The formation of dust ion-acoustic shocks (DIASs) in a four-component quantum plasma whose constituents are electrons, both positive and negative ions and immobile charged dust grains, is studied. The effects of both the dissipation due to kinematic viscosity and the dispersion caused by the charge separation as well as the quantum tunneling due to the Bohm potential are taken into account. The propagation of small but finite amplitude dust ion-acoustic waves (DIAWs) is governed by the Korteweg-de Vries-Burger (KdVB) equation which exhibits both oscillatory and monotonic shocks depending not only on the viscosity parameters, but also on the quantum parameter H (the ratio of the electron plasmon to the electron Fermi energy) and the positive to negative ion density ratio. Large amplitude stationary shocks are recovered for a Mach number exceeding its critical value. Unlike the small amplitude shocks, quite a smaller value of the viscosity parameter, H and the density ratio may lead to the large amplitude monotonic shock strucutres. The results could be of importance in astrophysical and laser produced plasmas.
In this article we are going to consider dust acoustic wave in dusty plasma whose constituents are inertial negative charged dust particles, Boltzmann distributed electrons and non-thermal distributed ions with variable dust charge. Using reductive perturbation method, we have obtained Korteweg-de Veries (kdv) and modified kdv(mkdv) equations. A Sagdeev potential for the system and stability conditions for solitonic solution are also derived.
Particles in a dusty plasma crystal disturbed by a shock wave are tracked using a three-mode interacting multiple model approach. Color-coded mode probabilities are used to visualize the shock wave propagation through the crystal.
The impacts of dust density inhomogeneity and dust size distribution (DSD) on linear dust acoustic (DA) wave propagation have been investigated theoretically in an inhomogeneous unmagnetized dusty plasma having powerlaw DSD. Two different types of wave modes, viz. slow and fast mode, are found to propagate in this inhomogeneous medium. It is shown that the linear dispersion characteristics of the DA waves are substantially affected by the DSD and density inhomogeneity. Also, it is found that the phase velocity increases with increasing dust density.
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…
We examine linear dust acoustic waves (DAWs) in a dusty plasma with strongly correlated dust grains, and discuss possibility of a twisted DA vortex beam carrying orbital angular momentum (OAM). For our purposes, we use the Boltzmann distributed electron and ion density perturbations, the dust continuity and generalized viscoelastic dust momentum equations, and Poisson's equation to obtain a dispersion relation for the modified DAWs. The effects of the polarization force, strong dust couplings, and dust charge fluctuations on the DAW spectrum are examined. Furthermore, we demonstrate that the D…
An experimental investigation of the propagation characteristics of shock waves in an inhomogeneous dusty plasma is carried out in the Dusty Plasma Experimental (DPEx) device. A homogeneous dusty plasma, made up of poly-dispersive kaolin particles, is initially formed in a DC glow discharge Argon plasma by maintaining a dynamic equilibrium of the pumping speed and the gas feeding rate. Later, an equilibrium density inhomogeneity in the dust fluid is created by introducing an imbalance in the original dynamic equilibrium. Non-linear wave structures are then excited in this inhomogeneous dusty p…
The propagation characteristics of small-amplitude dust-acoustic (DA) solitary waves (SWs) and shocks are studied in an unmagnetized dusty plasma with a pair of trapped positive and negative ions. Using the standard reductive perturbation technique with two different scaling of stretched coordinates, the evolution equations for DA SWs and shocks are derived in the forms of complex Korteweg-de Vries (KdV) and complex Burgers' equations. The effects of dust charge variation, the dust thermal pressure, and the ratios of positive to negative ion number densities as well as the free to trapped ion …
We present a fully nonlinear theory for dust acoustic (DA) shocks and DA solitary pulses in a strongly coupled dusty plasma, which have been recently observed experimentally by Heinrich et al. [Phys. Rev. Lett. 103, 115002 (2009)], Teng et al. [Phys. Rev. Lett. 103, 245005 (2009)], and Bandyopadhyay et al. [Phys. Rev. Lett. 101, 065006 (2008)]. For this purpose, we use a generalized hydrodynamic model for the strongly coupled dust grains, accounting for arbitrary large amplitude dust number density compressions and potential distributions associated with fully nonlinear nonstationary DA waves.…
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 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…
Widths of shocks are compared, under liquid and solid conditions, for a two-dimensional layer of charged microspheres levitated in a plasma. In this strongly coupled dusty plasma, a shock was launched as a blast wave by moving an exciter wire at a supersonic speed and then bringing it to a halt. Runs were repeated with the layer of microspheres prepared two ways: a crystalline-like solid, and a liquid. The liquid was sustained using laser heating, with conditions that were otherwise the same as in the solid. The shock width was found to be less in a liquid than in a solid, where it was 4 to 6 …
A theoretical model is presented to study characteristics of dust acoustic shock in a viscous, magnetized and rotating dusty plasma at both fast and slow time scales. By employing reductive perturbation technique the nonlinear Zakharov--Kuznetsov (ZK) equation has been derived for both cases when dust is inactive and dynamic (fast and slow time scales). Both electrons and ions are considered to follow kappa/Cairns distribution. It is observed that the viscosity in both cases when dust is in background and active plays as a key role in dissipation for the propagation of acoustic shock. Magnetic…
The propagation characteristics and interactions between the dust acoustic (DA) one and multi solitons in an unmagnetized dusty plasmas composing negatively charged mobile dust, Boltzmann distributed electrons, nonextensive distributed cold and nonthermal distributed hot ions are studied. The well known extended Poincar Lighthill Kuo (PLK) method is employed to derive the two sided Korteweg de Vries (KdV) equations. The solutions of KdV equations are constructed using the Hirota method both for one and multi solitons. The phase shifts are determined for the interaction of one, two and three DA…
We study the nonlinear propagation of dust-ion acoustic (DIA) solitary waves in an unmagnetized dusty plasma which consists of electrons, both positive and negative ions and negatively charged immobile dust grains. Starting from a set of hydrodynamic equations with the ion thermal pressures and ion kinematic viscosities included, and using a standard reductive perturbation method, the Kadomtsev-Petviashivili Burgers (KPB) equation is derived, which governs the evolution of DIA shocks. A stationary solution of the KPB equation is obtained and its properties are analysed with different plasma nu…
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…
We report the first experimental observations of the reflection of a dust acoustic solitary wave from a potential barrier in a dusty plasma medium. The experiments have been carried out in an inverted $Π$-shaped Dusty Plasma Experimental (DPEx) device in a DC glow discharge plasma environment. The dust acoustic solitary wave is excited by modulating the plasma with a short negative Gaussian pulse that is superimposed over the discharge voltage. The solitary wave structure is seen to move towards a potential barrier, created by the sheath around a biased wire, and turn back after reflecting off…
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 dust-acoustic waves and their stability driven by a flowing dusty plasma when it cross through a static (target) dusty plasma (the so-called permeating dusty plasma) are investigated when the components of the dusty plasma obey the power-law q-distributions in nonextensive statistics. The frequency, the growth rate and the stability condition of the dust-acoustic waves are derived under this physical situation, which express the effects of the nonextensivity as well as the flowing dusty plasma velocity on the dust-acoustic waves in this dusty plasma. The numerical results illustrate some n…
The nonlinear theory of dust-acoustic waves (DAWs) with Landau damping is studied in an unmagnetized dusty negative-ion plasma in the extreme conditions when the free electrons are absent. The cold massive charged dusts are described by fluid equations, whereas the two-species of ions (positive and negative) are described by the kinetic Vlasov equations. A Korteweg de-Vries (KdV) equation with Landau damping, governing the dynamics of weakly nonlinear and weakly dispersive DAWs, is derived following Ott and Sudan [Phys. Fluids {\bf 12}, 2388 (1969)]. It is shown that for some typical laborator…
The nonlinear propagation of small but finite amplitude dust ion-acoustic waves (DIAWs) in an ion-beam driven plasma with Boltzmannian electrons, positive ions and stationary charged dust grains, is studied by using the standard reductive perturbation technique (RPT). It is shown that there exist two critical values $(γ_{c1}$ and $γ_{c2})$ of ion-beam to ion phase speed ratio $(γ)$, beyond which the beam generated solitons are not possible. The effects of the parameters, namely $γ$, the ratio of the ion-beam to plasma ion density $(μ_{i})$, the dust to ion density ratio $(μ_{d})$ as well as th…
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…
An analytical model is presented for the description of nonlinear dust-ion-acoustic waves propagating in an unmagnetized, collisionless, three component plasma composed of electrons, ions and inertial dust grains. The formulation relies on a Lagrangean approach of the plasma fluid model. The modulational stability of the wave amplitude is investigated. Different types of localized envelope electrostatic excitations are shown to exist.
We derive dispersion relations for a system of identical particles confined in a two-dimensional annular harmonic well and which interact through a Yukawa potential, e.g., a dusty plasma ring. When the particles are in a single chain (i.e., a one-dimensional ring) we find a longitudinal acoustic mode and a transverse optical mode which show approximate agreement with the dispersion relation for a straight configuration for large radii of the ring. When the radius decreases, the dispersion relations modify: there appears an anticrossing of the modes near the crossing point resulting in a freque…
This manuscript, presents a theoretical study of the linear and nonlinear characteristics of acoustic and drift waves in a bounded inhomogenious dusty plasma which has potential applications in space and lab environments. In this analysis, flow of all plasma particles is assumed to be along the axial direction whereas gradients in velocity are considered to be along the radial direction. First we study coupling of dust modified ion acoustic (DMA) and drift (DMD) waves (linear analysis) at fast time when dynamics of dust remain inactive, later formation of nonlinear vortex like structures are e…
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…
Ion-acoustic modes propagating in unmagnetized dusty plasmas are studied by applying a generic collisionless fluid model. An Eulerian-to-Lagrangean variable transformation leads to a new system of evolution equations, which may be combined into a single (rather complex) equation for the mean ion density. The linear and weakly nonlinear oscillations regimes are studied and their modulational stability is investigated. This study extends known previous results on the Lagrangian description of electron- or ion-acoustic electrostatic plasma modes. The relevance with the description of dust-ion aco…
We report on experimental evidence of visco-elastic effects in a strongly coupled dusty plasma through investigations of the propagation characteristics of low frequency dust acoustic waves and by excitations of transverse shear waves in a DC discharge Argon plasma.
The dusty plasma system (containing nonthermally distributed inertialess electron species, warm inertial ion species, and positively charged stationary dust species) is considered. The basic features of subsonic and supersonic modified-ion-acoustic solitary and shock waves formed in such a dusty plasma system have been investigated by the reductive perturbation method. It has been shown that positively charged dust species play a new role in favor of the formation of subsonic solitary and shock waves. On the other hand, the ion fluid temperature (represented by the parameter $σ$) and the elect…
We study the effects of ion-dust collisions and ion kinematic viscosities on the linear ion-acoustic instability as well as the nonlinear propagation of small amplitude solitary waves and shocks (SWS) in a negative ion plasma with immobile charged dusts. {The existence of two linear ion modes, namely the `fast' and `slow' waves is shown, and their properties are analyzed in the collisional negative ion plasma.} {Using the standard reductive perturbation technique, we derive a modified Korteweg-de Vries-Burger (KdVB) equation which describes the evolution of small amplitude SWS.} {The profiles …
The excitation and propagation of finite amplitude low frequency solitary waves are investigated in an Argon plasma impregnated with kaolin dust particles. A nonlinear longitudinal dust acoustic solitary wave is excited by pulse modulating the discharge voltage with a negative potential. It is found that the velocity of the solitary wave increases and the width decreases with the increase of the modulating voltage, but the product of the solitary wave amplitude and the square of the width remains nearly constant. The experimental findings are compared with analytic soliton solutions of a model…
A viscous dusty plasma containing Kappa distributed electrons, positive warm viscous ions and constant negatively charged dust grains with viscosity have been considered to study the modes of dust ion acoustic waves (DIAWs) theoretically and numerically. The derivations and basic features of shock and solitary waves with different plasma parameters like Mach number, finite temperature coefficient, unperturbed dust streaming velocity, kinematic viscosity of dust etc. of this DIAWs mode have been performed. Considering the dynamical equation from Korteweg de Vries(KdV) equation, a phase portrait…
The nonlinear propagation of electrostatic dust-acoustic (DA) waves in a magnetized dusty plasma consisting of negatively charged mobile dusts, nonthermal fast electrons and trapped ions with vortex-like distribution is studied. Using the reductive perturbation technique, a Korteweg-de Vries (KdV)-like equation is derived which governs the dynamics of the small-amplitude solitary waves in a magnetized dusty nonthermal plasma. It is found that due to the dust thermal pressure, there exists a critical value $(β_c)$ of the nothermal parameter $β~(>1)$, denoting the percentage of energetic electro…
A two-dimensional generalized hydrodynamics (GH) model is developed to study the full spectrum of both longitudinal and transverse dust acoustic waves (DAW) in strongly coupled complex (dusty) plasmas, with memory-function-formalism being implemented to enforce high-frequency sum rules. Results are compared with earlier theories (such as quasi-localized charge approximation and its extended version) and with a self-consistent Brownian dynamics simulation. It is found that the GH approach provides good account, not only for dispersion relations, but also for damping rates of the DAW modes in a …
Theoretical investigation of the nonlinear propagation and modulational instability (MI) of the dust acoustic (DA) waves (DAWs) in an unmagnetized electron depleted dusty plasma (containing opposite polarity warm dust grains and non-extensive positive ions) has been made by deriving a nonlinear Schrödinger equation with the help of perturbation method. Two types of mode, namely, fast and slow DA modes, have been found. The criteria for the formation of bright and dark envelope solitons as well as the first-order and second-order rogue waves have been observed. The effects of various dusty plas…
A model is presented to explain the normal mode features of dust particles in a planar zigzag crystal chain for the first and second neighbors. The degrees of freedom of particles are the longitudinal and transverse displacements in plane coupled by the first and second neighbor harmonic forces in two-dimensions (2D). The constant electric force duded to the electrodes to keep the zigzag structure is calculated. The coupling between transverse and longitudinal dust-lattice (DL) modes is derived. The latter is considered due to the energy of the electrostatic (Yukawa) potential. Moreover couple…
We present a theoretical and numerical study of the self-steepening and shock formation of large-amplitude dust ion-acoustic waves (DIAWs) in dusty plasmas. We compare the non-dispersive two fluid model, which predicts the formation of large amplitude compressive and rarefactive dust ion-acoustic (DIA) shocks, with Vlasov/fluid simulations where ions are treated kinetically while a Boltzmann distribution is assumed for the electrons.
Dust-ion-acoustic damped solitary waves and shocks in laboratory and Saturn's E-ring magnetized nonthermal dusty plasmas with anisotropic ion pressure and dust-charge fluctuation
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…
The nonlinear dust acoustic waves in unmagnetized dusty plasma which consists of two temperature Boltzmann distributed ions and Boltzmann distributed electrons in spherical dimension investigated and obtained spherical Kadomtsev Petviashvili (SKP) equation and shown that the dust acoustic solitary wave can exist in the SKP equation.
In this paper we consider the influence of dust charge fluctuations on damping of the dust-ion-acoustic waves. Fluid approximation of longitudinal electrostatic waves in unmagnetized plasmas is considered. We show that for a weak acoustic wave the attenuation depends on a phenomenological charging coefficient.
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 …
One-dimensional and quasi-one-dimensional strongly-coupled dusty plasma rings have been created experimentally. Longitudinal (acoustic) and transverse (optical) dispersion relations for the 1-ring were measured and found to be in very good agreement with the theory for an unbounded straight chain of particles interacting through a Yukawa (i.e., screened Coulomb or Debye-Hückel) potential. These rings provide a new system in which to study one-dimensional and quasi-one-dimensional physics.
We study the influence of ion beam and charged dust impurity on the propagation of dust ion-acoustic (DIA) solitary wave (SW) in an unmagnetized plasma consisting of Boltzmann distributed electrons, positive ions, positive ion beam and negatively charged immobile dusts in a double plasma device. On interacting with an ion beam, the solitary wave is bifurcated into a compressive fast and a rarefactive slow beam mode, and appears along with the primary wave. However, there exists a critical velocity of the beam beyond which the amplitude of the fast solitary wave starts diminishing and rarefacti…
The Sagdeev pseudopotential method is used to investigate the occurrence and the dynamics of fully nonlinear electrostatic solitary structures in a plasma containing suprathermal hot electrons, in the presence of massive charged dust particles in the background. The soliton existence domain is delineated, and its parametric dependence on different physical parameters is clarified.
The existence of magnetosonic solitons in dusty plasmas is investigated. The nonlinear magnetohydrodynamic equations for a warm dusty magnetoplasma are thus derived. A solution of the nonlinear equations is presented. It is shown that, due to the presence of dust, static structures are allowed. This is in sharp contrast to the formation of the so called shocklets in usual magnetoplasmas. A comparatively small number of dust particles can thus drastically alter the behavior of the nonlinear structures in magnetized plasmas.
Collective response of the plasma medium is well known and has been explored extensively in several contexts. The single particle response is typically treated as collisional interactions leading to dissipative effects. In this manuscript a 2D molecular dynamics (MD) simulation of dusty plasma with Yukawa interactions amidst dust grains have been considered in a strongly coupled regime. It has been shown that disturbances induced in the crystal by introducing highly charged particle elicit both collective and single particle responses. The single particle collisional interaction often generate…
Non-relativistic collisionless shock waves are widespread in space and astrophysical plasmas and are known as efficient particle accelerators. However, our understanding of collisionless shocks, including their structure and the mechanisms whereby they accelerate particles remains incomplete. We present here the results of numerical modeling of an ion-acoustic collisionless shock based on one-dimensional (1D) kinetic approximation both for electrons and ions with a real mass ratio. Special emphasis is made on the shock-reflected ions as the main driver of shock dissipation. The reflection effi…
The propagation of ionic perturbations in a dusty plasma is considered through a three-species kinetic simulation approach, in which the temporal evolution of all three elements i.e. electrons, ions and dust particles are followed based on the Vlasov equation coupled with the Poisson equation. Two cases are focused upon: firstly a fully electron depleted dusty plasma, i.e., a plasma consisting of ions and dust-particles. The second case includes dusty plasmas with large electron-to-ion temperature ratios. The main features of the ionic waves in these two settings including the dispersion relat…
We consider the influence of dust charge fluctuations on damping of the dust-ion-acoustic waves. It is assumed that all grains have equal masses but charges are not constant in time - they may fluctuate in time. The dust charges are not really independent of the variations in the plasma potentials. All modes will influence the charging mechanism, and feedback will lead to several new interesting and unexpected phenomena. The charging of the grains depends on local plasma characteristics. If the waves disturb these characteristic, then charging of the grains is affected and the grain charge is …
The dissipative electron-ion-pcd (positively charged dust) plasma, which is observed in both space and laboratory plasmas, is considered. The basic features of nonplanar cylindrical and spherical ion-acoustic subsonic shock waves in such a medium are investigated by deriving a modified Burgers equation using the reductive perturbation method. It is found that the stationary pcd species reduces the phase speed of the ion-acoustic waves, and consequently supports the subsonic shock waves due to the kinematic viscosity (acting as a source of dissipation) of the ion species. It is observed that th…
The nonlinear longitudinal response of a strongly coupled dusty plasma system is analytically investigated using the Generalized Hydrodynamic (GHD) model. It is shown that the Galilean invariant form of the model does not have soliton solutions, but can support a variety of nonlinear singular (yet conservative) solutions like shock structures of zero strength and propagating solutions with cusp like singularities. These novel entities should be detectable in numerical simulations and experiments studying large amplitude longitudinal excitations in such systems.
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…
A theoretical investigation associated with obliquely propagating ion-acoustic shock waves (IASHWs) in a three-component magnetized plasma having inertialess non-extensive electrons, inertial warm positive and negative ions has been performed. A Burgers equation is derived by employing the reductive perturbation method. Our plasma model supports both positive and negative shock structures under the consideration of non-extensive electrons. It is found that the positive and negative shock wave potentials increase with the oblique angle ($δ$) which arises due to the external magnetic field. It i…
