Dispersion properties of a dusty plasma containing nonspherical rotating dust grains

The dispersion relation for a dusty plasma containing elongated and rotating charged dust grains is obtained by assuming that the dipole moments of the dust particulates are nonzero. The longitudinal waves with frequency close to the angular rotation frequency of the dust grains are found to be unstable. The results should be relevant to enhanced fluctuations in astrophysical environments.     

Acceleration of dust grains by means of the high energy ion beam

The acceleration of charged dust grains by a high energy ion beam is investigated by obtaining the dispersion relation. The Cherenkov and cyclotron acceleration mechanisms of dust grains are compared with each other. The role of dusty plasma parameters and the magnetic field strength in the acceleration process are discussed. In addition, the stimulated waves by an ion beam in a fully magnetized dust–ion plasma are studied. It is shown that these waves are unstable at different angles with respect to the external magnetic field. It is also indicated that the growth rates increase by either increasing the ion and dust densities or decreasing the magnetic field strength. Finally, the results of our research show that the high energy ion beam can accelerate charged dust grains.     

Linear propagation of dust acoustic modes in the presence of an electron beam

The physical and optical properties of plasmas are depended on dynamics of species in the discharge volume. Then, the presence of an electron beam, as a separate component, in a dusty plasma can modify the plasma structures through altering the discharge parameters. In this report, the linear propagation of acoustic modes in a collisionless dusty plasma contains electrons, ions and charged dust grains is investigated in the presence of an electron beam. Our analysis indicates that the electron beam can modify the dispersion relations of dust acoustic modes which resulted different data transportation in dusty plasmas. The obtained results are also examined for negative and positive charged dust grains with different number densities. The charge of dust grains represents an important role in the dynamics of the low frequency waves. Additionally, our findings reveal that the propagation of acoustic waves in dusty plasmas can be controlled by adjusting the electron number density of the beam and the cathode potential. Lastly, we obtian the destabilizing effects, originated from dust charge fluctuation, by reconsidering the dispersion relations of both dust acoustic modes.     

Waves propagating along a density gradient in a dusty plasma

The waves propagating in the direction of a density gradient in a dusty plasma are analyzed. The analysis includes the recently predicted electrostatic dust Rossby mode that can develop in a rotating dusty plasma with charged grains, as well as waves in magnetized plasmas, and dust acoustic waves. The spatial behavior of the mode amplitude is determined for a few realistic plasma density profiles.     

Mode transitions on the surface dust ion-acoustic wave in a semibounded dusty plasma

The effects of elongated rotating dust grains on the mode transitions of the dispersion relation of the surface dust ion-acoustic waves are investigated in a semi-bounded dusty plasma. The dispersion relation of the surface dust ion-acoustic wave is obtained by the plasma dielectric function with the specular reflection boundary condition. The result shows the existence of the dust ion-acoustic resonance modes in small and large wave number regions. It is also shown that the surface wave would be propagated in intermediate wave number domains. It is interesting to note that the wave propagation domain has been diminished with an increase of the rotation frequency.     

Theory of mach cones in magnetized dusty plasmas with strongly correlated charged dust grains

A theory for the formation of Mach cones in a magnetized dusty plasma with strongly correlated charged dust grains has been presented. We use the electron and ion susceptibilities for weakly correlated magnetized electrons and ions as well as the strongly correlated unmagnetized dust grain susceptibilities which are obtained by means of the quasilocalized charge approximation and a generalized hydrodynamic model. The plasma dielectric response of the present system reveals the parametric regimes for which Mach cones in a strongly coupled laboratory dusty magnetoplasma can be formed. We suggest conducting experiments in radiofrequency dusty plasma discharges with superconducting magnets for verifying the theoretical prediction of Mach cones that is made herein.     

The dust acoustic wave in a bounded dusty plasma with strong electrostatic interactions between dust grains

The dispersion relation for the dust acoustic wave (DAW) in an unmagnetized dusty plasma cylindrical waveguide is derived, accounting for strong electrostatic interactions between charged dust grains. It is found that the boundary effect limits the radial extent of the DAW. The present result should be helpful for understanding the frequency spectrum of the DAW in a dusty plasma waveguide with strongly coupled charged dust grains.     

Dispersion of Dust Acoustic Modes and Perturbations of Plasma Flux Balance

Previous considerations of dust acoustic waves is demonstrated to be inconsistent ‐ the required equilibrium state for perturbations was not defined since balance of plasma fluxes was neglecting. The self‐consistent treatment shows that plasma flux perturbations are accompanying any collective waves propagating in dusty plasmas and can play an important role in wave dispersion, wave damping and can create instabilities. This is illustrated by the derivation of dispersion relation for dust acoustic modes taking into account the plasma flux balances and plasma flux perturbations by waves. The result of this approach shows that the dust acoustic waves with linear dependence of wave frequency on the wave number exist only in restricted range of the wave numbers. Only for wave numbers larger than some critical wave number for low frequency modes the frequency can be have approximately a linear dependence on wave number and can be called as dust acoustic wave but the phase velocity of these waves is different from that which can be obtained neglecting the flux balance and depends on grain charge variations which are determined by the balance of fluxes. The presence of plasma fluxes previously neglected is the main typical feature of dusty plasmas. The dispersion relation in the range of small wave numbers is found to be mainly determined by the change of the plasma fluxes and is quite different from that of dust acoustic type, namely it is found to have the same form as the well known dispersion relation for the gravitational instability. This result proves in general way the existence of the collective grain attractions of negatively charged grains for for large distances between them and for any source of ionization. The attraction of grains found from dispersion relation of the dust acoustic branch coincides with that found previously for pair grain interactions using some models for the ionization source. For the existing experiments the effective Jeans length for such attraction is estimated to be about 8 – 10 times larger than the ion Debye length and the effective gravitational constant for the grain attraction is estimated to be several orders of magnitude larger than the usual gravitational constant. The grain attraction at large inter‐grain distances described by the gravitationlike grain instability is considered as the simplest explanation for observed dust cloud clustering, formation of dust structures including the plasma crystals. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sheared Flow Driven Drift Instability and Vortices in Dusty Plasmas with Opposite Polarity

Low-frequency electrostatic drift waves are studied in an inhomogeneous dust magnetoplasma containing dust with components of opposite polarity. The drift waves are driven by the magnetic-field-aligned (parallel) sheared flows in the presence of electrons and ions. Due to sheared flow in the linear regime, the electrostatic dust drift waves become unstable. The conditions of mode instability, with the effects of dust streaming and opposite polarity, are studied. These are excited modes which gain large amplitudes and exhibit interactions among themselves. The interaction is governed by the Hasegawa-Mima (HM) nonlinear equation with vector nonlinearity. The stationary solutions of the HM equation in the form of a vortex chain and a dipolar vortex, including effects of dust polarity and electron (ion) temperatures, are studied. The relevance of the present work to space and laboratory four component dusty plasmas is noted.     

Propagation of dust-acoustic waves in weakly ionized plasmas with dust-charge fluctuation

For an unmagnetized partially ionized dusty plasma containing electrons, singly charged positive ions, micron-sized massive negatively charged dust grains and a fraction of neutral atoms, dispersion relations for both the dust-ion-acoustic and the dustacoustic waves have been derived, incorporating dust charge fluctuation. The dispersion relations, under various conditions, have been exhaustively analysed. The explicit expressions for the growth rates have also been derived. International Conference on the Frontiers of Plasma Physics and Technology, 9–14 December 2002, Bangalore, India.     

Effect of polarization force on the Jeans instability of self-gravitating dusty plasma

The effect of polarization force acting on massive charged dust grains is investigated analytically on the Jeans instability of self-gravitating dusty plasma. The gravitational force acting on the massive negatively charged interstellar dust grains are considered in presence of both electrical and polarization forces. The basic equations of the problem are formulated and a general dispersion relation is obtained using plane wave approximation in low frequency wave mode. The effect of polarization force in the dispersion relation of the problem, condition of the Jeans instability and expression of the critical Jeans wave number is examined. The unstable growing modes due to self-gravitational force are studied in the situation when polarization force on the dust grain exceeds over the electrical force in magnitude. It is observed that the polarization force increases the growth rate of the system.     

The KP and ZK equations for electrostatic waves with grain charge fluctuation

The propagation of three-dimensional nonlinear dust-acoustic and dust-Coulomb waves in unmagnetized/magnetized dusty plasmas consisting of electrons, ions, and charged dust particles is investigated. The grain charge fluctuation effect is also incorporated through the current balance equation. By using the perturbation method, a Kadomtsev－Petviashvili equation and a Zakharov－Kuznetsov equation governing the nonlinear waves in the unmagnetized and magnetized systems are obtained respectively. It has been shown that with the combined effects of grain charge fluctuation, the transverse perturbation, and the external magnetic field would modify the wave structures. Waves in those systems are unstable to the high-order long-wave perturbations.     

Dispersion properties of low-frequency electrostatic oscillations in metallic carbon nanotubes

Dispersion properties of low-frequency electrostatic waves in metallic carbon nanotubes (CNTs) are investigated. We assume that metallic CNTs are charged due to the field emission, and hence the metallic nanotubes can be regarded as charged dust rods surrounded by degenerate electrons and ions. We deduce the perturbed electron and ion number densities by using the quantum hydrodynamic model, while the dust rod density perturbation follows the classical expression. The Poisson equation, in turn, gives the dispersion relation for the low-frequency electrostatic oscillations in our three-species bounded plasma system composed of metallic CNTs. The oscillation frequency of CNTs can be used for diagnostic purposes, e.g. for the determination of charge on nanotubes.     

Nonlinear Electrostatic Structures in Collisional Dusty Plasmas

A review of some problems of electrostatic waves in dusty plasmas is presented. It is concluded that in the most models of waves in dusty plasmas, the charge numbers of the ions and dusty grains are supposed to be constant. Besides most of the studies are elated to linear waves in collisionless systems. It is shown that even if the dynamics of dusty grains is not considered in the models, the physical processes causing wave dissipation have to be taken into account. The existing nonlinear models are mostly one‐dimensional ones. It is summarized that in dusty plasmas various types of nonlinear stationary structures may exist, and that these structures differ from the nonlinear structures found in ionospheric plasmas without dust. The nonlinear electrostatic stuctures seem to be observable in ionospheric, solar or interplanetary plasmas.     

On the dielectric response function and dispersion relation in strongly coupled magnetized dusty plasmas

Using the generalized viscoelastic fluid model, we derive the dielectric response function in a strongly coupled dusty magnetoplasma which reveals two different dust acoustic(DA) wave modes in the hydrodynamic and kinetic limits. The effects of the strong interaction of dust grains and the external magnetic on these DA modes, as well as on the shear wave are examined. It is found that both the real and imaginary parts of DA waves are significantly modified in strongly coupled dusty magnetoplasmas. The implications of our results to space and laboratory dusty plasmas are briefly discussed.     

The instability of dust acoustic waves in inhomogeneous dusty plasmas with non-adiabatic dust charge fluctuation

This paper investigates the propagation of linear dust acoustic waves in inhomogeneous dusty plasmas due to spatial gradients of dust charge, plasma densities. A linear dispersion relation is obtained with the non-adiabatic dust charge iguctuation and the non-thermally distributed ions. The numerical results show that the inhomogeneity, nonthermal ions and non-adlabatic dust charge iguctuatlon have strong iniguence on the frequency and the damping rate of waves.     

Dust acoustic waves in collisional uniform dense magnetoplasma

In order to study the characteristics of dust acoustic waves in a uniform dense dusty magnetoplasma system, a nonlinear dynamical equation is deduced using the quantum hydrodynamic model to account for dust–neutral collisions. The linear dispersion relation indicates that the scale lengths of the system are revised by the quantum parameter, and that the wave motion decays gradually leading the system to a stable state eventually. The variations of the dispersion frequency with the dust concentration, collision frequency, and magnetic field strength are discussed. For the coherent nonlinear dust acoustic waves, new analytic solutions are obtained, and it is found that big shock waves and wide explosive waves may be easily produced in the background of high dusty density, strong magnetic field, and weak collision. The relevance of the obtained results is referred to dense dusty astrophysical circumstances.     

Streaming instability of dust-acoustic mode with helical wavefronts

Making use of the kinetic approach for plasma species, the electrostatic twisted dust-acoustic (DA) waves are studied in a collisionless unmagnetized multi-component dusty plasma consisting of electrons, singly ionized positive ions and charged massive dust grains. The Vlasov-Poisson equations are coupled together to obtain a generalized response function by using the Laguerre-Gaussian (LG) perturbed electrostatic potential and distribution function in the paraxial limit. The dispersive properties and growth rate instability of twisted DA waves are examined with distinct OAM states in a multi-component dusty plasma. Various significant modifications associated with the real wave frequency and growth rate are shown with respect to twist parameter and dust concentration. It is examined that dust concentration enhances the growth rate of twisted DA waves, whereas an increase in twist parameter reduces the growth rate instability. The excitation of twisted DA mode is also found to enhance with streaming speed of inertialess electrons. Our results may be useful for particle transport and trapping phenomena due to wave excitation in laboratory dusty plasmas.     

Boundary Effects on Microwave Propagation in a Large Waveguide Containing a Magnetoplasma

Solution of Maxwell's equations for a cold, uniform magnetoplasma bounded by conducting walls shows (i) how plane waves evolve in the space of (?/?c,?p/?c) with (kc/?c) as parameter, and (ii) the range of parameters in which whistler mode propagation without Wieder's fine structure can be expected. In this space, the whistler evolves from an electrostatic mode at low densities, the whistler characteristic appears in a range of densities where the static approximation is invalid, and at still higher densities, residual effects of boundaries show up in the fine structure, as accounted for by J. C. Lee. The asymptotic form of the solution when lateral dimensions are large shows the existence of classes of solutions which are inadmissible because none can be reached along a continuous locus in this space. Effects of finite boundaries on the dispersion characteristic and the interpretation of experimental data are discussed.