Nonlinear Development of a Low-Frequency Hall Current Instability in a Dusty Plasma

The nonlinear evolution of dust waves generated by a low‐frequency Hall current instability in a magnetized collisional dusty plasma is investigated with theory and nonlinear numerical simulations. This instability is believed to have broad applications to irregularity production in regions where dust is present in the earth's ionosphere such as noctilucent clouds and meteor trails. The instability is driven by an electron current and is an analog, in the dust acoustic type wave regime, of the well‐known Farley‐Buneman instability. The results indicate that the instability nonlinearly saturates with dust heating and the production of secondary waves that propagate in a direction perpendicular to the primary dust acoustic type waves.

Rayleigh Taylor instability in a dusty plasma

A numerical simulation model is presented to study an important effect of dust charging on waves and instabilities in unmagnetized dusty plasmas. In this study, the background plasma is treated as a two-component fluid whose density self-consistently varies due to dust charging. The dust is treated with a particle-in-cell model in which the dust charge varies with time according to the standard dust-charging model. An ion acoustic streaming instability due to dust charging when the ion fluid drifts with respect to stationary charged dust grains and electrons is investigated. The numerical simulation results show good agreement with theoretical predictions and provide further insight into dust-charging effects on wave modes and instabilities in dusty plasmas.

Theoretical and experimental studies of low-frequency electrostatic waves in plasmas containing negatively charged dust grains are described. The presence of charged dust is shown to modify the properties of ion-acoustic waves and electrostatic ion-cyclotron waves through the quasineutrality condition even though the dust grains do not participate in the wave dynamics. If the dust dynamics is included in the analysis, new “dust modes” appear—dust acoustic and dust cyclotron modes. The results of laboratory experiments dealing with dust ion acoustic (DIA) waves and electrostatic dust ion cyclotron (EDIC) waves are shown. These modes are more easily excited in a plasma containing negatively charged dust. Finally, observations of dust acoustic (DA) waves are presented and measurements of the dispersion relation are compared with one obtained from fluid theory.

Theoretical study is carried out for the dust acoustic waves in a dusty plasma. The dispersion relation is obtained from the fluid dynamical model. It is found that the wave frequency depends on the electron number density, wave number, and the speed of electrons or ions. The dependencies of the instability on the system parameters are also discussed. It is found that the long wavelength wave is usually unstable, which may be useful in the plasma physics, especially in the magnetic confined fusion system or the charged beam dynamics in the accelerated driven system.

In the present research paper, the nonlinear propagation of dust ion acoustic solitary waves in a collisional dusty plasma, which consists of negatively charged small dust grains, positively charged ions and isothermal electrons with background neutral particles, is investigated. The low rates compared to the ion oscillation frequency, of the charge-fluctuation dynamics of the dust grains, the ionization, ion-neutral and dust-neutral collisions (i.e. weak dissipations) are considered. Using the reductive perturbation theory, a damped Korteweg-de Vries (DKdV) equation is derived. On the other hand, the dynamics of solitary waves at a critical phase velocity is governed by a damped modified Korteweg-de Vries (DMKdV) equation. The nonlinear properties of dust ion acoustic waves in the presence of weak dissipations in the two cases are discussed.

A new dust-dynamics-induced interchange instability in dusty plasmas

Effect of magnetic field and radiative condensation on the Jeans instability of dusty plasma with polarization force

The effect of an external magnetic field on an ion-dust two-stream instability in a collisional dusty plasma is investigated. We consider the parameter regime in which the ions and electrons are strongly magnetized, while the charged dust is unmagnetized. The presence of a magnetic field tends to hinder the growth of the instability. The implications for laboratory dusty plasmas such as 'plasma crystals' are discussed.

A rigorous theoretical investigation is made to study the characteristics of dust-acoustic (DA) waves (DAWs) in an electron depleted unmagnetized opposite polarity dusty plasma system that contains super-thermal ($\kappa$-distributed) ions, mobile positively and negatively charged dust grains for the first time. The reductive perturbation method is employed to obtain the NLSE to explore the modulational instability (MI) conditions for DAWs as well as the formation and characteristics of gigantic rogue waves. The nonlinear and dispersion properties of the dusty plasma medium are the prime reasons behind the formation of rogue waves. The height and thickness of the DARWs associated with DAWs as well as the MI conditions of DAWs are numerically analyzed by changing different dusty plasma parameters, such as dust charges, dust and ion number densities, and ion-temperature, etc. The implications of the results for various space dusty plasma systems (viz., mesosphere, F-rings of Saturn, and cometary atmosphere, etc.) as well as laboratory dusty plasma produced by laser-matter interaction are briefly mentioned.

Dynamical properties of dust-ion-acoustic waves (DIAWs) are analysed in a collisional nonextensive dusty plasma composing of mobile ions, q-nonextensive electrons and stationary dust grains with slight collisions between dusts and ions. Reductive perturbation technique (RPT) is practiced to acquire the damped Korteweg-de Vries (DKdV) equation. In absence of collision between dusts and ions, the damping term vanishes and the DKdV equation reduces to the KdV equation. Bifurcation analysis of the dynamical system obtained from the KdV equation is carried out. Analytical solitary wave solution and numerical periodic wave solution of the KdV equation are presented. Approximate analytical DIAW solutions for the DKdV equation are furnished using the novel ( G ′ / G ) -expansion technique. As an outcome, novel approximate analytical solutions of DIAWs are obtained for the DKdV equation. The application of our work is significant to explore nonextensive plasma environment, such as, ionosphere of Earth.

A detailed investigation of electrostatic dust wave modes in unmagnetized dusty plasmas consisting of electrons, ions and dust grains has been carried out over a wide range of dust fugacity and wave frequency by using fluid as well as kinetic (Vlasov) theories. The dust fugacity parameter is defined by f≡4πnd0λD2R∼ND R/λD where nd0, λD and R are respectively the dust number density, the plasma Debye length and the grain size (radius), and ND=4πnd0λD3/3 is the dust plasma parameter. Dusty plasmas are considered to be tenuous, dilute or dense according as f≪1, ∼1, or ≫1. In particular, attention is focused on the “dust–acoustic waves” (DAWs) and the “dust–Coulomb waves” (DCWs) which exist in the tenuous (low fugacity) and the dense (high fugacity) regimes, respectively, when the wave frequency is much smaller than the grain charging frequency. Unlike the DAWs, which exist even with constant grain charge, the DCWs [N. N. Rao, Phys. Plasmas 6, 4414 (1999)] are the normal modes associated with grain charge fluctuations, and exist in dense dusty plasmas. In the long wavelength limit, the DCW phase speed scales as ∼CDA/f where CDA is the DAW phase speed. In the dilute (medium fugacity) regime, the two modes merge into a single mode, which may be called the “dust charge–density wave” (DCDW) since the latter involves contributions arising from both the DAW and the DCW. On the other hand, for frequencies much larger than the charging frequency, DAWs are shown to exist also in the dilute regime. The real frequency as well as the damping rate in each case are explicitly calculated from both the fluid as well the kinetic theories, and a comparison between the two has been carried out. In the allowed fugacity regimes (tenuous, dilute or dense), all the three waves are weakly damped and, hence, can propagate as normal modes. The present analysis of wave propagation in dusty plasmas over different fugacity regimes suggests the introduction of a new length scale defined by λR≡dWSdWS/3Rδ, where dWS is the Wigner–Seitz radius and δ is a parameter related to the charging frequencies. This length scale which governs the dispersive properties of the DCW modes is most useful in the dense regime, and plays a role which is very similar to that of the Debye length in the tenuous regime. The ratio of λR to λD is a measure of the dust fugacity, and is given through fδ=λD2/λR2. The very recent experimental observation [S. Nunomura et al., Phys. Rev. Lett. 83, 1970 (1999)] on a self-excited instability associated with grain charge fluctuations may be an indication of DCWs in the strong coupling regime. The possibility of the existence of a dust thermal wave (DTW) in the super-dense regime has been pointed out. A heuristic, but simple, derivation of DCWs based on grain dynamics but supplemented by physical inputs from the plasma response has also been presented.

The effects of nonextensive electrons on nonlinear ion acoustic waves in dusty negative ion plasmas with ion-dust collisions are investigated. Analytical results show that both solitary and shock waves are supported in this system. The wave propagation is governed by a Korteweg-de Vries Burgers-type equation. The coefficients of this equation are modified by the nonextensive parameter q. Numerical calculations indicate that the amplitude of solitary wave and oscillatory shock can be obviously modified by the nonextensive electrons, but the monotonic shock is little affected.

The influence of polarization force (PF) (arises due to dust density inhomogeneity), nonthermal electrons, and dust density inhomogeneity associated with positively charged dust on linear dust-acoustic (DA) waves in an inhomogeneous unmagnetized dusty plasma are investigated. By taking the normal mode analysis, the dispersion relation in such a non-Maxwellian inhomogeneous plasma is obtained, and that the dispersion properties of the DA waves are significantly modified by the presence of PF and nonthermal electrons. The PF is increased with the increase of nonthermal electrons. It is found that the phase speed of the DA waves is significantly decreased with the presence of PF and nonthermal electrons. The potential associated with the DA waves is de-enhanced with the increase of equilibrium dust number density. The role of positive dust number density on dispersion properties is also shown. The present findings relevant to different scenarios in laboratory and space dusty plasma, such as Martian ionosphere, solar flares, TEXTOR-94 tokamak plasmas, rf excited argon magnetoplasma, etc., can be useful to understand the properties of localized electrostatic disturbances in those dusty plasma system, are also briefly addressed.

Nonlinear Dynamics of Dust-Ion-Acoustic Waves in Magnetized Collisional Opposite Polarity Dusty Plasmas