Nonlinear Excitations in Strongly-Coupled Plasma Lattices: Envelope Solitons, Kinks and Intrinsic Localized Modes

Abstract

Ensembles of charged particles (plasmas) are a highly complex form of matter, most often modeled as a many-body system characterized by weak inter-particle interactions (electrostatic coupling). However, strongly-coupled plasma configurations have recently been produced in laboratory, either by creating ultra-cold plasmas confined in a trap or by manipulating dusty plasmas in discharge experiments. In this paper, the nonlinear aspects involved in the motion of charged dust grains in a one-dimensional plasma monolayer (crystal) are discussed. Different types of collective excitations are reviewed, and characteristics and conditions for their occurrence in dusty plasma crystals are discussed, in a quasi-continuum approximation. Dust crystals are shown to support nonlinear kink-shaped supersonic solitary longitudinal excitations, as well as modulated envelope localized modes associated with longitudinal and transverse vibrations. Furthermore, the possibility for intrinsic localized modes (ILMs) — Discrete Breathers (DBs) — to occur is investigated, from first principles. The effect of mode-coupling is also briefly considered. The relation to previous results on atomic chains, and also to experimental results on strongly-coupled dust layers in gas discharge plasmas, is briefly discussed.

Combined breathing–kink modes in the FPU lattice

“…Kourakis and Shukla have noted the existence of breather-kink modes in models of dusty plasma crystals, though they named them 'asymmetric bright envelope solutions'; see Figs. 5b and 6 of [16,17] respectively.…”

Existence and stability of multisite breathers in honeycomb and hexagonal lattices

“…Further contribution to nonlinearity is furnished by Debye-type (screened Coulomb) electrostatic inter-dust-particle interactions, yet the associated anharmonicity is of lesser order of magnitude for the transverse mode and can be neglected. Details on dusty plasma modelling can be found, e.g., in [29,30], while the experimental setting is described in [28,31].…”

Discrete breathers in hexagonal dusty plasma lattices

“…The linear TDL eigenfrequency ω 0 [in (1)], is typically as low as ≈ 20 Hz [30,31,37]. The anharmonicity cofficients α and β may be determined experimentally [38,39,40].…”