Transverse Dust Lattice Waves Research Articles

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.

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 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.

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.

Dressing effects on transverse dust lattice waves in dusty plasmas

It is shown that the transverse dust lattice waves become unstable due to the dressing effects in strongly coupled dusty plasmas. It is also found that the growth rate of the instability increases for 3 + 1 < a / λ D < 2 2 + 2 and decreases for a / λ D > 2 2 + 2 , where a is the spacing of dust grains and λ D is the Debye length.

Nonlinear modulation of transverse dust lattice waves in complex plasma crystals

The occurrence of the modulational instability in transverse dust lattice waves propagating in a one-dimensional dusty plasma crystal is investigated. The amplitude modulation mechanism, which is related to the intrinsic nonlinearity of the sheath electric field, is shown to destabilize the carrier wave under certain conditions, possibly leading to the formation of localized envelope excitations. Explicit expressions for the instability growth rate and threshold are presented and discussed.

Modulated Wave Packets and Envelope Solitary Structures in Complex Plasmas

A theoretical study is presented of the nonlinear amplitude modulation of waves propagating in unmagnetized plasmas contaminated by charged dust particles. Distinct well-known dusty plasma modes are explicitly considered, namely, the dust-acoustic wave, the dust-ion acoustic wave, and transverse dust-lattice waves. Using a multiple-scale technique, a nonlinear Schrodinger-type equation is derived, describing the evolution of the wave amplitude. A stability analysis reveals the possibility for modulational instability to occur, possibly leading to the formation of different types of envelope-localized excitations (solitary waves), under conditions which depend on the wave dispersion laws and intrinsic dusty plasma parameters.

Weakly Nonlinear Effects Associated with Transverse Oscillations in Dusty Plasma Crystals

We study the amplitude modulation of transverse dust lattice waves (TDLW) propagating in a single- and double-layer dusty plasma (DP) crystal. It is shown that a modulational instability mechanism, which is related to an intrinsic nonlinearity of the sheath electric field, may occur under certain conditions. Possibility of the formation of localized excitations (envelope solitons) in the dusty plasma crystal is discussed.

Dispersion properties of the out-of-plane transverse wave in a two-dimensional Coulomb crystal.

The formation of a two-dimensional (2D) Coulomb crystal in a typical experimental environment was simulated with a computer code called BOX_TREE. The dispersion properties of a novel dust lattice wave (DLW) mode, the out-of-plane transverse wave, were obtained. The dispersion relation was determined to be an opticlike inverse dispersion when wave number k is lower than a critical value k(critical), and a positive dispersion when k>k(critical). The negative group velocity of the wave for k<k(critical) depends on the kappa value (with kappa=a/lambda(D), where a is the interparticle spacing and lambda(D) is the Debye length) and the positive group velocity for k>k(critical) depends on the propagation direction. The value of k(critical) depends on both kappa and propagation direction, but changes very little for all propagation directions and the range of kappa investigated. An analytical method has also been used to derive the dispersion relations assuming a hexagonal 2D lattice and Yukawa interparticle potential. These dispersion relations compare favorably with the simulation results. The dispersion relation for a 1D string was also obtained via BOX_TREE simulation and shown to agree with the analytical result given by Vladimirov [Physica A 315, 222 (2002)]. Comparison shows that the out-of-plane transverse DLW in a 2D lattice when k<k(critical) has a negative group velocity much larger than that of the 1D string, given the same particle parameters and operating environment. Again k(critical) for 1D string and 2D lattice are in the same range.

Melting of monolayer plasma crystals.

Melting of a monolayer plasma crystal in a radio-frequency discharge with no particles suspended above or below is studied. The experimental data are compared with results of molecular dynamics simulations and theory. It is shown that the melting is caused by the resonance coupling between the longitudinal and the transverse dust-lattice wave modes, due to the interaction of particles with the plasma wakes.

Dynamic behaviors of dust particles in the plasma–sheath boundary

A variety of dynamic behaviors in dusty plasmas is expected under the experimental condition of weak friction with gas molecules. The device “KAGEROU” provides such an environment for dynamic collective phenomena. Self-excited dust oscillations in Coulomb crystals have been observed at low values of plasma density and gas pressure. An instability mechanism was identified to be delayed charging in an inhomogeneous equilibrium dust charge in the sheath. The theoretical growth rate was formulated in relation to the destabilization of a transverse dust lattice wave (T-DLW), which was found to be very sensitive to the presence of a small amount of hot electrons which produces a substantial positive equilibrium charge gradient ∇Qd-eq around the equilibrium position of dust particles in the plasma–sheath boundary. The first experimental observation of a correlated self-excited vertical oscillations in a one-dimensional dust chain indicates a destabilization of T-DLW. The experimental condition is very consistent with the parameter area which predicts numerically an instability of T-DLW.

Experimental observation of vertically polarized transverse dust-lattice wave propagating in a one-dimensional strongly coupled dust chain.

Externally driven, vertically polarized transverse dust-lattice waves were observed in a one-dimensional strongly coupled dust chain levitated in the plasma-sheath boundary of a dc argon plasma at low gas pressure around 5 mtorr. Real and imaginary parts of the complex wave number were measured in the experiments. The experimental result clearly shows that the observed transverse dust-lattice wave propagates as a backward wave, which is in good agreement with the theoretical prediction.