Anisotropic Dust Lattice Modes and Stability of Two-Dimensional Plasma Crystals

We study longitudinal and transverse dust lattice (DL) waves in a horizontal monolayer of particles suspended in the plasma sheath. The ion flow in the sheath introduces an anisotropy, in particular “ion wakes” below the crystal particles. Using a simplified model of the wake 1 we demonstrate that the vertical transverse DL mode and the longitudinal DL mode are coupled due to the particle-wake interaction. The longitudinal wave has acoustic dispersion ( ∂ω/∂k>0), whereas the transverse wave is described by inverse optical-like characteristics ( ∂ω/∂k<0). Therefore, the branches ω(k) of these modes can intersect at a certain point, ( ω0, k0), as shown in Fig. 1. The wake-induced coupling close to this point can drive an instability of the modes if the particle density in a monolayer is sufficiently high. 2 Analysis shows that for typical experimental conditions the growth rate of the wake-induced instability can exceed the damping due to neutral gas friction. Thus the instability might be responsible for observed melting of 2D plasma crystals.