Longitudinal Dust Lattice Waves Research Articles

The nonlinear longitudinal lattice waves in a one-dimensional dusty chain with the plasma absorption effect

The nonlinear longitudinal dust lattice wave of a one-dimensional dust chain under the influence of the plasma absorption effect was investigated. A modified KdV-Burgers’ equation with the plasma absorption effect is derived under the continuum limit by the reductive perturbation method. Based on solutions of the Burgers’ equation, the effects of dynamic damping, absorption coefficient, characteristic length and shielding parameter on the shock structure are investigated. It is found that shock wave polarity is determined by hydrodynamical damping. Furthermore, as the electron-to-ion temperature ratio increases, shock amplitude increases correspondingly, but its width remains basically unchanged. Therefore, the shock structure of nonlinear longitudinal dust lattice wave with plasma absorption potential is different from the one under the conventional Debye–Hückel potential.

Influence of the Plasma Absorption on the Longitudinal Dust Lattice Waves in Dusty Plasmas

We investigate the influence of the plasma absorption on the longitudinal dust lattice wave in highly collisional dusty plasmas. The dispersion relation for the dust lattice wave has been obtained by the considering of the screened effective nearest-neighbor interactions. It is found that the plasma absorption effect strongly suppresses the frequency of the longitudinal dust lattice wave. It is also found that the frequency of the dust lattice wave decreases with increasing the inter-dust grain spacing. In addition, we have found that the frequency of the dust lattice wave decreases with an increase of the ratio of the electron temperature to the ion temperatures, in dusty plasmas. Hence, we have found that the amplitudes of the dust lattice waves in one-temperature plasmas are always greater than those in highly nonequilibrium dusty plasmas.

Nonlinear theory of longitudinal dust-lattice wave in a magnetic dusty plasma crystal

AbstractThe propagation of dust-lattice waves in two-dimensional hexagonal dusty plasma crystals in the presence of an external weak magnetic field is considered. Linear and nonlinear properties of the longitudinal dust-lattice waves are investigated. Dispersion relation, group velocity and evolution equation are found. The influence of the magnetic field on the propagation of dust-lattice waves is studied. We obtain the envelope evolution equation for longitudinal modes in the presence of a weak magnetic field, which is in the form of the Gross–Pitaevskii equation.

Shock wave in a two-dimensional dusty plasma crystal

Two-dimensional (2D) shock structures of longitudinal dust lattice wave (LDLW) in a hexagonal Yukawa crystal are studied. The nonlinear evolution equation derived for dusty plasma crystal is found to be a 2D Burgers’ equation, where the Burgers’ term, i.e., the dissipation is provided by “hydrodynamic damping” due to irreversible processes that take place within the system. Analytical and numerical solutions of this equation on the basis of crystal experimental parameters show the development of compressional shock structures of LDLW in 2D dusty plasma crystal. The shock strength decreases (increases) with the increase in lattice parameter κ (angle of propagation of the nonlinear wave). The results are discussed in the context of 2D monolayer hexagonal dusty plasma crystal experiments.

“Damped Dust Lattice Shock Wave in a Strongly Coupled Complex (Dusty) Plasma,”

Taking into account “hydrodynamic damping” due to irreversible processes that occur within the system and the neutral drag due to the dust-neutral collision, a Burgers’ equation with a linear damping term is derived for a 1D nonlinear longitudinal dust lattice wave (LDLW) in homogeneous strongly coupled complex (dusty) plasma. The hydrodynamic damping generated-dissipative effect causes the generation of a shock wave in a dusty plasma crystal, whereas the neutral drag-induced dissipative effect causes the decay of the shock intensity with time. The width of the observed compressive shock increases (decreases) with an increase in shielding parameter κ (characteristic length L). Its implication in a glow-discharge plasma is briefly discussed.

Longitudinal Dust Lattice Shock Wave in a Strongly Coupled Complex Dusty Plasma

AbstractThe effect of hydrodynamical damping that arises due to the irreversible processes within the system have been studied on 1D nonlinear longitudinal dust lattice wave (LDLW) in homogeneous strongly coupled complex (dusty) plasma. Analytical investigation shows that the nonlinear wave is governed by Korteweg‐de Vries Burgers' equation. This hydrodynamical damping induced dissipative effect is responsible for the Burgers' term that causes the generation of shock wave in dusty plasma crystal. Numerical investigation on the basis of the glow‐discharge plasma parameters reveal that LDLW exhibits both oscillatory and monotonic shock. The shock is compressive in nature and its strength decreases (increases) with the increase of the shielding parameter κ (characteristic length L). The effects of dust‐neutral collision are also discussed. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

“Damped Dust Lattice Shock Wave in a Strongly Coupled Complex (Dusty) Plasma”

Taking into account “hydrodynamic damping” due to irreversible processes that occur within the system and the neutral drag due to the dust-neutral collision, a Burgers’ equation with a linear damping term is derived for a 1D nonlinear longitudinal dust lattice wave (LDLW) in homogeneous strongly coupled complex (dusty) plasma. The hydrodynamic damping generated-dissipative effect causes the generation of a shock wave in a dusty plasma crystal, whereas the neutral drag-induced dissipative effect causes the decay of the shock intensity with time. The width of the observed compressive shock increases (decreases) with an increase in shielding parameter κ (characteristic length L). Its implication in a glow-discharge plasma is briefly discussed.

Nonlinear excitations in Debye bi-crystals

The nonlinear dynamics of longitudinal dust lattice waves propagating in a dusty plasma bi-crystal is investigated. A “diatomic”-like one-dimensional dust lattice configuration is considered, consisting of two distinct dust grain species with different charges and masses. Two different frequency dispersion modes are obtained in the linear limit, namely, an optical and an acoustic wave dispersion branch. Nonlinear solitary wave solutions are shown to exist in both branches, by considering the continuum limit for lattice excitations in different nonlinear potential regimes. For this purpose, a generalized Boussinesq and an extended Korteweg de Vries equation is derived, for the acoustic mode excitations, and their exact soliton solutions are provided and compared. For the optic mode, a nonlinear Schrödinger-type equation is obtained, which is shown to possess bright- (dark-) type envelope soliton solutions in the long (short, respectively) wavelength range. Optic-type longitudinal wavepackets are shown to be generally unstable in the continuum limit, though this is shown not to be the rule in the general (discrete) case.

Modulated wavepackets associated with longitudinal dust grain oscillations in a dusty plasma crystal

The nonlinear amplitude modulation of longitudinal dust lattice waves (LDLWs) propagating in a dusty plasma crystal is investigated in a continuum approximation. It is shown that long wavelength LDLWs are modulationally stable, while shorter wavelengths may be unstable. The possibility for the formation and propagation of different envelope localized excitations is discussed. It is shown that the total grain displacement bears a (weak) constant displacement (zeroth harmonic mode), due to the asymmetric form of the nonlinear interaction potential. The existence of asymmetric envelope localized modes is predicted. The types and characteristics of these coherent nonlinear structures are discussed.