Dust Acoustic Shock Waves Research Articles

Simulating overtaking interactions of dust-acoustic N-shock waves in oppositely charged dusty plasmas with Q-distributed electrons

Simulating overtaking interactions (OIs) of dust-acoustic N-shock waves (DANSWs) in dust plasmas with opposite polarities and q-distributed electrons and Boltzmann distributed ions are examined in this work. Reductive perturbation theory is used to obtain a Burgers’ equation (BE), and dust-acoustic N-shock wave solutions are derived using the Cole-Hopf transformation and exponential function. Numerical simulations show that the evolution and OIs of DANSWs and their electric fields are modified by the effects of negative/positive dust fluid kinematic viscosity, the ratio of negative dust to positive dust mass, and the nonextensive q-distribution of electrons. This work may help explain the properties of dust-acoustic shock waves in cometary tails and Jupiter's magnetosphere that support the propagation of nonlinear waves.

Dust acoustic nonlinearity of nonlinear mode in plasma to compute temporal and spatial results

Our manuscript is related to use Caputo fractional order derivative (CFOD) to investigate results of non-linear mode in plasma. We establish results for both temporal and spatial approximate solution. For the require results, we use reduction perturbation method (RPM) to find the analytical solution of the dust acoustic shock waves. Further, using the same technique we find the solitary wave potential and compared the solutions obtained with another very useful technique known as Homotopy perturbation method (HPM). The comparison of results for both approaches are more precise and agreed with the exact solution of the problem. Finally, we present graphical representation for different fractional order for both temporal and spatial approximate solution.

Effects of dust size distribution and non-Maxwellian electrons on shock waves in a dusty plasma

We present a study of dust acoustic shock waves in a non-Maxwellian plasma with dust charge fluctuations, which are seen to cause a dissipation term in fluid model, and consequently shocks are generated. In particular, we focus on dust acoustic waves as affected by various dust size distributions. Two distinct dust size distributions—the polynomial and the power law distributions—have been used. For analytical investigation of nonlinear wave propagation in complex plasmas, a reductive perturbation approach is used to obtain the Burgers equation. A dusty plasma system with non-Maxwellian Kappa distribution is considered and it is shown that the amplitude of a shock wave, for the dust size distribution is larger than that for the mono-sized counterpart, while the shock width manifests an opposite trend. Furthermore, the shock wave speed is also affected by the dust size distributions as well as by the nature of velocity distribution function. To benchmark our findings, we apply the proper limit on the spectral index, i.e., κ→∞, and retrieve the Maxwellian results. The current findings are crucial for comprehending respective shock distributions for a plasma system exhibiting non-thermal characteristics and having dust size distributions.

Dust acoustic shock waves in nonuniform dusty plasmas with kappa-distributed ions and electrons, nonadiabatic dust charge fluctuation and dust size distribution

Dust acoustic shock waves in nonuniform dusty plasmas with kappa-distributed ions and electrons, nonadiabatic dust charge fluctuation and dust size distribution

On the characteristics of DA shock waves in a polarized electron-depleted plasma with a mixed nonextensive high energy-tail ion distribution

A first theoretical attempt is made to understand the characteristics of dust acoustic shock waves (DASWs) in a polarized electron-depleted plasma with a mixed nonextensive high energy–tail ion distribution and to examine the impact of the generalized nonthermal polarization force on DASWs in an electron-depleted dusty plasma. First, a short numerical investigation illustrating the behavior of the mixed nonextensive high energy–tail (or Cairns–Tsallis) ion distribution and the domain of validity of its two parameters (q and [Formula: see text]) is carried out. Next, the generalized nonthermal polarization acting on dust grain in electron-depleted dusty plasma is determined within the context of Tsallis’ statistical mechanics. The behavior of this generalized polarization force is significantly affected by the nonextensive character of the nonthermal ions. Specifically, we have shown that, for both space and experimental dusty plasmas, the magnitude of the polarization force (in the case where [Formula: see text]) decreases as the nonextensivity of the nonthermal ions becomes significant. As an application, we have analyzed the changes caused by the nonthermal nonextensive polarization force on the main characteristics of DASW (viz. phase velocity, polarity, amplitude, width, etc.). Numerical results showed that our plasma model supports rarefactive and compressive DASWs that are significantly affected by the effects of nonthermal ion nonextensivity and polarization force. In particular, we have shown that for large values of the nonthermal parameter [Formula: see text], the increase in q allows the transition from rarefactive to compressive DASW structures. The present theoretical investigation is helpful to fully understand electrostatic disturbances in space and experimental dusty plasmas.

Dynamics and head-on collisions of multidimensional dust acoustic shock waves in a self-gravitating magnetized electron-depleted dusty plasma

The dynamics and collisions of dust acoustic (DA) shock excitations traveling in opposite directions are theoretically investigated in a three-dimensional self-gravitating magnetized electron-depleted dusty plasma whose ingredients are extremely warm positively and negatively charged massive dust grains as well as ions that follow the q-nonextensive distribution. A linear analysis and the extended Poincare–Lighthill–Kuo method are used to derive the dispersion relation, the two-sided Korteweg–de Vries Burgers equations, and the phase shift that occurs due to the wave interaction. It is found that gravitation introduces Jeans-like instability, reduces the wave damping rate, decays the aperiodic oscillatory structure of DA excitations, and strongly affects the amplitude, steepness, and occurrence of monotonic compressive and rarefactive shocks. Numerical simulations also highlighted the stabilizing role of the magnetic field and the singularities of the collision process of monotonic shock fronts as well as the undeniable influence of viscosity, ion nonextensivity, and obliqueness between counter-traveling waves on the phase shift and collision profiles. The present results may be useful to better understand interactions of dust acoustic shock waves in the laboratory and astrophysical scenarios, such as dust clouds in the galactic disk, photo-association regions separating H II regions from dense molecular clouds, Saturn's planetary ring, and Halley Comet.

Dust Acoustic Shock Waves in a Warm Magnetized Dusty Plasma with Kappa Distributed Electrons and Ions

Dust Acoustic Shock Waves in a Warm Magnetized Dusty Plasma with Kappa Distributed Electrons and Ions

Studies on the Dust Acoustic Shock, Solitary, and Periodic Waves in an Unmagnetized Viscous Dusty Plasma with Two-Temperature Ions

Studies on the Dust Acoustic Shock, Solitary, and Periodic Waves in an Unmagnetized Viscous Dusty Plasma with Two-Temperature Ions

Obliquely propagating dust acoustic shock waves in magnetized plasma under the influence of polarization force and nonadiabaticity of dust charge variation

In this work, we have analyzed the impact of polarization force, angle of obliqueness under the influence of nonadiabatic dust charge fluctuation on shock waves formation in magneto rotating plasma. The present plasma model is consisting of negatively charged dust grains, Maxwellian electrons, non-Maxwellian hybrid distributed ions. The dissipation is introduced in the system via nonadiabaticity, a new mechanism for the formation of shock waves. Using the standard reductive perturbation method, nonlinear equation, namely, Korteweg-de Vries-Burgers (KdVB) equation is derived and solution is obtained using the Tanh method. It is shown that dust charge fluctuation is the main source of dissipation. We have studied the various parameteric influences on such shock structure and also showed how the gradual variations of these parameters affect the generation and structure of the shocks in their respective domain. Much of the experiments on dusty plasma with nonadiabatic dust charge fluctuation will benefit from the parametric study.

Evolution of cylindrical/spherical shock formation in a dusty plasma with nonadiabatic dust charge variation

Cylindrical/spherical dust acoustic shock waves are studied in an unmagnetized plasma consisting of Maxwellian electrons, superthermal ions under the effect of nonadiabatic dust charge fluctuation. The dissipation is introduced in the system via nonadiabaticity, a new mechanism for the formation of shock waves. Using standard reductive perturbation method, nonplanar equation namely Korteweg–de Vries Burgers (KdVB) equation is derived and solution is obtained using the Weighted residual method. By use of weighted residual method, a progressive wave solution to nonplanar modified KdV Burgers equation is presented. It is shown that dust charge fluctuation produces dissipation which is responsible for shock formation. The solution shows that as one goes towards the axis of the cylinder or center of the sphere, the wave attenuates faster and the effects are shown in some 2D figures. We have studied various parametric influences on such shock structure and also showed how the gradual variations of these parameter affect the generation and structure of the shocks in their respective domain. Our results should be applicable to the formation of nonlinear DIA shock wave structures in regions in which dust grain is embedded in a Kappa distributed plasma, such as Saturn's magnetosphere.

Dust Acoustic Nonlinear waves in Pair-ion-electron Superthermal Plasma

We present a study of dust acoustic nonlinear waves in a collisionless, weakly inhomogeneous non-Maxwellian (κ) distributed pair-ion-electron plasmas with dust charge fluctuation. The nonlinear partial differential equations in the form of Korteweg-de-Vries (KdV) and Kortweg-de-Vries-Burger (KdVB) are obtained (in which particulary the nonlinear, dispersion and dissipative coefficients depend on the κ factor and plasma species densities) that describe the evolution of nonlinear dust acoustic solitary and shock wave structures. The mode analyzed nonlinearly by using reductive perturbation method in space-time stretching coordinates appropriate for inhomogeneous plasma show the dependence of these structures on number densities, temperature, superthermal particles population and on dust charge fluctuation. These behaviors are illustrated and shown graphically. These investigations may be helpful in analyzing the nature of such waves in both space and laboratory plasma systems.

On the analytical and numerical solutions of the damped nonplanar Shamel Korteweg–de Vries Burgers equation for modeling nonlinear structures in strongly coupled dusty plasmas: Multistage homotopy perturbation method

The dissipative cylindrical and spherical (nonplanar) electrostatic low-frequency dust-acoustic waves (DAWs) including solitary and shock waves in a collisional and unmagnetized strongly coupled dusty plasma are investigated analytically and numerically. The present plasma model consists of inertialess particles including thermal elections and vortex-like positive ions distribution as well as inertial strongly coupled negatively charged dust grains. In the hydrodynamic regime, the fluid governed equations of the present model are reduced to the damped nonplanar Shamel Korteweg–de Vries Burgers (SKVB) equation using the reductive perturbation technique. In the absence of the dissipative effect, the damped nonplanar Shamel Korteweg–de Vries (SKdV) equation is recovered and solved analytically for the first time using a novel analytical approach in order to describe the dynamical mechanism of the dissipative nonplanar dust-acoustic solitary waves. Also, the damped nonplanar SKdV equation is solved numerically using the homotopy perturbation method (HPM) and the hybrid homotopy perturbation method with the moving boundary method which is called multistage HPM (MsHPM). Furthermore, in the presence of the dissipative effect, the damped nonplanar SKdVB equation is solved numerically via the HPM and MsHPM for studying the characteristics of the dissipative nonplanar dust-acoustic solitary and shock waves. For checking the accuracy of the obtained solutions, the maximum global residual error is estimated. Moreover, a comparison between the approximate analytical and numerical solutions is reported. Furthermore, the dependence of dissipative nonplanar structures (solitons and shocks) characteristics on various plasma parameters is examined.

Weak dust acoustic shock wave in strongly coupled two-dimensional complex plasma

By using the equation of the state of P=αd+βdTd, we studied a shock wave propagation in a strongly coupled complex plasma. A Korteweg-de Vries–Burgers equation is obtained to describe a shock wave in strongly coupled complex plasma. Dependence of the shock wave speed on the piston velocity and the plasma parameters such as the screening parameter of the strongly coupled complex plasma are given analytically for a weak shock wave. It is in good agreement with previous results. It shows in the present paper that there are density oscillations in the postshock region which is similar to that found in the previous works. Dependence of the length between two first peaks of the density oscillation on the piston velocity and the plasma parameter are also given analytically which is also in agreement qualitatively with previous results.

Nonlinear dust acoustic perturbations within dusty plasma over sunlit lunar surface

A photoelectron sheath couples with positively charged floating fine dust to constitute a two-component dusty plasma over the sunlit locations on the Moon—the possibility of small amplitude nonlinear dust acoustic (DA) excitations in this plasma environment is investigated. The standard reductive perturbation approach has been adopted to analyze the nonlinear evolution of photoelectron-dust plasma dynamics, including the equations for dust fluid continuity and momentum, plasma potential (Poisson equation), and nonadiabatic dust charge variation. The photoemission from and photoelectron accretion on dust particles are considered dominant charging mechanisms where Fowler's formulation for the photoemission from the positively charged spherical dust and non-Maxwellian nature of the sheath photoelectrons are consistently accounted for. The dust charge variation induces collisionless dissipation, which damps amplitude and reduces the velocity of propagating DA waves. Under typical solar irradiation conditions, the nonlinear analysis of the sunlit lunar dusty plasma is supposed to support DA solitary and DA shock wave structures of both rarefied and compressive nature; the dominance of dispersion and dissipation effects in the fluid dynamics is shown to exhibit oscillatory and monotonic shock waves, respectively. The passage of such nonlinear DA structures might energize the ambient charged dust and photoelectrons locally and could be an important mechanism for energy/particle transport in the vicinity of the sunlit locations over the Moon.

Interaction of Dust-Acoustic Shock Waves in a Magnetized Dusty Plasma under the Influence of Polarization Force

The interaction of dust-acoustic (DA) shock waves in a magnetized dusty plasma under the influence of nonextensively modified polarization force is investigated. The plasma model consists of negatively charged dust, Maxwellian electrons, nonextensive ions, and polarization force. In this investigation, we have derived the expression of polarization force in the presence of nonextensive ions and illustrated the head-on collision between two DA shock waves. The extended Poincaré–Lighthill–Kuo (PLK) method is employed to obtain the two-sided Korteweg–de Vries–Burgers (KdVB) equations and phase shifts of two shock waves. The trajectories and phase shifts of negative potential dust-acoustic shock waves after collision are examined. The combined effects of various physical parameters such as polarization force, nonextensivity of ions, viscosity of dust, and magnetic field strength on the phase shifts of DA shock waves have been studied. The present investigation might be useful to study the process of collision of nonlinear structures in space dusty plasma such as planetary rings where non-Maxwellian particles such as nonextensive ions, negatively charged dust, and electrons are present.

Excitation of dust acoustic shock waves in an inhomogeneous dusty plasma

An experimental investigation of the propagation characteristics of shock waves in an inhomogeneous dusty plasma is carried out in the dusty plasma experimental device. A homogeneous dusty plasma, made up of poly-dispersive kaolin particles, is initially formed in a direct current 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 plasma by a sudden compression in the dust fluid. These structures are identified as shock waves, and their amplitude and width profiles are measured spatially. The amplitude of a shock structure is seen to increase, whereas the width broadens as it propagates down a decreasing dust density profile. A modified-Korteweg–de Vries–Burger equation is derived and used to provide a theoretical explanation of the results, including the power law scaling of the changes in the amplitude and width as a function of the background density.

Nonlinear interaction phenomenon of dust acoustic solitary and shock waves in dusty plasma

AbstractThe effects of head‐on collision on dust acoustic (DA) solitary and shock waves in dusty plasma are investigated considering positively charged inertial dust, Boltzmann distributed negatively charged heavy ions, positively charged light ions, and superthermal electrons in the plasma system. The nonlinear Korteweg‐de‐Vries (KdV) Burger equations are derived taking the extended Poincaré‐Lighthill‐Kuo method into account to study the characteristic properties of nonlinearity and production of solitary shock due to collisions. The study reveals that the amplitudes and widths of the DA shock waves are decreasing with increasing viscosity, electron to dust density ratio, and dust to ion temperature ratio, while they are increasing due to the presence of superthermal electrons. The nonlinearity of DA waves are enhanced with increasing density ratio of electron to dust and temperature ratio of dust to ion and electron, respectively, but it is reducing with superthermal electrons. The phase shifts of DA solitary waves are found to decrease with rising superthermality of electrons and increase with the density ratio of electron to dust.

Dust-acoustic shock waves in a plasma system with opposite polarity dust fluids and trapped ions

The propagation of dust-acoustic (DA) shock waves (SWs) is studied in a four-component dusty plasma system containing viscous dust fluids of opposite polarity, Schamel distributed ions and Boltzmann distributed electrons. The reductive perturbation method is employed to derive a modified Burgers equation which gives rise to the DA shock waves with stronger nonlinearity. The viscous force acting in the dust fluids is identified as a source of dissipation, and is responsible for the formation of the DA shock waves. The basic characteristics (viz., speed, amplitude, width) of the DA shock waves are found to be significantly modified by the combined effects of opposite polarity dust fluids and trapped ions. The applications of this investigation in different space plasma environments and laboratory devices are pinpointed.

Dust-Acoustic Shock Waves in a Self-Gravitating Opposite Polarity Dusty Plasmas With Trapped Ions

The basic characteristics of dust-acoustic (DA) shock waves (DASHWs) in self-gravitating dusty plasmas containing massive dust of opposite polarity, trapped ions, and Boltzmann electrons has been studied. The reductive perturbation technique has been employed to derive standard modified Burgers equation (mBE). The basic properties (viz., amplitude, width, and speed) of small but finite-amplitude DASHWs are significantly modified by the combined effects of positively and negatively charged dust component, self-gravitational force, and trapped ions. The implication of our investigation can be very effective for understanding and studying the nonlinear characteristics of the DA waves (DAWs) in laboratory and space dusty plasmas.

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.