Stability of two-dimensional complex plasma monolayers in asymmetric capacitively coupled radio-frequency discharges.

In this article, the stability of a complex plasma monolayer levitating in the sheath of the powered electrode of an asymmetric capacitively coupled radio-frequency argon discharge is studied. Compared to earlier studies, a better integration of the experimental results and theory is achieved by operating with actual experimental control parameters such as the gas pressure and the discharge power. It is shown that for a given microparticle monolayer at a fixed discharge power there exist two threshold pressures: (i) above a specific pressure p_{cryst}, the monolayer always crystallizes; (ii) below a specific pressure p_{MCI}, the crystalline monolayer undergoes the mode-coupling instability and the two-dimensional complex plasma crystal melts. In between p_{MCI} and p_{cryst}, the microparticle monolayer can be either in the fluid phase or the crystal phase: when increasing the pressure from below p_{MCI}, the monolayer remains in the fluid phase until it reaches p_{cryst} at which it recrystallizes; when decreasing the pressure from above p_{cryst}, the monolayer remains in the crystalline phase until it reaches p_{MCI} at which the mode-coupling instability is triggered and the crystal melts. A simple self-consistent sheath model is used to calculate the rf sheath profile, the microparticle charges, and the microparticle resonance frequency as a function of power and background argon pressure. Combined with calculation of the lattice modes the main trends of p_{MCI} as a function of power and background argon pressure are recovered. The threshold of the mode-coupling instability in the crystalline phase is dominated by the crossing of the longitudinal in-plane lattice mode and the out-of plane lattice mode induced by the change of the sheath profile. Ion wakes are shown to have a significant effect too.