Huckel potential, a long range interaction contributes to the formation of a dust crystal. For cubic symmetry and small dust grains (when the dust grain sizes are smaller than the inter-grain spacing), the calculation of the potential has been performed analytically. Also discussed is the possibility of both longitudinal (or compressional) and transverse oscillations of our cubic dust lattice. Explicit expressions for the dust lattice mode frequencies are presented. (C) 2001 Elsevier Science B.V. All rights reserved.