Dust Lattice Waves Research Articles

Comparison of Dust Lattice Waves in Three-Dimensional Cubic Configurations

A three-dimensional (3D) dusty plasma crystalline with cubic configurations is considered. We calculate the interaction between particles up to distance √2a, implying the second-neighbor interactions for the simple cubic structure, the third-neighbor interactions for the body-centered cubic structure, and the forth-neighbor interactions the for face-centered cubic structure. Longitudinal and transverse dispersion relations are derived in arbitrary directions. The dispersion relations are studied in special directions, i.e. (1,0,0), (1, 1, 0)/√2, and (1, 1, 1)/√3. Study of dispersion relations with more neighbor interactions show that in some cases the results change physically.

Gradient effects on dust lattice waves in paramagnetic dusty plasma crystals

Dust lattice modes are studied in a hexagonal two-dimensional lattice in plasma crystal, including paramagnetic dust particles. The gradients of magnetic fields, electric fields, and dust charge and also the interaction of dipole-dipole take into account. These gradients modify the levitation condition and affect the frequencies of dust lattice waves. The coupling between in-plane and out-of-plane modes gives rise to the hybrid mode, which is always an unstable mode. However, intersection of the in-plane mode with other modes does not result in mode-coupling instability.

Direct Observation of Mode-Coupling Instability in Two-Dimensional Plasma Crystals

Dedicated experiments on melting of two-dimensional plasma crystals were carried out. The melting was always accompanied by spontaneous growth of the particle kinetic energy, suggesting a universal plasma-driven mechanism underlying the process. By measuring three principal dust-lattice wave modes simultaneously, it is unambiguously demonstrated that the melting occurs due to the resonance coupling between two of the dust-lattice modes. The variation of the wave modes with the experimental conditions, including the emergence of the resonant (hybrid) branch, reveals exceptionally good agreement with the theory of mode-coupling instability.

Dissipation of Nonlinear Wave in Inhomogeneous Dust Plasma Crystal

A Korteweg-de Vires-type (KdV-type) equation and a modified Nonlinear Schrödinger equation (NLSE) for the dust lattice wave (DLW) are derived in a weakly inhomogeneous dust plasma crystal. It seems that the amplitude and the velocity of the dust lattice solitary waves decay exponentially with increasing time in a dust lattice. The modulational instability of this dust lattice envelope waves is investigated as well. It is found that the waves are modulational stable under certain conditions. On the other hand, the waves are modulational unstable if the conditions are not satisfied.

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.

Dust lattice waves in a hexagonal lattice of paramagnetic grains

Dust lattice waves in a hexagonal lattice of paramagnetic grains

Dust grain oscillations in two-dimensional hexagonal dusty plasma crystals in the presence of a magnetic field

The influence of a constant magnetic field on the propagation of dust-lattice waves in a two-dimensional hexagonal strongly coupled dusty plasma crystal is considered. The expression for the wave dispersion relation clearly shows that high- and low-frequency dust lattice vibrations exist as a result of the coupling between the longitudinal and transverse dust lattice modes due to the Lorentz force acting on the charged dust particles. It is found that in an external magnetic field the damping rate of the high-frequency (low-frequency) dust lattice wave is increased (decreased). For special values of the wave number and the direction of the wave propagation, the imaginary part of low-frequency is zero and the imaginary part of high-frequency attains a maximum value. The present investigation indicates that the damping rates depend on direction of the external magnetic field. The polarization of dust lattice wave modes is found for different magnetic field strengths and for different directions.

Modulated transverse off-plane dust-lattice wave packets in hexagonal two-dimensional dusty plasma crystals

The propagation of nonlinear dust-lattice waves in a two-dimensional hexagonal crystal is investigated. Transverse (off-plane) dust grain oscillatory motion is considered in the form of a backward propagating wave packet whose linear and nonlinear characteristics are investigated. An evolution equation is obtained for the slowly varying amplitude of the first (fundamental) harmonic by making use of a two-dimensional lattice multiple scales technique. An analysis based on the continuum approximation (spatially extended excitations compared to the lattice spacing) shows that wave packets will be modulationally stable and that dark-type envelope solitons (density holes) may occur in the long wavelength region. Evidence is provided of modulational instability and of the occurrence of bright-type envelopes (pulses) at shorter wavelengths. The role of second neighbor interactions is also investigated and is shown to be rather weak in determining the modulational stability region. The effect of dissipation, assumed negligible in the algebra throughout the article, is briefly discussed.

Colloquium: Fundamentals of dust-plasma interactions

Dusty plasmas are ubiquitous in low-temperature laboratory discharges as well as in the near-earth environment, planetary rings, and interstellar spaces. In this paper, updated knowledge of fundamentals of collective dust-plasma interactions and several novel phenomena are presented that have been observed in laboratories and in space dusty plasmas. Mechanisms that are responsible for the charging of dust grains are discussed, and the fact that the dust charge perturbation is a new dynamical variable in a dusty plasma. The underlying physics of different forces that act on a charged dust grain is reviewed. In dusty plasmas, there are new attractive forces (e.g., due to wakefield and ion focusing effects and dipole-dipole interactions between unevenly charged dust rods). Furthermore, in the presence of an ensemble of charged dust grains, there are collective dust-plasma interactions featuring new waves (e.g., the dust acoustic wave, the dust ion-acoustic wave, the dust lattice wave, etc.), new instabilities, and coherent nonlinear structures (dust acoustic and dust ion-acoustic shocks, dust voids, and dust vortices), which are also discussed. Theoretical models for numerous collective dust-plasma interactions are compared with existing observations from laboratories and space environments.

“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

Damped dust lattice shock wave in a strongly coupled complex (dusty) plasma

“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.

Dust Lattice Waves of Dusty Plasma Chain with an ExternalMagnetic Field

Dust lattice waves of a one-dimensional plasma crystal chain withan external magnetic field are investigated. When the magneticfield is in the vertical direction (θ = 0), perpendicular tothe chain, the vertical transverse mode is not affected, while thehorizontal transverse mode is coupled with the longitudinal mode.In the high frequency range, we obtain an `upper-hybrid' dust latticemode and in the low frequency range, we obtain a `lower-hybrid' dustlattice mode. Between the two modes, a `gap' is formed. When themagnetic field is oriented to the chain (θ = π/2), thelongitudinal mode is not affected while both the horizontal and verticaltransverse modes are shifted due to the effect of the magnetic field.

Nonlinear modulated dust lattice wave packets in two-dimensional hexagonal dust crystals

The amplitude modulation of dust lattice waves (DLWs) propagating in a two-dimensional hexagonal dust crystal is investigated in a continuum approximation, accounting for the effect of dust charge polarization (dressed interactions). A dusty plasma crystalline configuration with constant dust grain charge and mass is considered. The dispersion relation and the group velocity for DLWs are determined for wave propagation in both longitudinal and transverse directions. The reductive perturbation method is used to derive a (2+1)-dimensional nonlinear Schrödinger equation (NLSE). New expressions for the coefficients of the NLSE are derived and compared, for a Yukawa-type potential energy and for a “dressed” potential energy, taking into account interaction and geometric nonlinearities.

Dust lattice wave dispersion relations in two-dimensional hexagonal crystals including the effect of dust charge polarization

A dusty plasma crystalline configuration with equal charge dust grains and mass is considered. Both charge and mass of each dust species are taken to be constant. Two differential equations for a two-dimensional hexagonal crystal on the basis of a Yukawa-type potential energy and a “dressed” potential energy, accounting for dust charge polarization, are derived and compared. The dispersion relation for both longitudinal and transverse wave propagation in an arbitrary direction is derived. A comparison to analytical and experimental results reported previously is carried out.

Nonlinear Correction Effects on Transverse Dust Lattice Waves in Dusty Plasmas

The nonlinear correction effects on the transverse dust lattice mode wave are investigated in dusty plasmas. It is shown that the nonlinear correction effects on the dispersion relation increase with decreasing a/λD, where a is the spacing of dust grains and a/λD is the Debye length. It is also found that the nonlinear correction effects enhance the frequency of the transverse dust lattice wave.

Effects of Dipole Moment on the Lattice Waves inOne-Dimensional Dust Chain

Effects of dipole moment on the horizontal dust lattice waves inone-dimensional dust chain are investigated. The generaldispersion relations are derived. The waves are sensitive to thedirection of the dipole moment, which has an angle θ(0⩽θ⩽π) with respect to the vertical direction.When the waves are self-excited, it is shown that the real part offrequency for longitudinal wave is increased, while it isdecreased for the horizontal transverse wave with increasingθ. When the waves are externally exited, both the real andimaginary parts of wave number are decreased for the longitudinaland transverse waves with increasing θ.

Stability of dust lattice modes in the presence of charged dust grain polarization in plasmas

We discuss the effect of the attractive force associated with overlapping Debye spheres on the dispersion properties of the longitudinal and transverse dust lattice waves in strongly coupled dust crystals. The dust grain attraction is shown to contribute to a destabilization of the longitudinal dust lattice oscillations. The (optic-like) transverse mode dispersion law is shown to change, due to the Debye sphere dressing effect, from the known inverse-dispersive (“backward wave”) form into a normal dispersive law (i.e. the group velocity changes sign). The stability of one-dimensionless bi-layers, consisting of (alternating) negatively and positively charged dust particles, is also discussed. The range of parameter values (mainly in terms of the lattice parameter κ) where the above predictions are valid, are presented.