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The correlations in dusty plasmas in the gaseous state is considered. It is shown that the long-ranged correlations of dust particles, contrary to usual matter, start to form in a weakly correlated state, leading finally to the formation of dust crystals and dust liquids with not strong but intermediate strength correlations. The physical mechanism leading to long-ranged correlations is the dust attraction due to shadow effects of the plasma particle fluxes. An analytic theory for the long-ranged dust density correlation function is developed and the numerical results for a broad range of dust densities and plasma temperatures are presented. The long-ranged correlations induced by dust for electron densities, ion densities, and dust charges are also investigated, and the results for electron density correlations are presented in a way that permits measurement of the long-ranged correlation function in laser and radio-wave scattering experiments

A large number of laboratory observations reveal the formation of ordered linear chains and sheets composed of charged dust grains levitated in the sheath region of radio-frequency or dc plasma discharges at very low pressures. At higher pressures, three-dimensional structures are typically formed. Recently, a number of low gas pressure experiments have explored the generation of large amplitude vertical oscillations by lowering either the background pressure or the plasma power below a threshold value, or by imposing an external force that arises from a low-frequency sinusoidal voltage in the sheath region. A theoretical model is presented that successfully describes the phenomenology in various experiments, including the observed self-excited oscillations, nonlinear resonance and parametric oscillations. A new forcing mechanism, namely the modulational forcing, for exciting nonlinear resonances is proposed.