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 pcryst, the monolayer always crystallizes; (ii) below a specific pressure pMCI, the crystalline monolayer undergoes the mode-coupling instability and the two-dimensional complex plasma crystal melts. In between pMCI and pcryst, the microparticle monolayer can be either in the fluid phase or the crystal phase: when increasing the pressure from below pMCI, the monolayer remains in the fluid phase until it reaches pcryst at which it recrystallizes; when decreasing the pressure from above pcryst, the monolayer remains in the crystalline phase until it reaches pMCI 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 pMCI 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.