Mode-coupling instability of two-dimensional plasma crystals

The dispersion relations for three principal wave modes sustained in two-dimensional (2D) plasma crystals are derived taking into account particle-wake interactions. The rigorous analysis of the mode coupling shows that if the normalized frequency of the vertical confinement is below a certain critical value, then resonance coupling between the longitudinal in-plane mode and out-of-plane mode sets in. This results in the emergence of a hybrid mode and drives the mode-coupling instability. The universal dependence of the critical confinement frequency on plasma parameters is calculated, which allows us to specify the conditions when stable 2D plasma crystals can be formed in experiments. (C) 2009 American Institute of Physics. [DOI: 10.1063/1.3205894]