Mode-coupling instability of two-dimensional plasma crystals

Abstract

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.

Observation of particle pairing in a two-dimensional plasma crystal

“…The intensities of the spectra are in arbitrary units (the logarithmic scale spans over two decades). The theoretical dispersion relations [33] for the two main crystallographic directions (solid and dashed lines) are very close to each other. A reasonably good agreement of the theoretical and experimental results is evident.…”

“…Therefore, the particle motion is not overdamped and studying of the naturally occurring waves (fluctuations) can give reliable information about the lattice layer. The values of the particle charge Q, interaction range κ = a/λ D (where λ D is the screening length), and the vertical confinement parameter f v were estimated from the fluctuation spectra of particle velocity [33,35,36]. These parameters are collected in Table I along with the parameter set adopted for numerical calculations performed for comparison reasons.…”

Anisotropic confinement effects in a two-dimensional plasma crystal

“…The horizontal confinement of the crystal is often assumed to be insignificant in theoretical considerations, see, e.g., [17,39]. On the contrary, the finiteness and symmetry of the confinement have a great influence on the delicate symmetry breaking effects.…”

“…In (a), the increment is calculated for isotropic loading as in Ref. [17]. In (b) and (c), there is an anisotropic loading of strength p = 14% in the direction α = 0…”

“…In theory and simulations, the plasma wake is often modeled as a pointlike effective charge below each particle [16]. If the vertical particle confinement is small enough, a mode-coupling instability (MCI) can occur in such a model, coupling the out-of-plane mode to the longitudinal mode [16,17]. Near the intersection of the modes, the unstable hybrid mode grows until the crystalline order breaks.…”