Dust Ion-acoustic Shock Waves Research Articles

Oblique dust-ion acoustic shock and oscillatory periodic wave excitations in space magnetized complex plasma regimes

The collisionless magnetized complex plasma (MCP) is considered to describe the nonlinear oblique propagation of dust-ion acoustic (DIA) shock wave and oscillatory wave having periodicity due to the impact of plasma parameters. Such plasma is composed of the dynamic ions having viscous influence, (α, q)-velocity distributed electrons, and static positive or negative dust charged particles. By implementing only the expansion of perturb quantities, the Burgers equation (BE) having quadratic nonlinearity (QN), cubic nonlinearity (CN), and composition of QN and CN are derived. Based on the useful exact solutions of these equations, the effect of physical parameters on the propagation of DIA shock wave, DIA oscillatory wave having periodicity and DIA double layer are discussed. It is found that the plasma system supports the shock and periodic wave excitations with both positive and negative polarity described by BE having QN. In addition, BE having CN supports shock and periodic wave excitations with only positive polarity. BE having a composition of QN and CN supports both shock wave excitations and double layer as well as both left to right and right to left propagating oscillatory waves having periodicity. The presented results would be applicable to space MCP regimes and further experimental verification.

Dust‐ion‐acoustic shock wave excitations at super‐critical points with quartic nonlinearity

AbstractProgress in understanding the propagation of dust ion acoustic shock waves for the super critical values of any specific parameter which accompany an unmagnetized collisionless four‐component dusty multi‐ion nonextensive plasma is presented. To accomplish this goal, the formation of modified Burgers‐type equation having quartic nonlinearity via the reductive perturbation method and its analytical solution is yielded for the first time. It is found that the compressive electrostatic shocks are supported not only around the super critical values but also at the super critical values of the specific parameters. The presented results would be applicable to comprehend wave propagation in interplanetary plasmas and laboratory plasmas.

Dust ion acoustic bi-soliton, soliton, and shock waves in unmagnetized plasma with Kaniadakis-distributed electrons in planar and nonplanar geometry

Dust ion acoustic bi-soliton, soliton, and shock waves in unmagnetized plasma with Kaniadakis-distributed electrons in planar and nonplanar geometry

Dust ion acoustic shock and solitary waves in a magnetized multi-component plasma with superthermal electrons

The nonlinear wave propagation in dusty plasmas has received great interest in recent decades due to its significance in interpreting some astrophysical phenomenon. Wave propagation in dust-particle plasmas is likely to differ significantly from that in normal plasmas. Depending on their time scales, several types of acoustic waves propagate in dusty plasmas. The propagation of DIA waves was investigated through a system of multi-component dusty plasma. The study shows the effect of the magnetic field and superthermal parameters on the Sagdeev potential. The Sagdeev potential falls with decreasing ω ci values and rising superthermal parameter k values. Bifurcation analysis is taken into our consideration and shown graphically under the two conditions (A > 0 ) and (A < 0). The presented theoretical work is useful in fully understanding disturbances of the electrostatic in space dusty plasmas.

Investigation of dust ion acoustic shock and solitary waves in a viscous dusty plasma

A viscous dusty plasma containing Kappa-(κ − ) 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, the 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 has been drawn and the position of the saddle point or col. and center have also been discussed. This type of dusty plasma can be found in celestial bodies. The results of this research work can be applied to study the properties of DIAWs in various astrophysical situations where κ-distributive electrons are present and careful modification of the same model can help us to understand the nature of the DIAWs of laboratory plasma as well.

Linear analysis and head-on collision of dust ion-acoustic shock waves in un-magnetized electronegative collisional plasmas

The linear properties and head-on collision of dust ion-acoustic shock waves (DIASWs) are investigated in un-magnetized electronegative collisional plasmas comprising non-inertial thermal electron and light negative ion, inertial positive ion, and stationary dust grain with negative charges. In this regard, the dispersion relation is derived using the standard normal mode analysis and the two-sided damped Korteweg–deVries (dKdV) equations are derived employing the extended Poincaré Lighthill Kuo (ePLK) method. The effects of physical parameters on linear dispersion relation, formation of shocks, phase shift due to head-on collision, and collision process are studied. It is found that the effect of is more dominant to the wave frequency than that of and in a certain range of the group velocity of the DIASWs is increasing and then decreasing for the effect of the ratio of negative ion to electron density. The amplitude and width of the DIASWs increase with the enhancement of electron temperature and the ion-neutral collision plays a significant role in the formation of shock. The consequence of () the phase shift is increasing (decreasing). The results of this study may be useful to the investigation of space and astrophysical environment where the electronegative collisional plasma exists.

Nonlinear behaviour of ion acoustic shock waves in a two-electron temperature nonthermal complex plasma

Abstract The nonlinear propagation of dust-ion-acoustic shock waves (DIASWs) in unmagnetized dusty plasma comprising inertial ions, non-Maxwellian electrons with two distinct temperatures, and negatively charged dust is investigated in this article using a different approach based on the Sagdeev pseudopotential theory. The reductive perturbation approach is used to produce the KdVB and mKdVB equations and a comparison of their analytical and numerical solutions is shown. The effects of various parameters consisting of macroscopic non-thermal, ion-kinematic viscosity, etc. that significantly alternate the qualitative properties of DIASW are discussed. Both oscillatory and monotonic natures of the dispersive-diffusive shock wave structures are described in the present study. It has also been concentrated on nonlinear dynamics in such a plasma environment. The findings of this study should aid in understanding the nonlinear dynamics of wave damping and interactions in space and laboratory dusty plasmas, where the most relevant plasma parameters are kinematic viscosity and macroscopic non-thermality.

Effects of non‐thermality and plasma parameters on dust‐ion‐acoustic shock waves

AbstractThe nonlinear characteristics of dust‐ion‐acoustic shock waves (DIASHWs) in a plasma consisting of charge‐fluctuating dust, inertial ions, and non‐Maxwellian electrons is examined. In particular, the electron velocity distribution function (VDF) is assumed to follow Kappa and Cairns distributions. In this regard, a reductive perturbation (RP) approach (in a weakly nonlinear limit) is used to derive the corresponding Burger's equation, and, from its solution, the effects of various physical parameters, for example, non‐thermal indices, number density, and temperature ratios, on the properties of shock waves are investigated. It is observed that the magnitude of the shock reduces as ion‐electron temperature ratio increases and vice versa. Furthermore, when the ion to electron (equilibrium) density ratio increases, the shock profile gets steepened. The resultant potential amplitude as well as the shock width is also shown to be strongly related to the spectral indices, namely κ and α in the case of Kappa‐ and Cairns‐distributed electrons, respectively. Hence, the potential distribution is strongly affected by the non‐thermal nature of the electron VDF. The relevant Maxwellian results are recovered in the limiting cases, namely κ → ∞ and α → 0. The present study will be useful in understanding the nonlinear propagation of DIASHWs in non‐thermal (space and laboratory) plasmas.

Investigation of dust ion acoustic shock waves in dusty plasma using Cellular Neural Network

The Cellular Neural Network (CNN) is implemented to investigate the features of dust ion acoustic shock waves in a two-fluid model of magnetized dusty plasma. The electrons in this model obey the hybrid Cairns-Tsallis distribution. The reductive perturbation method is used to derive the corresponding Zakharov Kuznetsov Burger (ZKB) equation. Then, the CNN algorithm is integrated with the Finite Difference Method to simulate the ZKB equation with a high accuracy. The obtained solution is approximately identical to the analytical solution which is obtained from the Tanh method. An algorithm to solve ZKB equation using the Finite Difference Method is employed to asses the accuracy of the CNN method. Moreover, it is found that the plasma parameters (viscosity coefficients, cyclotron frequency, nonextensive parameter,…etc.) have significant effects on the shock wave characteristics.

Dust-ion-acoustic shock waves in the presence of dust charge fluctuation in non-Maxwellian plasmas with Kappa-distributed electrons

A three-component plasma composed of nonthermal Kappa-distributed electrons, mobile ions, stationary and dust-fluctuating (spherical) dust particles is considered. By employing reductive perturbation method in a weakly nonlinear limit, the Burger’s equation has been derived and the basic properties of dust ion acoustic shock waves are analyzed. It is observed that for increasing ion–electron temperature ratio, the shock’s amplitude decreases, and vice versa. Moreover, shock steepens for increasing electron–ion equilibrium density ratio. Furthermore, it is observed that the shock potential distribution is directly proportional to the spectral index κ, whereas the shock’s width is inversely proportional to the latter. Thus, the non-Maxwellian nature of the electronic velocity distribution significantly modifies the perturbed potential profile. In the limiting case κ→∞, the corresponding Maxwellian results are retrieved. Present work will be useful in understanding the nonlinear propagation of dust-ion-acoustic shock waves (DIASHW) in space plasmas where nonthermal population of electrons exist due to various physical phenomena, and in laboratory (e.g., in a double plasma (DP) device, or in tokamak where runaway electrons may result in a non-Maxwellian plasma).

Parametric study of cylindrical and spherical dust ion acoustic shock waves with two temperature electrons in dusty plasma relevant to Saturn's E ring

AbstractWe have performed numerical analysis of the one‐dimensional dynamics of the cylindrical/spherical dust ion acoustic shock waves in unmagnetized dusty plasma consisting of positive ions, immobile dust particles, and nonextensive distributed cold and hot electrons. A multiple‐scale expansion method is used to derive Burgers Equation (BE) and modified Burgers equation (MBE) by including higher order nonlinearity. The basic characteristics of the shock waves have been analysed numerically and graphically for different physical parameters relevant to Saturn' E ring through 2D figures. The parametric dependence of dust ion acoustic shock waves on some plasma parameters nonextensive index, density, and temperature of cold and hot electrons, concentration of dust particles, thermal effects and kinematic viscosity of ions is explored. Furthermore, it is found that the nonplanar geometry effects have an important impact on the establishment of shock waves. The amplitude of the wave decreases faster as one departs away from the axis of the cylinder or centre of the sphere. Such decaying behaviour continues as time progresses. It is also found that an increasing dust concentration decreases the amplitude of the dust ion acoustic shock waves.

Dust Ion–Acoustic Shock Waves in Laboratory, Ionospheric, and Astrophysical Plasmas

Methods of description of ion–acoustic shock waves in dusty plasma are presented. A new type of dust ion–acoustic shock waves related to anomalous dissipation is described. The main dissipative processes related to charging of dust particles, absorption of ions by dust particles, Coulomb collisions between ions and dust particles, and Landau damping are analyzed. Proposed methods of theoretical analysis enable explaining all major specific features of dust ion–acoustic shock waves observed in the laboratory experiments. The shock waves of this type are present in the near-Earth plasma and the universe. Their investigation is possible in active ionospheric experiments of the Fluxus type. Important astrophysical problems in which the appearance of shock waves under consideration should be taken into consideration are the shock waves of supernovas, evolution of Local Interstellar medium, etc.

On stretching of plasma parameters and related open issues for the study of dust-ion-acoustic and dust-acoustic shock waves in dusty plasmas

To study the properties of the shock structures associated with dust-ion-acoustic (DIA) and dust-acoustic (DA) waves, the stretching of the plasma parameters [viz., kinematic or longitudinal viscosity coefficient ηi (ηd) for DIA (DA) waves and the plasma parameter δi (δd) associated with the dust charge fluctuation for DIA (DA) waves] has been used by many authors. It is argued that the stretching of such plasma parameters is not usually valid. The valid stretching coordinates for deriving the Burgers equation, which leads to the formation of DIA and DA shock waves, are provided. A few open issues related to the sources of dissipation [viz., different viscous forces giving rise to ηi and ηd and dust charge fluctuation giving rise to δi and δd] are also pinpointed. To remove the stretching of plasma parameters, which is not usually valid, from our future research work, and to address some related open issues will be able not only to enhance the quality of our future research work but also to help us in working on some challenging research problems in dusty plasma physics.

Investigation of cylindrical shock waves in dusty plasma

Electronegative dusty plasma composed of Boltzmann electrons, Boltzmann negative ions, inertial positive ions and charge fluctuating dust has been considered. The fractional modified Burgers’ (FMB) equation, which is derived using Euler–Lagrange variational technique, is analytically obtained and solved for studying the cylindrical geometry effect on the propagation of the dust ion acoustic shock wave. The Laplace homotopy perturbation method, the so-called LHPM is applied to solve the FMB equation. The effect of the fractional parameter, positive ion number density at equilibrium, the number of equilibrium electrons residing on the dust grain surface and shock velocity on the behavior of the shock waves in the dusty plasma has been investigated.

Dust Ion-Acoustic Shock Waves in a Multicomponent Magnetorotating Plasma

Abstract The nonlinear properties of dust ion-acoustic (DIA) shock waves in a magnetorotating plasma consisting of inertial ions, nonextensive electrons and positrons, and immobile negatively charged dust are examined. The effects of dust charge fluctuations are not included in the present investigation, but the ion kinematic viscosity (collisions) is a source of dissipation, leading to the formation of stable shock structures. The Zakharov–Kuznetsov–Burgers (ZKB) equation is derived using the reductive perturbation technique, and from its solution the effects of different physical parameters, i.e. nonextensivity of electrons and positrons, kinematic viscosity, rotational frequency, and positron and dust concentrations, on the characteristics of shock waves are examined. It is observed that physical parameters play a very crucial role in the formation of DIA shocks. This study could be useful in understanding the electrostatic excitations in dusty plasmas in space (e.g. interstellar medium).

The tanh solution of KdV-B equation in four-component quantum plasma by taking into account dust charge variation

Nonlinear propagation of quantum dust-ion acoustic shock and solitary waves in an unmagnetized and collisionless four-component plasma medium containing inertialess quantum electrons and positrons, and also classical ions and stationary negative dust grains, which are affected by dust charge variations and viscosity of ions, are investigated using a quantum hydrodynamic model by employing the tanh method. The Korteweg–de Vries-Burgers and the Korteweg–de Vries equations indicate the behavior of shocks and solitons in this plasma model, respectively. Consideration of the dust charge variation requires the evaluation of charging currents. These currents are determined with the orbit limited motion theory and using the corresponding velocity distribution function. In the following, the effects of chemical potential and the density of dust grains on the structure of oscillatory and monotonic shock waves and solitary waves are investigated. The current study extends our understanding of the characteristics of quantum nonlinear structures in superdense astrophysical systems, inertial confinement fusion plasmas, and ultrasmall micro- and nano- electronic devices.

Nonlinear dust ion acoustic waves behaviors analysis in warm viscous dusty plasma with trapped ions

The nonlinear excitation of a dust ion acoustic (DIA) wave packet in a viscous dusty plasma consisting of Boltzmann distributed electrons, trapped ions, and variable charged dust is investigated. The dependence of the damping rate of the waves on the plasma parameters is discussed via the linear stability analysis. The standard reductive perturbation method is employed to derive the modified Korteweg-de Vries-Burgers equation due to an interplay among the nonlinearity, dispersion, and dissipation effects, and, the non-dissipative case gives the modified Korteweg-de Vries equation. Bifurcation analysis is discussed for the non-dissipative and dissipative systems assuming a Boltzmann distribution for electrons and a vortex-like distribution for ions. The effects of plasma parameters, among which the dusty plasma viscosity ν, trapping ion parameter β, and dust charge variation γ1 on solitary waves (SWs) and shock wave solutions, are discussed. It is observed that parameters ν and β significantly influence the characteristics of nonlinear dust ion acoustic solitary structures. It is seen that without viscosity (ν = 0), the system has the DIA solitary wave solutions, whereas, the viscous system supports DIA shock waves. By increasing the kinematic viscosity, the opportunity for formation of higher energy shock solitary waves increases and the solitary waves become monotonic shock waves.

Dust-Charge Variation Effects on Dust ion Acoustic Shock Waves in Four Component Quantum Plasma

The behavior of nonlinear quantum dust ion acoustic (QDIA) shock waves in a collisionless, unmagnetized plasma consisting of inertialess quantum electrons and positrons, classical cold ions and stationary negatively charged dust grains with dust charge variation is investigated using quantum hydrodynamic (QHD) equations. The propagation of small amplitude QDIA shock waves is governed by Burgers equation. It is shown that the dust charge variation plays an important role in the formation of such QDIA shock structures. The dependence of the shock wave’s amplitude and thickness on the chemical potential is investigated. The present theory is applicable to analyze the formation of nonlinear structures at quantum scales in dense astrophysical objects.

Dust ion acoustic solitary and shock waves in strongly coupled dusty plasma in presence of attractive interparticle interaction potential

The streaming of ions through the dust particles significantly modifies the repulsive Debye-Hückel type of interaction in the sheath and pre-sheath regions and leads to the appearance of oscillatory and attractive wake type interaction. In this paper, we investigate the formation of dust-ion acoustic solitary and shock waves in the presence of streaming ions in a strongly coupled dusty plasma. The generalized hydrodynamic equation is used to describe the dust dynamics, and the dust-dust interaction has been taken into account via the electrostatic pressure term. The novel feature of the present study is the incorporation of both the repulsive and attractive interactions in the electrostatic pressure term. The flow of ions along the vertical direction in the sheath/presheath region of the plasma brings asymmetry to the dust dynamics, which has been carefully handled while considering the effect of strong coupling in the formation of nonlinear structures in such plasma. The study reveals that the ion streaming velocity has a crucial role in controlling the nonlinear coherent structures.

K–P–Burgers equation in negative ion-rich relativistic dusty plasma including the effect of kinematic viscosity

The stationary solution is obtained for the K–P–Burgers equation that describes the nonlinear propagations of dust ion acoustic waves in a multi-component, collisionless, un-magnetized relativistic dusty plasma consisting of electrons, positive and negative ions in the presence of charged massive dust grains. Here, the Kadomtsev–Petviashvili (K–P) equation, three-dimensional (3D) Burgers equation, and K–P–Burgers equations are derived by using the reductive perturbation method including the effects of viscosity of plasma fluid, thermal energy, ion density, and ion temperature on the structure of a dust ion acoustic shock wave (DIASW). The K–P equation predictes the existences of stationary small amplitude solitary wave, whereas the K–P–Burgers equation in the weakly relativistic regime describes the evolution of shock-like structures in such a multi-ion dusty plasma.