In this work linear stability analysis of a four-fluid optically thin plasma consisting of electrons, ions, neutral atoms, and charged dust particles is performed with respect to the radiation-condensation (RC) instability. The energy budget of the plasma involves the input from heating through photo-electron emission by dust particles under external ultraviolet radiation as well as radiative losses in inelastic electron-neutral, electron-ion, neutral-neutral collisions. It is shown that negatively charged particles stimulate the RC instability in the sense that the conditions for the instability to hold are wider than similar conditions in a single-fluid description.
The dynamics of linear perturbations in a radiatively cooling dusty plasma is considered, with the charge of both dust ($Z_d$) and plasma ($Z_p$) components being allowed to vary with their densities. It is shown that in the long-wavelength limit corresponding to the characteristic cooling length, when the plasma can be treated as quasineutral, the presence of dust particles changes the criteria for radiation instability, regardless the charging process of the dust particles. In particular, the condensation (isobaric) mode is shown to be stabilized (destabilized) if in the equilibrium, the rel…
Low frequency longitudinal wave instability in magnetized high correlation dusty plasmas is investigated. The dust charging relaxation is taken into account. It is found that the instablity of wave is determined significantly by the frequency of wave, the dust charging relaxation, the shear viscosity and viscoelastic relaxation time, the coupling parameter of high correlation of dust as well the strength of magnetic field.
A model for the condensation of a dusty plasma is constructed by considering the spherical shielding layers surrounding a dust grain test particle. The collisionless region less than a collision mean free path from the test particle is shown to separate into three concentric layers, each having distinct physics. The method of matched asymptotic expansions is invoked at the interfaces between these layers and provides equations which determine the radii of the interfaces. Despite being much smaller than the Wigner-Seitz radius, the dust Debye length is found to be physically significant because…
It is demonstrated that low frequency shear modes in a strongly coupled, inhomogeneous, dusty plasma can grow on account of an instability involving the dynamical charge fluctuations of the dust grains. The instability is driven by the gradient of the equilibrium dust charge density and is associated with the finite charging time of the dust grains. The present calculations, carried out in the generalized hydrodynamic viscoelastic formalism, also bring out important modifications in the threshold and growth rate of the instability due to collective effects associated with coupling to the compr…
Linear stability analysis of strongly coupled incompressible dusty plasma in presence of shear flow has been carried out using Generalized Hydrodynamical(GH) model. With the proper Galilean invariant GH model, a nonlocal eigenvalue analysis has been done using different velocity profiles. It is shown that the effect of elasticity enhances the growth rate of shear flow driven Kelvin- Helmholtz (KH) instability. The interplay between viscosity and elasticity not only enhances the growth rate but the spatial domain of the instability is also widened. The growth rate in various parameter space and…
Rayleigh-Taylor and Buoyancy-driven instabilities are very common instabilities for an inhomogeneous medium. We examine here how these instabilities grow for incompressible viscoelastic fluids like a strongly coupled dusty plasma by using incompressible generalized hydrodynamic (i-GHD) fluid model. Since the dust particles are pretty massive, the gravitational attraction of earth has a significant role in its dynamics. In this paper the acceleration due to gravity g and the role of strong coupling in the context of gravitationally stratified dusty plasma fluid have been considered. We find tha…
We investigate the role of thermal instability, arising from radiative cooling of an optically thin, dusty plasma, by linear stability analysis. The corresponding isobaric stability condition for condensation mode is found to be modified significantly by the degree of ionization and concentration of finite sized, relatively heavy, and negatively charged dust particles. It has been shown that though the fundamental wave mode is similar in nature to the one in absence of dust particles, a new dust-wave mode can propagate in such a plasma. It is conjectured that the presence of negatively charged…
A hypothesis on the physical mechanism generating the heartbeat instability in complex (dusty) plasmas is presented. It is suggested that the instability occurs due to the periodically repeated critical transformation on the boundary between the microparticle-free area (void) and the complex plasma. The critical transformation is supposed to be analogous to the formation of the sheath in the vicinity of an electrode. The origin of the transformation is the loss of the electrons and ions on microparticles surrounding the void. We have shown that this hypothesis is consistent with the experiment…
In this paper we introduce an algebraic form of the dispersion relation for a non ideal inhomogeneous dusty plasma in order to improve drastically the calculation of the drift instability growth rate. This method makes use of the multipole approximation of the Z dispersion function, previously published, and valid for the entire range. A careful analysis of the solutions spectra of this kind of polynomial equation permits us to calculate easily the growth rate of the drift instability for the ion-dust and dust acoustic mode. The value of the parallel to magnetic field wavelength for which the …
The dispersion relation of kinetic Alfvén wave in inertial regime is studied in a three component non-degenerate streaming plasma. A lin- ear dispersion relation using fluid- Vlasov equation for quantum plasma is also derived. The quantum correction CQ raised due to the insertion of Bohm potential in Vlasov model causes the suppression in the Alfven wave frequency and the growth rates of instability. A number of analytical expressions are derived for various modes of propagation. It is also found that many system parameters, i.e, streaming velocity, dust charge, num- ber density and quantum co…
We present an analysis of radiation induced instabilities in an expanding plasma with considerable presence of dust particles and equilibrium cooling. We have shown that the equilibrium expansion and cooling destabilize the radiation condensation modes and the presence of dust particles enhances this effect. We have examined our results in the context of ionized, dusty-plasma environments such as those found in planetary nebulae (PNe). We show that due to the non-static equilibrium and finite equilibrium cooling, small-scale localized structures formed out of thermal instability, become transi…
Along with crossed electric and magnetic fields in a Hall thruster, a radial component of electric field is generated that takes ions toward the walls, which causes sputtering and produces dust contamination in the thruster plasma. Considering negatively charged dust particles in the Hall thruster, we approach analytically the resistive instability by taking into account the oscillations of dust particles, ions and electrons along with finite temperatures of ions and electrons. In typical Hall thruster regimes, the resistive instability growth rate increases with higher collision rates in the …
Ion-ion instability is excited due to the counter streaming of ion beams in any plasma system. An experiment has been carried out to observe the ion-ion instability in dusty plasma and in presence of different gas compositions viz., H2, Ar, Xe and He. The experiment is performed in a double plasma device consisting of 90 cm in diameter and 120 cm in length and separated by a mesh grid of 81% optical transparency. Glass beads of 10 mm average dust distributions are used as a dust grains for the whole set of experiment and are allowed to fall within a particular region of plasma column inside th…
Motivated by observations of localized electrostatic wavepackets by the Voyager 1 and 2 and Cassini missions in Saturn's magnetosphere, we have investigated the evolution of modulated electrostatic wavepackets in a dusty plasma environment. The well-known dust-ion acoustic (DIA) mode was selected to explore the dynamics of multi-dimensional structures, by means of a Davey-Stewartson (DS) model, by taking into account the presence of a highly energetic (suprathermal, kappa-distributed) electron population in combination with heavy (immobile) dust in the background. The modulational (in)stabilit…
Kelvin-Helmholtz (KH) instability plays a significant role in transport and mixing properties of any medium. In this paper, we numerically explore this instability for a two-dimensional strongly coupled dusty plasma with rotational shear flows. We study this medium using generalized hydrodynamic fluid model which treats it as viscoelastic fluid. We consider the specific cases of rotating vorticity with abrupt radial profiles of rotation. In particular: single-circulation, and multi-circulation vorticity shell profiles have been chosen. We observe the KH vortices at each circular interface betw…
It is shown that the grain mass fluctuation, which is due to the grain sputtering by the attracted ions, may be at the root of a new instability in infinite, unmagnetized and homogeneous dusty plasmas. The growth rate is determined in the framework of two plasma models, viz., a cold and electron depleted plasma, and a plasma where electrons and ions are taken Boltzmannian. This instability may affect the Jeans as well as the agglomeration instabilities.
In part I (arXiv:2006.12393) (accepted in JPP), we simulated individual dynamics of a rising bubble and a falling droplet in an incompressible limit of a strongly coupled dusty plasma (SCDP) using a generalized hydrodynamic viscoelastic fluid model. In interest to understand hetero- (bubble-drop) interactions between them, we extend this study to their combined evolution through two arrangements: First, both are placed side-by-side in a row at the same height. We observe that the overall dynamic governs by the competition between the rotational motion induces due to the pairing between two co-…
A perpendicular ion drift is investigated as a mechanism for the generation of magnetic field structures in a highly collisional dusty plasma. The basic dissipation mechanism is assumed to be the dust-neutrals momentum exchange, so that plasmas with a small ionization fraction are natural candidates for experiments. The model reduces to a nonlinear partial differential equation for the vector potential. The conditions for linear instability are determined. The stationary states are periodic arrangements for the magnetic field, described by a Lienard equation. The fully depleted (ion-dust) case…
Dust-acoustic (DA) waves (DAWs) and their modulational instability (MI) have been investigated theoretically in a plasma system consisting of inertial opposite polarity (positively and negatively) warm adiabatic charged dust particles as well as inertialess non-extensive $q$-distributed electrons and non-thermal ions. A nonlinear Schrödinger (NLS) equation is derived by using the reductive perturbation method. It has been observed from the analysis of NLS equaion that the modulationally stable solitary DAWs give rise to the existence of dark envelope solitons, and that the modulationally unsta…
We study the dispersion relation for parallel propagating ion-cyclotron (IC) waves in a dusty plasma, considering situations where the velocity dispersion along perpendicular direction is greater than along the parallel direction, and considering the use of product-bi-kappa (PBK) velocity distributions for the plasma particles. The results obtained by numerical solution of the dispersion relation, in a case with isotropic Maxwellian distributions for electrons and PBK distribution for ions, show the occurrence of the electromagnetic ion-cyclotron instability (EMIC), and show that the decrease …
The standard nonlinear Schrödinger equation (NLSE) is one of the elegant equations to find the information about the modulational instability criteria of dust-ion-acoustic (DIA) waves (DIAWs) and associated DIA rogue waves (DIARWs) in a three-component dusty plasma medium having inertialess super-thermal kappa distributed electrons, and inertial warm positive ions and negative dust grains. It can be seen that under the consideration of inertial warm ions along with inertial negatively charged dust grains, the plasma system supports both fast and slow DIA modes. The charge state and number dens…
In this work linear stability analysis of a magnetized dusty plasma with an anisotropic dust component having transversal motions much stronger than motions parallel to the external magnetic field, and isotropic light plasma components is described. Such a situation presumably establishes in a shock compressed space dusty plasma downstream the shock front. Oblique low-frequency magneto-hydrodynamic waves ($ω\ll ω_{cd}$, $ω_{cd}$ being the dust cyclotron frequency) are shown to be undergone to the mirror instability. Consequences for nonthermal dust destruction behind shock fronts in the inters…
The formation of the gigantic dust-acoustic rouge waves (DARWs) in an electron depleted unmagnetized opposite polarity dusty plasma system is theoretically observed for the first time. The nonlinear Schrödinger equation (derived by utilizing the reductive perturbation method) has been analytically as well as numerically analyzed to identify the basic features (viz., height, thickness, and modulational instability, etc.) of DARWs. The results obtained form this investigation should be useful in understanding the basic properties of these rouge waves which can predict to be formed in electron de…
A numerical study of gravity-driven instability in strongly coupled dusty plasma. Part 3: Homo-interaction between a pair of rising/falling bubbles/droplets
We present an investigation of the combined effects of the Debye-Huckel (DH) repulsive and overlaping Debye spheres (ODS) attractive interaction potentials around charged dust particles on collective modes, phase separation and ordered dust structures in a strongly coupled dusty plasma. We obtain static and dynamical information via Molecular Dynamics simulations in the liquid and crystallized phases and identify the onset of an instability in the transverse collective mode, by using (zero-temperature) lattice summation method. The present results are useful for understanding the origin of coa…
Dusty plasma experiments can be performed quite easily in strong coupling regime. In our previous work [Phys. Plasmas 21, 073705 (2014)], we numerically explored such plasmas with constant density and observed the transverse shear (TS) waves from a rotating vortex. Laboratory dusty plasmas are good examples of homogeneous plasmas however heterogeneity (e.g. density, temperature, charge) may be due to the existence of voids, different domains with different orientations, presence of external forces like magnetic and/or electric, size/charge imbalance, etc. Here, we examine how the density heter…
Instabilities of ion-acoustic waves in a dusty plasma with electron-drift, collisional, and dust charge fluctuations effects, have been investigated. The regimes are clearly marked out where the theory is applicable. The critical electron-drift velocity required to drive the instability is predicted. It is also shown that electron thermal conductivity and charged grains concentration enhance the growth of the ion-acoustic mode whereas ion-viscosity, ion-thermal conductivity, and dust charge fluctuations have a stabilizing effect.
The basic features of dust-acoustic (DA) waves (DAWs) in four component dusty plasma system (containing inertial cold and hot dust grains, inertialess non-extensive ions and electrons) have been theoretically investigated by deriving the nonlinear Schrödinger equation. The analytic analysis under consideration demonstrates two types of modes, namely, fast and slow DA modes. The unstable domain for the fast DA mode, which can be recognized by the critical wave number ($k_c$), gives rise to the DA rogue waves (DARWs). It is observed that the amplitude and width of the DARWs are significantly mod…
Ordered dusty structures influence plasma conditions. This influence can be revealed, when plasma spectral characteristics change, as dusty particles are injected. For example, a variation in the atomic temperature leads to a variation in the profiles of spectral lines. We studied the profile of a 585 nm neon spectral line in the dusty structures. The structures levitated in a positive column of a glow discharge at a pressure of 50-150 Pa and with a current of 1-9 mA. We scanned the profile with the use of a Fabry-Perot interferometer, by changing the air pressure between the interferometer mi…
The modulational instability of dust-acoustic (DA) waves (DAWs), and corresponding DA rogue waves (DARWs) in a realistic space dusty plasma system (containing inertial warm positively and negatively charged dust, isothermal ions, and nonthermal kappa distributed electrons) has been theoretically investigated. The nonlinear Schrödinger (NLS) equation is derived by using reductive perturbation method for this investigation. It is observed that the dusty plasma system under consideration supports two modes, namely fast and slow modes, and that both of these two modes can be stable or unstable dep…
The melting of 2D dust clusters caused by one additional particle in the lower layer has experimentally been observed to undergo a two-step transition, which divides the phase of the cluster into three stages. The first transition is a jump of the dust kinetic energy due to the onset of an instability of the lower-layer particle, shifting the cluster from an ordinary to a hot crystalline state. The second transition is the actual phase transition into a liquid state, which occurs at a decisively lower gas pressure. The detailed dynamical properties of the system during the transition were dete…
The nonlinear propagation of the dust-acoustic bright and dark envelope solitons in an opposite polarity dusty plasma system (composed of non-extensive $q$-distributed electrons, isothermal ions, and positively as well as negatively charged warm dust) have been theoretically investigated. The reductive perturbation method (which is valid for a small, but finite amplitude limit) is employed to derive the nonlinear Schrödinger equation. Two types of modes (namely, fast and slow dust-acoustic (DA) modes) have been observed. The conditions for the modulational instability (MI) and its growth rate …
The omnipresence of dust particulates in space and astrophysical plasmas has been attracting numerous researchers to study the collective excitation and propagation dynamics of different eigen-mode structures in diversifed astrocosmic circumstances for years. It includes planetary rings, interplanetary space, cometary tails, asteroid zones, planetary atmospheres, etc. The ubiquitous charged dust particulates possess collective degrees of dynamic freedom resulting in the excitation of relatively low-frequency modes, such as dust-ion-acoustic waves (DIAWs), dust-acoustic waves (DAWs), dust-Coulo…
The influence of viscosity gradient (due to shear flow) on low frequency collective modes in strongly coupled dusty plasma is analyzed. It is shown that for a well known viscoelastic plasma model, the velocity shear dependent viscosity leads to an instability of the shear mode. The inhomogeneous viscous force and velocity shear coupling supply the free energy for the instability. The combined strength of shear flow and viscosity gradient wins over any stabilizing force and makes the shear mode unstable. Implication of such a novel instability and its applications are briefly outlined.
The amplitude modulation of three dimensional (3D) dust ion-acoustic wave (DIAW) packets is studied in a collisionless magnetized plasma with inertial positive ions, superthermal electrons and negatively charged immobile dust grains. By using the reductive perturbation technique, a 3D-nonlinear Schrödinger (NLS) equation is derived, which governs the slow modulation of DIAW packets. The latter are found to be stable in the low-frequency $(ω<ω_c)$ regime, whereas they are unstable for $ω>ω_c$, and the modulational instability (MI) is related to the modulational obliqueness $(θ)$. Here, $ω~(ω_c)…
The weakly nonlinear regime of transverse paramagnetic dust grain oscillations in dusty (complex) plasma crystals is discussed. The nonlinearity, which is related to the sheath electric/magnetic field(s) and to the inter--grain (electrostatic/magnetic dipole) interactions, is shown to lead to the generation of phase harmonics and, in the case of propagating transverse dust-lattice modes, to the modulational instability of the carrier wave due to self--interaction. The stability profile depends explicitly on the form of the electric and magnetic fields in the plasma sheath. The long term evolut…
A rigorous theoretical investigation is made to study the characteristics of dust-acoustic (DA) waves (DAWs) in an electron depleted unmagnetized opposite polarity dusty plasma system that contains super-thermal ($κ$-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 be…
The Kelvin-Helmholtz (KH) instability is studied in a non-Newtonian dusty plasma with an experimentally verified model [Phys. Rev. Lett. {\bf 98}, 145003 (2007)] of shear flow rate dependent viscosity. The shear flow profile used here is a parabolic type bounded flow. Both the shear thinning and shear thickening properties are investigated in compressible as well as incompressible limits using a linear stability analysis. Like the stabilizing effect of compressibility on the KH instability, the non-Newtonian effect in shear thickening regime could also suppress the instability but on the contr…
The dust-acoustic waves and their stability in the permeating dusty plasma with the Maxwellian velocity distribution are investigated. We derive the dust-acoustic wave frequency and instability growth rate in two limiting physical cases that the thermal velocity of the flowing dusty plasma is (a) much larger than, and (b) much smaller than the phase velocity of the waves. We find that the stability of the waves depend strongly on the velocity of the flowing dusty plasma in the permeating dusty plasma. The numerical analyses are made based on the example that a cometary plasma tail is passing t…
New developments in the theory and numerical simulation of a recently proposed one-dimensional nonlinear time-dependent fluid model [K. Avinash, A. Bhattacharjee, and S. Hu, Phys. Rev. Lett. 90, 075001 (2003)] for void formation in dusty plasmas are presented. The model describes an initial instability caused by the ion drag, rapid nonlinear growth, and a nonlinear saturation mechanism that realizes a quasi-steady state containing a void. The earlier one-dimensional model has been extended to two and three dimensions (the latter, assuming spherical symmetry), using a more complete set of dynam…
Modulational instability (MI) of dust acoustic waves (DAWs), which propagates in an opposite polarity dusty plasma system, containing inertial warm negatively and positively charged dust particles as well as non-extensive q-distributed elec- trons and ions, has been theoretically investigated. The nonlinear Schrodinger (NLS) equation is derived by employing the reductive perturbation method. The NLS equation leads to the MI of DAWs as well as to the formation of DAW rogue waves (DARWs), which are formed due to the effects of nonlinearity in the propagation of DAWs. Both stable and unstable re…
The nonlinear dynamics of coupled electrostatic upper-hybrid (UH) and Alfven waves (AWs) is revisited in a magnetized electron-ion plasma with charged dust impurities. A pair of nonlinear equations that describe the interaction of UH wave envelopes (including the relativistic electron mass increase) and the density as well as the compressional magnetic field perturbations associated with the AWs is solved numerically to show that many coherent solitary patterns can be excited and saturated due to modulational instability of unstable UH waves. The evolution of these solitary patterns is also sh…
The modulational instability of dust-ion-acoustic (DIA) mode and associated rogue waves in a three component dusty plasma system (containing inertial warm ion and negatively charged dust fluids along with inertialess $q$-distributed electrons) has been theoretically investigated. A nonlinear Schrödinger equation (NLSE) has been derived by employing the reductive perturbation method. It is observed that the dusty plasma system under consideration supports the fast and slow DIA modes, and that the dispersion and nonlinear coefficients of the NLSE determine the parametric regimes not only for the…
In a dusty plasma, an impulsively generated shock, i.e., blast wave, was observed to decay less than would be expected due to gas friction alone. In the experiment, a single layer of microparticles was levitated in a radio-frequency glow-discharge plasma. In this layer, the microparticles were self-organized as a 2D solid-like strongly coupled plasma, which was perturbed by the piston-like mechanical movement of a wire. To excite a blast wave, the wire's motion was abruptly stopped, so that the input of mechanical energy ceased at a known time. It was seen that, as it propagated across the lay…
In flare-relevant current sheets, tearing instability may trigger explosive reconnection and plasmoid formation. We explore how the thermal and tearing modes reinforce each other in the fragmentation of a current sheet in the solar corona through an explosive reconnection process, characterized by the formation of plasmoids which interact and trap condensing plasma. We use a resistive magnetohydrodynamic (MHD) simulation of a 2D current layer, incorporating the non-adiabatic effects of optically thin radiative energy loss and background heating using \texttt{MPI-AMRVAC}. Our parametric survey …
We report on a novel investigation of the nonlinear regime of the electron cyclotron drift instability, using a grid-based Vlasov simulation. It is shown that the instability occurs as a series of cyclotron resonances with the electron beam mode due to the $E\times B$ drift. In the nonlinear regime, we observe condensation of fluctuations energy toward the lowest resonance mode and below, i.e., an inverse energy cascade. It is shown that the characteristics of the nonlinear saturation state remain far from the ion-sound regime.
