Dust Ion-acoustic Shock Research Articles

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.

Effect of ion viscosity on dust ion-acoustic shock waves in a nonextensive magnetoplasma

The nonlinear features of dust ion-acoustic shock waves (DIASWs) in a magnetoplasma containing cold positive ions, nonextensive electrons, and immobile negatively charged dust grains taking into account the cold ion kinematic viscosity are investigated. The reductive perturbation technique is used to derive a Zakharov-Kuznetsov-Burgers (ZK-Burgers). It is found that the fundamental properties of the DIASWs are significantly modified by the different system parameters such as the nonextensive parameter, the ion gyrofrequency, the dust concentration, the viscosity parameter, and the direction cosines. Also, the polarities (positive and negative shocks) of the potential are found to exist in the plasma under consideration. The implications of our results may be used in understanding the acoustic shock waves propagation in laboratory and space plasmas.

Variational principle, conservation laws and exact solutions for dust ion acoustic shock waves modeling modified Burger equation

The nonlinear dust ion acoustic (DIA) shock waves have been investigated in one-dimensional, collisionless and unmagnetized dusty plasma consisting of mobile ion, vortex-like electron and charge fluctuating static dust particles. The basic set of fluid equations is reduced to the modified Burger equation by using the reductive perturbation method. The effects of dust grain charge fluctuation and vortex-like (trapped) electron are found to modify the properties of the DIA shock waves significantly. By the semi-inverse method, a variational principle, and conservation laws for the modified Burger equation are obtained. It is shown that the modified Burger equation is non-integrable using Painlevé analysis. A set of new exact solutions are obtained by the auto-Bäcklund transformations. Finally, we will study the physical meanings of solutions.

Effect of dust size distribution and dust charge fluctuation on dust ion-acoustic shock waves in a multi-ion dusty plasma

The effects of dust size distribution and dust charge fluctuation of dust grains on the small but finite amplitude nonlinear dust ion-acoustic shock waves, in an unmagnetized multi-ion dusty plasma which contains negative ions, positive ions and electrons, are studied in this paper. A Burgers equation and its stationary solutions are obtained by using the reductive perturbation method. The analytical and numerical results show that the height with polynomial dust size distribution is larger than that of the monosized dusty plasmas with the same dust grains, but the thickness in the case of different dust grains is smaller than that of the monosized dusty plasmas. Furthermore, the moving speed of the shock waves also depend on different dust size distributions.

Nonplannar Nonlinear Dust ion Acoustics Solitary and Shock Waves in a Dusty Multi-ion Plasma

We have presented a stern theoretical exploration of the nonplannar and nonlinear propagation of dust-ion acoustic (DIA) waves in a dusty multi-ion plasma. We studied the progation of nonplannar non-linear DIA waves by the reductive perturbation method which leads to the the derivation of the Burgers [Korteweg de-Vries (K-dV)] equation for the shock (solitary) wave propagation. The shock (solitary) waves are found to be formed in a multi-ion dusty plasma due to the balance between nonlinearity and dissipation (dispersion), and that the dissipation (dispersion) arises due to the dust charge fluctuation (deviation of charge neutrality condition). We have analized the effects of nonplannar and nonlinear geometry on the DIA shock and solitary waves propagating in such a dusty multi-ion plasma. We have shown that the nonplanar (cylindrical and spherical) solitary and shock structures are significantly different from planner ones.

Roles of negatively-charged heavy ions and nonextensivity in cylindrical and spherical dust-ion-acoustic shock waves

A rigorous theoretical investigation has been carried out on the propagation of nonplanar (cylindrical and spherical) dust-ion-acoustic (DIA) waves in an unmagnetized dusty multi-ion plasma system containing nonextensive electrons, inertial negatively-charged heavy ions, positively-charged Maxwellian light ions, and negatively-charged stationary dust. The well-known reductive perturbation technique has been used to derive the modified Burgers-type equation (which describes the shock wave’s properties), and its numerical solution is obtained. The basic features (viz. polarity, amplitude, width, etc.) of the cylindrical and the spherical DIA shock waves are investigated. The basic features of the cylindrical and the spherical DIA shock waves are found to have been significantly modified in a way that depends on the intrinsic parameters (viz. electron nonextensivity, heavy-ion’s kinematic viscosity, heavy-to-light-ion number density ratio, electron-to-light-ion temperature ratio, etc.) of the considered plasma system. The characteristics of the cylindrical and the spherical DIA shock waves are observed to be qualitatively different from those of planar ones.

Dust-ion-acoustic shock waves in nonextensive dusty multi-ion plasmas

A theoretical and numerical analysis of dust-ion-acoustic (DIA) shock waves has been carried out in an unmagnetized dusty multi-ion plasma containing nonextensive electrons, inertial negatively charged heavy ions, positively charged Maxwellian light ions, and negatively charged stationary dusts. The normal mode analysis is used to examine the linear properties of DIA waves (DIAWs). The reductive perturbation technique is employed in order to derive the nonlinear time evolution Burgers type equation (which describes the shock waves properties). The basic features (viz. polarity, amplitude, width, etc.) of the DIA shock waves are investigated. It is found that the basic features of DIA shock waves are significantly modified depending on the intrinsic parameters (viz. electron nonextensivity, heavy ions kinematic viscosity, heavy-to-light ion number density ratio, electron-to-light ion temperature ratio, etc.) of the considered plasma system. Both polarities (positive and negative potential) are also found to exist in the plasma under consideration in this paper. The findings of this investigation may be used in understanding the wave propagation in laboratory and space plasmas.

Dust-ion acoustic shock waves in a dusty multi-ion plasma with negatively dust-charge fluctuation

The nonlinear propagation of dust-ion acoustic shock waves in a collisionless, unmagnetized multi-ion dusty plasma contains Botlzemann-distributed electrons, negative and positive ions with extremely massive and stationary negative charge dust grains with dust charge fluctuations is investigated. By employing the reductive perturbation method, we obtain a Burgers equation that describes the two-ion fluid dynamics. The dust charge variation is found to play an important role in the formation of such dust-ion acoustic shock structures. The viscosity only affects the thickness of the shock waves. The dependences of the shock wave’s velocity, height and thickness on the system parameters are investigated.

Dust-ion acoustic shock waves for nonplanar geometry with nonthermal electrons and adiabatic dusty plasma

The nonplanar Burgers' equation for dust-ion-acousti shock waves was derived for unmagnetized adiabatic dusty plasmas, comprising static negatively charged dust uid, nonthermal distributed electrons, and Boltzmann dis- tributed positron and adiabatic ion uid, by employing the standard reductive perturbation method. The solution of the modied Burgers' equation for nonplanar geometry is numerically analyzed. The dependence of dust-ion-acousti shock waves on some plasma parameters is explored. It is observed that inclusion of the nonthermal electron distribution mod- ies the shock wave prole signicantly. Likewise, it is found that the nonplanar geometry effects have an important role on the establishment of shock waves. It is also found that an increasing positron concentration decreases the amplitude of the dust-ion-acousti shock waves.

Ion-Scale Electrostatic Nonplanar Shock Waves in Dusty Plasmas with Two-Temperature Superthermal Electrons

The basic properties of nonplanar (viz. cylindri- cal and spherical) dust-ion-acoustic (DIA) shock waves in an unmagnetized dusty plasma system (consisting of inertial ions, negatively charged immobile dust, and superthermal electrons with two distinct temperatures) are investigated by employing the reductive perturbation method. The modified Burgers equation is derived and is numerically analyzed in order to examine the basic properties of DIA shock struc- tures. The effects of nonplanar geometry, electron superther- mality, and ion kinematic viscosity on the basic features of DIA shock waves are discussed. It is found that the prop- erties of the cylindrical and spherical DIA shock waves in dusty plasmas with two-temperature superthermal elec- trons significantly differ from those of one-dimensional planar shocks. The implications of our results in space plasmas (viz. star formation, supernovae explosion, solar wind, pulsar magnetosphere, Saturn's outer magnetosphere (R ∼ 13−18 RS ,w hereRS is the radius of Saturn), Saturn's inner magnetosphere (R <9 RS , etc.)) and laboratory plas- mas (viz. laser-induced implosion, capsule implosion, shock tube, etc.), where superthermal electrons with two distinct temperatures occurs, are briefly discussed.

Kadomtsev—Petviashvili (KP) Burgers Equation in Dusty Negative Ion Plasmas: Evolution of Dust-Ion Acoustic Shocks

We study the nonlinear propagation of dust-ion acoustic (DIA) shock waves in an un-magnetized 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 (K-P-Burgers) equation is derived, which governs the evolution of DIA shocks. A stationary solution of the K-P-Burgers equation is obtained and its properties are analysed with different plasma number densities, ion temperatures and masses. It is shown that a transition from shocks with negative potential to positive one occurs depending on the negative ion concentration in the plasma and the obliqueness of propagation of DIA waves.

Higher-order corrections to nonlinear dust-ion-acoustic shock waves in a degenerate dense space plasma

A reductive perturbation technique is employed to investigate the contribution of higher-order nonlinearity and dissipation to nonlinear dust-ion-acoustic (DIA) shock waves in a three-component degenerate dense space plasma. The model consists of degenerate electron (being either ultrarelativistic or nonrelativistic), nonrelativistic ion fluid and stationary heavy dust grains. A nonlinear Burger equation and a linear inhomogeneous Burger-type equation are derived. The present model admits only compressive DIA shocks. Including these higher-order corrections results in creating new solitary wave structures “humped DIA shock” waves. For the case of ultrarelativistic (nonrelativistic) electrons, one (two) humped DIA shock is (are) created. The DIA shock wave amplitude and velocity is larger in case of ultrarelativistic electrons than of nonrelativistic electrons. It is shown that the effects of kinematic viscosity, heavy dust grains number density, and equilibrium ion number density have important roles in the basic features of the produced DIA shocks and the associated electric fields. The implications of our results to dense plasmas in astrophysical objects (e.g., non-rotating white dwarf stars) are briefly discussed.

Electro-acoustic shock structures in dusty plasmas

Two types of electro-acoustic shock structures, namely dust-ion-acoustic (DIA) and dust-acoustic (DA) shock structures, formed in two different kind of dusty plasma systems have been theoretically investigated. The sources of dissipation, which are responsible for the formation of DIA and DA shock structures in these dusty plasma systems, are identified. The conditions for the formation of these shock structures and their new basic features are pinpointed. The implications of the results in experimental observations are also discussed.

Dynamics of dust-ion acoustic shock waves in a magnetized charge variable superthermal complex plasma

A theoretical investigation is carried out to study the characteristic properties of dust-ion acoustic (DIA) shock waves in a magnetized, charge varying, complex (dusty) plasma which consists of immobile dust grains, fluid ions and superthermal electrons. The effects of collisions are not included here, but the dissipation leading to the formation of stable shock structures is provided by the dust charge fluctuations. The Korteweg–de Vries–Burgers (KdV–Burgers) equation is derived using the reductive perturbation technique. The combined effects of obliqueness, magnitude of the magnetic field, and electron superthermality on the DIA shock waves are then investigated. It is shown that the effects of obliqueness, electron non-thermality and dust charge fluctuation significantly modify the basic properties of DIA shock waves.

Formation of obliquely propagating dust-ion-acoustic shock waves due to dust charge fluctuation in magnetized nonthermal dusty plasma

A theoretical investigation is made on the formation as well as basic properties of dust-ion-acoustic (DIA) shock waves in a magnetized nonthermal dusty plasma consisting of immobile charge fluctuating dust, inertial ion fluid and nonthermal electrons. The reductive perturbation method is employed to derive the Korteweg-de Vries-Burgers equation governing the DIA shock waves. The combined effects of external static magnetic field, obliqueness, nonthermal electron distribution and dust charge fluctuation on the DIA shock waves are also investigated. It is shown that the dust charge fluctuation is a source of dissipation, and is responsible for the formation of the DIA shock waves. It is also observed that the combined effects of obliqueness, nonthermal electron distribution and dust charge fluctuation significantly modify the basic properties of the DIA shock waves. The implications of our results in space and laboratory dusty plasma situations are briefly discussed.

Effects of bi-kappa distributed electrons on dust-ion-acoustic shock waves in dusty superthermal plasmas

The basic properties of dust-ion-acoustic (DIA) shock waves in an unmagnetized dusty plasma (containing inertial ions, kappa distributed electrons with two distinct temperatures, and negatively charged immobile dust grains) are investigated both numerically and analytically. The hydrodynamic equation for inertial ions has been used to derive the Burgers equation. The effects of superthermal bi-kappa electrons and ion kinematic viscosity, which are found to modify the basic features of DIA shock waves significantly, are briefly discussed.

Characteristic of ion acoustic shock waves in a dissipative quantum pair plasma with dust particulates

The behavior of quantum dust ion-acoustic (QDIA) shocks in a plasma including inertialess quantum electrons and positrons, classical cold ions and stationary negative dust grains are studied, using a quantum hydrodynamic model (QHD). The effect of dissipation due to the viscosity of ions is taken into account. The propagation of small but finite amplitude QDIA shocks is governed by the Kortoweg-de Vries-Burgers (KdVB) equation. The existence regions of oscillatory and monotonic shocks will depend on the quantum diffraction parameter (H) and dust density (d) as well as dissipation parameter (η0). The effect of plasma parameters (d,H,η0), on these structures is investigated. Results indicate that the thickness and height of monotonic shocks; oscillation amplitude of the oscillatory shock wave and it’s wavelength effectively are affected by these parameters. Additionally, the possibility of propagation of both compressive and rarefactive shocks is investigated. It is found that depending on some critical value of dust density (dc), which is a function of H, compressive and rarefactive shock waves can’t propagate in model plasma. The present theory is applicable to analyze the formation of nonlinear structures at quantum scales in dense astrophysical objects.

Arbitrary amplitude solitary and shock waves in an unmagnetized quantum dusty electron-positron-ion plasma

The behavior of quantum dust ion acoustic soliton and shocks in a plasma including inertialess quantum electrons and positrons, classical cold ions, and stationary negative dust grains are studied, using arbitrary amplitude approach. The effect of dissipation due to viscosity of ions is taken into account. The numerical analysis of Sagdeev potential for small value of quantum diffraction parameter (H) shows that for chosen plasma, only compressive solitons can exist and the existence domain of this type of solitons is decreased by increasing dust density (d). Additionally, the possibility of propagation of both subsonic and supersonic compressive solitons is investigated. It is shown that there is a critical dust density above which only supersonic solitons are observed. Moreover, increasing d leads to a reduction in the existence domain of compressive solitons and the possibility of propagation of rarefactive soliton is provided. So, rarefactive solitons are observed only due to the presence of dust particles in this model quantum plasma. Furthermore, numerical solution of governed equations for arbitrary amplitude shock waves has been investigated. It is shown that only compressive large amplitude shocks can propagate. Finally, the effects of plasma parameters on these structures are investigated. This research will be helpful in understanding the properties of dense astrophysical (i.e., white dwarfs and neutron stars) and laboratory dusty plasmas.