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.

Charge-gradient instability of compressional dust lattice waves in electrorheological plasmas

It is shown that the longitudinal dust lattice mode in the one-dimensional string of microparticles oriented along the electric field (it highlights the major aspect of the electrorheological plasmas) can be subjected to a specific charge-gradient instability, associated with inhomogeneous dust charge distribution along the string due to the ion flow. This instability leads to the spontaneous excitation of compressional waves at elevated gas pressures with implications for the electrorheological plasmas studied in the Plasmakristall-4 facility in the ground based conditions and in microgravity on board the International Space Station. The obtained results can also be relevant for the stability analysis of the laboratory multilayer plasma crystals observed in the sheath of gas discharges.

Effect of plasma absorption on dust lattice waves in hexagonal dust crystals

In the present paper, the effect of plasma absorption on lattice waves in 2D hexagonal dust crystals is investigated. The dispersion relations with the effect of plasma absorption are derived. It is found that the temperature effect (electron-to-ion temperature ratio τ) enhances the frequency of the dust lattice waves, while the spatial effect (dimensionless Debye shielding parameter weakens the frequency of the dust lattice waves. In addition, the system stabilities under the conditions of plasma absorption are studied. It is found that the temperature effect narrows the range of instability, while the spatial effect extends this range. And the range of instability is calculated, i.e. the system will always in the stable state regardless of the value of when τ > 3.5. However, the system will be unstable when τ = 1 and .

Transport properties of disordered two‐dimensional complex plasma crystal

In this study, we numerically investigate the transport properties of a two‐dimensional (2D) complex plasma crystal using diffusion of coplanar dust lattice waves. In the limit where the Hamiltonian interactions can be decoupled from the non‐Hamiltonian effects, we identify two distinct types of wave transport: Anderson‐type delocalization and long‐distance excitation. We use a recently developed spectral approach to evaluate the contribution of the Anderson problem and compare it to the results of the simulation. The benefit of our approach to transport problems is twofold. First, we employ a highly tuneable macroscopic hexagonal crystal, which exhibits many‐body interactions and allows for the investigation of transport properties at the kinetic level. Second, the analysis of the transport problem in 2D is provided using an innovative spectral approach, which avoids the use of scaling and boundary conditions. The comparison between the analytically predicted and numerically observed wave dynamics allows for the study of important characteristics of this open system. In our simulations, we observe long‐distance lattice excitation, which occurs around lattice defects even when the initial perturbation does not spread from the centre to the exterior of the crystal. In the decoupled Hamiltonian regime, this many‐body effect can be attributed to the dust lattice interaction with the plasma environment.

Coupling of Noncrossing Wave Modes in a Two-Dimensional Plasma Crystal.

We report an experimental observation of the coupling of the transverse vertical and longitudinal in-plane dust-lattice wave modes in a two-dimensional complex plasma crystal in the absence of mode crossing. A new large-diameter rf plasma chamber was used to suspend the plasma crystal. The observations are confirmed with molecular dynamics simulations. The coupling manifests itself in traces of the transverse vertical mode appearing in the measured longitudinal spectra and vice versa. We calculate the expected ratio of the trace to the principal mode with a theoretical analysis of the modes in a crystal with finite temperature and find good agreement with the experiment and simulations.

Dust lattice waves in Debye binary dust chain

The dust lattice waves in a one-dimensional Debye binary dust chain consisting of two distinct dust particle species with different charges and masses are investigated. It is found that there are two branches for both longitudinal and transverse modes, namely the optical mode of high frequency and the acoustic mode of low frequency, which will be merged into one ordinary longitudinal (transverse) mode of single dust chain. The influence of the parameters, i.e., the dimensionless lattice parameter α, the mass ratio σ, and the charge ratio ε of the two particles, on the dispersion relation of longitudinal and transverse waves is discussed. Furthermore, the branching and the merging of longitudinal and transverse waves are discussed in detail.

Modified screening interaction potential on dust lattice waves in dusty plasma ring

In the present paper, the modified screening interaction potential was adopted to investigate the dust lattice waves in dusty ring. Firstly, the influence of parameter ε on the modified screening interaction potential was analyzed; and it was found that the parameter ε has a long-range effect on the pairwise interaction between the particles. Secondly, the dispersion relations of longitudinal and transverse waves are obtained, and the effect of long-range action parameter ε, dimensionless lattice parameter α and dimensionless shielding parameter on the dust lattice waves propagation in dusty ring are studied. Some interesting phenomena, such as the coupling of longitudinal and transverse waves, and instabilities of transverse waves are found, which are in good agreement with some previous works. Finally, the transverse wave instabilities and the relevant critical lattice parameter αc are presented and discussed.

Effects of nonlinear plasma wake field on the dust-lattice wave in complex plasmas

The influence of a nonlinear ion wake field on the dust-lattice wave is investigated in complex dusty plasmas. The dispersion relation for the dust-lattice wave is derived from the equation of motion including the contribution due to the nearest-neighbour dust grain interaction. The results show that the nonlinear wake-field effect increases the wave frequency, especially at the maximum peak positions. It is found that the oscillatory behaviour of the dust-lattice wave enhances with an increase of the spacing of the dust grains. It is also found that the amplitude of the dust-lattice wave significantly decreases with an increase of the inter-dust grain distance. In addition, it is found that the amplitude of the dust-lattice wave increases with increasing Debye length. The variation of the dust-lattice wave due to the Mach number and plasma parameters is also discussed.

Theory of correlation effects in dusty plasmas

A theory of correlation effects in dusty plasmas based on a suitably augmented Debye Huckel approximation is proposed. A model which takes into account the confinement of the dust within the plasma (by external fields) is considered. The dispersion relation of compressional modes with correlation effects is obtained. Results show that strong coupling effects may be subdominant even when Г ≫ 1. Thus, in the limit Γ→0 and/or κ → ∞, one obtains the weakly coupled dust thermal mode. In the range of values of Г ≫ 1, the strong coupling effects scale with κ instead of Г; increasing Г increases the dust acoustic waves phase velocity CDAW in this regime. In the limit Γ≫1,κ≪1, one obtains the weakly coupled dust acoustic wave. Only in the limit Γ≫1,κ≥1, one obtains strong coupling effects, e.g., the dust lattice waves (κ=a/λd, a is the mean particle distance and λd is the Debye length). Observations from a number of experiments are explained.

Dispersion characteristics of dust lattice waves in two-dimensional bi-crystal and mono-crystal

Propagation of dust lattice waves (DLWs) in a two-dimensional bi-crystal lattice in an arbitrary direction in zero gravity is studied. Interaction of the nearest neighbor in comparison with the second neighbor under the Yukawa and overlapping Debye sphere (ODS) potential is illustrated. In the last part of this article, DLW modes for mono-crystals, for more simplification, are found to be hybrid and have both longitudinal and transverse components; however, they become purely longitudinal or transverse modes when the angle of propagation becomes equal to zero or . Dispersion relations for the Yukawa and ODS potentials are compared with experimental data and good agreement is found.

Mode coupling of dust lattice wave propagation in an external magnetic field in 2D plasma crystal with wake effect

The effect of particle–wake interaction on the coupling between the longitudinal and transverse dust lattice waves in two-dimensional hexagonal lattice in an external magnetic field is investigated. Meanwhile the electrostatic interactions between a particle charge and all other particle charges together with the corresponding effective wake charges are taken into account. Explicit formulations of dispersion relations of dust lattice waves are given when both the primary wave vector and the external magnetic field are parallel to axes. The dispersion relations are calculated numerically and hybrid phonon mode and hybrid optical mode are obtained. Furthermore, the mode mixing rates of the hybrid phonon mode and the hybrid optical mode are calculated and the mode changing points are obtained. Finally, the mode coupling is very intense in the region where the dispersion curves are close together and the mode coupling intensity increases when the magnitude of the external magnetic field increases.

Effect of dust–dust interaction type on normal modes of two-dimensional dust crystals

Dispersion relations for longitudinal and transverse dust lattice waves in two-dimensional hexagonal dust crystals of negatively charged particles were investigated and compared for two different interaction types, namely, Coulomb and screened Yukawa potentials. Results showed that the interaction type and the wave propagation direction change the characteristics of the dispersion relation as well as the group velocity. The screening parameter is also found to reduce the mode frequencies.

Effect of strong wakes on waves in two-dimensional plasma crystals

We study the effects of the particle-wake interactions on the dispersion and polarization of dust lattice wave modes in two-dimensional plasma crystals. Most notably, the wake-induced coupling between the modes causes the branches to "attract" each other, and their polarizations become elliptical. Upon the mode hybridization the major axes of the ellipses (remaining mutually orthogonal) rotate by 45°. To demonstrate the importance of the obtained results for experiments, we plot representative particle trajectories and spectral densities of the longitudinal and transverse waves. These characteristics reveal distinct fingerprints of the mixed polarization. Furthermore, we show that at strong coupling the hybrid mode is significantly shifted towards smaller wave numbers, away from the border of the first Brillouin zone (where the hybrid mode is localized for a weak coupling).

Wakefield effects on three-dimensional dust-lattice modes

AbstractDispersion relations of dust-lattice waves in three-dimensional body-centered cubic (bcc) and face-centered cubic (fcc) dusty plasma crystals are derived taking into account particle–wake interactions. Results show that resonance coupling between the longitudinal and out-of-plane transverse wave modes set in if the vertical confinement is below a certain critical value. The imaginary part of the wave frequency shows that the hybrid mode cannot propagate in the crystal.

Damping and instability of solitons in weakly inhomogeneous dust plasma crystals

By using reductive perturbation method, we derive a Korteweg-de Vries-type equation and a modified Nonlinear Schrodinger equation for dust lattice wave in a weakly inhomogeneous dust plasma crystal. It seems that amplitude and velocity of dust lattice solitary wave decay exponentially. The modulational instability of this dust lattice envelope wave is investigated. It is found that the wave is modulational stable under certain conditions and unstable otherwise.

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.

Dispersion relations of dust lattice waves in two-dimensional honeycomb configuration

AbstractThe linear dust lattice waves propagating in a two-dimensional honeycomb configuration is investigated. The interaction between particles is considered up to distance 2a, i.e. the third-neighbor interactions. Longitudinal and transverse (in-plane) dispersion relations are derived for waves in arbitrary directions. The study of dispersion relations with more neighbor interactions shows that in some cases the results change physically. Also, the dispersion relation in the different direction displays anisotropy of the group velocity in the lattice. The results are compared with dispersion relations of the waves in the hexagonal lattice.

Influence of the nonthermal and nonlinear shielding on the dust-lattice wave in Lorentzian plasmas

The nonthermal and nonlinear shielding effects on the transverse dust-lattice wave are investigated in Lorentzian complex dusty plasmas. It is found that the nonthermal effect strongly suppresses the wave frequency, especially at the maximum peak position. It is also found that the nonthermal effect weakens the oscillatory behavior of the dust-lattice wave for the large-dust spacing case. In addition, it is found that the nonthermal effect on the transverse dust-lattice wave increases with increasing inter-dust grain distance. It is also found that the nonlinear effect enhances the frequency amplitude of the dust-lattice wave in the small-spacing domain.

Nonlinear instabilities in two-dimensional hexagonal dust-lattice formed by paramagnetic particles

The propagation of linear and nonlinear transverse off-plane dust lattice waves in 2D hexagonal dusty plasma crystals including the paramagnetic effects (magnetized particles) is investigated theoretically. The linear dispersion characteristics of transverse dust lattice waves are studied, including the dispersion relations, group velocities, and an evolution equation for the modulated amplitude of the first harmonic. The dispersion relations show a negative group velocity of the wave for a weak paramagnetic effect and a positive group velocity for a strong paramagnetic effect. The modulated wave packet is described by a nonlinear Schrodinger equation. The modulational stability of carrier wave depends on the form of the electric field, the magnetic field, and the magnetic permeability of dust particles. We found that the wave is modulationally unstable for long wavelength limit and weak (or zero) paramagnetic effects.

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.