Nonlinear dispersion relation for dust-acoustic waves in complex plasmas.

Nonlinear dispersion relation for the finite-amplitude dust acoustic modes is obtained taking into account resonant particle trapping in the wave. The kinetic model predicts a frequency shift scaling ∝sqrt[ϕ] relative to the linear dispersion relation with ϕ being the wave amplitude of the electrostatic potential. The species contributions to the nonlinear frequency shift have opposite sign: positive for trapped electrons and ions and negative for particles. It is shown that the relative importance of these contributions depends on the electron-to-ion or particle temperature ratio, particle charge, and Havnes parameter. In typical complex plasma experiments, the kinetic frequency shift is dominated by the positive ion contribution. As a result, the nonlinear modification of the dispersion relation affects the wave dispersion properties and may provide the acoustic-like behavior to the wave number domain kλ_{Di}∼1.

Dust-acoustic shocks in strongly coupled dusty plasmas.

Electrostatic dust-acoustic shock waves are investigated in a viscous, complex plasma consisting of dust particles, electrons, and ions. The system is modelled using the generalized hydrodynamic equations, with strong coupling between the dust particles being accounted for by employing the effective electrostatic temperature approach. Using a reductive perturbation method, it is demonstrated that this model predicts the existence of weakly nonlinear dust-acoustic shock waves, arising as solutions to Burgers's equation, in which the nonlinear forces are balanced by dissipative forces, in this case, associated with viscosity. The evolution and stability of dust-acoustic shocks is investigated via a series of numerical simulations, which confirms our analytical predictions on the shock characteristics.

Nonlinear dust-acoustic solitary waves in strongly coupled dusty plasmas.

Dust-acoustic waves are investigated in a three-component plasma consisting of strongly coupled dust particles and Maxwellian electrons and ions. A fluid model approach is used, with the effects of strong coupling being accounted for by an effective electrostatic "pressure" which is a function of the dust number density and the electrostatic potential. Both linear and weakly nonlinear cases are considered by derivation and analysis of the linear dispersion relation and the Korteweg-de Vries equation, respectively. In contrast to previous studies using this model, this paper presents the results arising from an expansion of the dynamical form of the electrostatic pressure, accounting for the variations in its value in the vicinity of the wave.

Influence of a polarization force on dust acoustic waves.

The effect of the polarization force acting on the grains in a nonuniform plasma background on the propagation of low-frequency waves in complex (dusty) plasmas is analyzed. It is shown that polarization interaction leads to a renormalization (decrease) of the dust acoustic phase velocity. The effect becomes more pronounced as the grain size increases. Finally, there is a critical grain size above which the dust acoustic waves cannot propagate, but aperiodic (nonpropagating) perturbations form instead.

Particle charge in the bulk of gas discharges.

An experimental determination of particle charge in a bulk dc discharge plasma covering a wide range of neutral gas pressures, was recently reported [S. Ratynskaia, Phys. Rev. Lett. 93, 085001 (2004)]. The charges obtained were several times smaller than the predictions of collisionless orbital motion limited theory. This discrepancy was attributed to the effect of ion-neutral collisions. In the present paper a more detailed description of this experiment is provided and additional experimental results obtained with particles of different sizes are reported. The measurements are compared with molecular dynamics simulations of particle charging for conditions similar to those of the experiment, with other available experimental data on particle charge in the bulk of gas discharges, and with a simple analytical model accounting for ion-neutral collisions. All the considered evidence indicates that ion-neutral collisions represent a very important factor, which significantly affects (reduces) the particle charge under typical discharge conditions.

Coupled dust-lattice modes in complex plasmas.

The coupling between transverse and longitudinal dust-lattice modes due to the particle-wake interactions and vertical dust charge gradient is considered. It is shown that the dust-lattice waves can be subjected to a specific instability, the criterion for which has been derived. This instability can explain experimentally observed spontaneous excitation of vibrational modes in a plasma crystal when the pressure is decreased below a critical value.

Electrostatic modes in collisional complex plasmas under microgravity conditions.

A linear dispersion relation in a highly collisional complex plasma, including ion drift, was derived in the light of recent PKE-Nefedov wave experiment performed under microgravity conditions onboard the International Space Station. Two modifications of dust density waves with wave frequencies larger than the dust-neutral collision frequency were obtained. The relevance to the space observations was analyzed and a comparison of theory and observations was made for two different complex plasma domains formed by small and large microparticles. Good qualitative agreement is found between the measurements and the theoretical dispersion relations. This allows a determination of the basic complex plasma parameters.

Vertical oscillations of paramagnetic particles in complex plasmas.

Vertical vibrations of a single magnetized dust grain and a one-dimensional string of magnetized particles in discharge plasmas are treated taking into account the magnetic force associated with gradients of an external magnetic field. For a single particle a novel type of oscillation associated with these gradients is found. Such vibrations can be stable or unstable depending on the distribution of the magnetic field inside the particle cloud. In a one-dimensional particle string the magnetic force causes a new low-frequency oscillatory mode which is characterized by inverse optical-like dispersion when the wavelength far exceeds the intergrain distance. The study of vertical vibrations of magnetized grains provides a tool for determining complex plasma parameters.

Jeans instability in partially ionized self-gravitating dusty plasmas.

By employing the Boltzmann distributions for electrons and ions and by retaining the full dynamics of charged dust and neutral fluids, we derive a dispersion law for coupled dust-acoustic and neutral sound waves in partially ionized self-gravitating dusty plasmas. This dispersion law exhibits new classes of Jeans instability in both collisionless and highly collisional regimes. The result should help understand the origin of molecular cloud collapse in interstellar space.

Low-frequency electrostatic waves in self-gravitating dusty plasmas with dust-ion collisions.

The influence of dust-ion collisions on low-frequency modes in a self-gravitating dusty plasma is studied. The stability of the system is easily determined using elementary principles of rootlocus theory. It shows that collisions between ions and dust grains do not change the criteria for gravitational collapse at any value of their collision frequency, but diminish the growth rate of unstable dusty plasmas. Moreover, the rootlocus plots visualize qualitatively the evolution of the real frequencies and damping decrements of the dust-acoustic and ion-acoustic modes as the dust-ion collision frequency increases.

Vibrational modes in plasma crystals due to nonlinear temperature distribution in gas discharge plasmas.

It is shown that a nonlinear temperature distribution in gas discharge plasma leads to a specific low-frequency mode of a quasi-two-dimensional plasma crystal. Linear dispersion characteristics of the mode are obtained. The characteristics of the mode can depend strongly on the temperature gradients and therefore can be effectively controlled by the experimental conditions.

Dust-acoustic modes in self-gravitating plasmas with dust size distributions.

Using a kinetic description, dust-acoustic waves are considered for dusty plasmas containing, besides the electrons and ions, dust particles with continuous mass (size) distributions. For broad size spectra, self-gravitational effects cannot be neglected anymore because in the competition between electromagnetic and gravitational forces, the scale tips over towards gravitation for the heavier dust grains. Self-gravitational effects are clearly interwoven with the grain size distribution and here the effects of different power-law size distributions on the propagation, damping, and instability of low-frequency waves are discussed.

Kinetic approach to low-frequency waves in dusty self-gravitating plasmas.

A kinetic model is derived for the propagation of low-frequency waves in a dusty plasma containing very heavy dust particles, when the self-gravitational interaction due to these grains is included in the analysis. Analytical expressions for the dispersion function are used to examine the instability and damping of the modes. The stability regions of low-frequency waves are compared in the kinetic and the analogous hydrodynamic models, showing that there are only slight differences. However, the kinetic analysis modifies the growth rates of the Jeans instability and can considerably alter the conditions for the propagation of stable dust modes.