Shock Waves In Dusty Plasma Research Articles

Exploring dust-ion acoustic shocks in a plasma in the light of phase plane analysis

This paper presents a comprehensive exploration of shock waves in a dusty plasma, incorporating the dynamics of inertial dust and ions with Maxwellian distributed electrons. By deriving the Korteweg-de Vries-Burgers (KdV-B) equation and by using its standard solution we analyze the characteristics of the shock front under varying parameters. Furthermore, we conduct a phase plane analysis to elucidate the system's behavior and dynamics by tuning in the parameters that provide various types of perturbation in the system. The investigation sheds light on the intricate behavior of shock waves in dusty plasmas and contributes valuable insights to the understanding of plasma dynamics.

The Effects of the Dust Size Distribution and the Dust Charging on Shock Waves in Dusty Plasma

The Effects of the Dust Size Distribution and the Dust Charging on Shock Waves in Dusty Plasma

Effects of the dust size distribution on shock waves in dusty plasma

By using a Korteweg-deVries-Burgers(KdV-Burgers) equation and considering the dust size distribution, we have studied effects of the dust size distribution on the shock wave in dusty plasma. The dependence of characteristics of the shock wave on different dust size distributions has been given. It is found that the speed and amplitude of a shock wave considering the dust size distribution are larger than that of the dusty plasma with the averaged dust size. However, the width of a shock wave considering the dust size distribution is smaller than that of the dusty plasma with the averaged dust size.

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.

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.

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 acoustic shock waves in magnetized dusty plasma

We have presented a theoretical study of the dust acoustic (DA) shock structures in a magnetized, electron depleted dusty plasma in the presence of two temperature superthermal ions. By deriving a Korteweg–de Vries–Burgers equation and studying its shock solution, we aim to highlight the effects of magnetic field and obliqueness on various properties of the DA shock structures in the presence of kappa-distributed two temperature ion population. The present model is motivated by the observations of Geotail spacecraft in the Earth's magnetotail and it is seen that the different physical parameters such as superthermality of the cold and hot ions, the cold to hot ion temperature ratio, the magnetic field strength, obliqueness and the dust kinematic viscosity greatly influence the dynamics of the shock structures so formed. The results suggest that the variation of superthermalities of the cold and hot ions have contrasting effects on both positive and negative polarity shock structures. Moreover, it is noted that the presence of the ambient magnetic field affects the dispersive properties of the medium and tends to make the shock structures less wide and more abrupt. The findings of present investigation may be useful in understanding the dynamics of shock waves in dusty plasma environments containing two temperature ions where the electrons are significantly depleted.

Dust-acoustic shock waves in a dusty plasma with non-thermal ions and super-thermal electrons

The propagation of dust-acoustic shock waves (DASWs) in a collisionless unmagnetized dusty plasma (containing super-thermal electrons of two distinct temperatures, non-thermal ions, and a negatively charged viscous dust fluid) has been theoretically investigated by deriving and solving the nonlinear Burgers' equation. It has been observed that the viscous force acting on the dust fluid is a source of dissipation, and is responsible for the formation of DASWs, and that the basic features (viz., amplitude, polarity, width, etc.) of the DASWs are significantly modified by the presence of super-thermal electrons and non-thermal ions. The possible applications of this investigation in Earth's mesosphere, the solar atmosphere, Saturn's magnetosphere, etc., have also been briefly addressed.

Shock waves in dusty plasma with two temperature superthermal ions

An investigation of dust acoustic shock waves in dusty plasma containing two temperature ions is presented. The present investigation is motivated by the observations of Geotail spacecraft that report the occurrence of two temperature ion populations in Earth’s magnetotail. We have derived Burgers equation to study dust acoustic shock structures in an unmagnetized plasma with two temperature superthermal ions. We have also derived the modified Burgers equation at critical values of physical parameters for which nonlinear coefficient (\(A\)) of Burgers equation vanishes. The numerical analysis is performed in context with observations in Earth’s magnetotail and the influence of various plasma parameters viz. ions temperature ratio, superthermality of hot and cold ions, kinematic viscosity etc. has been observed on characteristics of DA shocks. It is observed that the amplitude of positive shocks via Burgers equation decreases whereas that of modified shocks with higher order nonlinearity increases with increase in superthermality of cold ions.

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.

Space—time fractional KdV—Burgers equation for dust acoustic shock waves in dusty plasma with non-thermal ions

The KdV—Burgers equation for dust acoustic waves in unmagnetized plasma having electrons, singly charged nonthermal ions, and hot and cold dust species is derived using the reductive perturbation method. The Boltzmann distribution is used for electrons in the presence of the cold (hot) dust viscosity coefficients. The semi-inverse method and Agrawal variational technique are applied to formulate the space—time fractional KdV—Burgers equation which is solved using the fractional sub-equation method. The effect of the fractional parameter on the behavior of the dust acoustic shock waves in the dusty plasma is investigated.

Dust acoustic shock waves in dusty plasma of opposite polarity with non-extensive electron and ion distributions

A theoretical investigation has been made of obliquely propagating nonlinear electrostatic shock structures. The reductive perturbation method has been used to derive the Korteweg-de Vries-Burger (KdV-Burger) equation for dust acoustic shock waves in a homogeneous system of a magnetized collisionless plasma comprising a four-component dusty plasma with massive, micron-sized, positively, negatively dust grains and non-extensive electrons and ions. The effect of dust viscosity coefficients of charged dusty plasma of opposite polarity and the non-extensive parameters of electrons and ions have been studied. The behavior of the oscillatory and monotonic shock waves in dusty plasma has been investigated. It has been found that the presence of non-extensive parameters significantly modified the basic properties of shock structures in space environments.

SADDLE-NODE BIFURCATION AND ITS CONTROL OF BURGERS–KdV EQUATION

The Burgers–Korteweg-de Vries (KdV) equation had been used as nonlinear modes for acoustic shock waves in dusty plasmas and so on. The variable transformation and the Jacobi elliptic function method was introduced to find the exact solution. In this paper, we will research into the saddle-node bifurcation and its control of the forced Burgers–KdV. By the transformation, PDEs are reduced to ODEs. Analyzing the frequency response function and its unstable region of the trivial steady state, we know that the saddle-node bifurcation which leads to jump and hysteresis may appear in the resonance response. Controllers for bifurcation modification purpose are designed in order to remove or delay the occurrence of jump and hysteresis phenomena. By means of numerical simulations we compare the uncontrolled system with the controlled system and clarify that controllers are adequate for the saddle-node bifurcation control of the forced Burgers–KdV equation.

Arbitrary amplitude dust ion-acoustic shock waves in a dusty plasma with positive and negative ions

Arbitrary amplitude dust ion-acoustic shock waves in a multi-ion dusty plasma (composed of electrons, light positive ions, heavy negative ions, and stationary massive dust grains) has been studied. For this purpose, the coupled Poisson and dust-charging equations, which accounts for the fluctuation of charges on static dust, have been numerically solved. The large amplitude shocks are associated with a sudden decrease in the electrostatic potential and of the dust grain charge. It is found that in the lower speed limit small amplitude shocks are formed, while in the larger speed limit large amplitude shocks are formed. It is anticipated that the profiles and amplitudes of the DIA shocks predicted here will be observed in forthcoming laboratory and space experiments.

Nonplanar dust-ion acoustic shock waves with transverse perturbation

The nonlinear dust-ion acoustic shock waves in dusty plasmas with the combined effects of bounded cylindrical/spherical geometry, the transverse perturbation, the dust charge fluctuation, and the nonthermal electrons are studied. Using the perturbation method, a cylindrical/spherical Kadomtsev–Petviashvili Burgers equation that describes the dust-ion acoustic shock waves is deduced. A particular solution of the cylindrical/spherical Kadomtsev–Petviashvili Burgers equation is also obtained. It is shown that the dust-ion acoustic shock wave propagating in cylindrical/spherical geometry with transverse perturbation will be slightly deformed as time goes on.

Dust ion-acoustic shock-wave structures: Theory and laboratory experiments

An evolutionary theoretical model is developed that describes dust ion-acoustic shock waves in dusty plasma consisting of ions (treated in the hydrodynamic approximation), Boltzmann electrons, and variable-charge dust grains. Account is taken not only of ionization, absorption, momentum loss by electrons and ions in collisions with dust grains, and gas-kinetic pressure effects but also of the processes peculiar to laboratory plasmas. It is shown that the model is capable of describing all the main experimental results on dust ion-acoustic shock waves [Q.-Z. Luo et al., Phys. Plasmas 6, 3455 (1999); Y. Nakamura et al., Phys. Rev. Lett., 83, 1602 (1999)].

Shocks in dusty plasmas: theory and experiment

The main theoretical and experimental results on ion acoustic shock waves in dusty plasmas are reviewed. Two situations are considered: when the dust charge variation is caused by only the microscopic electron and ion currents at the grains and when it is caused by the microscopic currents and the photoelectric current of electrons. The possibilities of observation of shock waves related to the dust charging process in laboratory experiments, in active geophysical rocket experiments, and in astrophysical phenomena are discussed.

Shocks In Space Dusty Plasmas

An anomalous dissipation originating from the dust particle charging processes results in a possibility of existence of a new kind of shock waves in a dusty plasma. The shock waves related to this dissipation can be important for description of star formation, shocks in supernova explosions, particle acceleration in shocks, etc. The hydrodynamical description of shock waves in space dusty plasmas is presented. The possibility of the experimental study of the shock waves related to the dust charging process in active space experiments in the Earth's magnetosphere is discussed.

One-dimensional Self-organised Structures in Dusty Plasmas

A dusty plasma is an open system in which the formation of structures is a natural phenomenon. The first part of the present review is devoted to an introduction to dusty plasma physics and a formulation of the new theoretical kinetic and new hydrodynamic approaches used in subsequent parts. In the new hydrodynamic approach only dust–plasma particle collisions are taken into account and the usual binary plasma collisions are neglected. This description takes into account the possibility of plasma absorption on dust particles and is appropriate for open systems. The second part of the review contains a description of one-dimensional plasma–dust self-organised structures where the energy source corresponds to the plasma fluxes towards the dust regions from the plasma regions where the dust is absent. The fluxes are created by the structures in a self-consistent manner to increase the ion density and decrease the electron density, drift velocity and electrostatic potential inside the structure. The third part contains the theory of shock waves in dusty plasmas, modification of the Gugoniot relation and analyses of the possibility of an increase of dust density behind the shock front. All parts are based on the modern point of view of the physics of dusty plasmas and mainly new material is presented. The review is written in the form of lectures and therefore the references to the existing literature are given in the text, with more details in the last section devoted to some historical comment. The references to general reviews are given separately as [A]-[D].

Shock Structures in Plasmas Containing Variable-Charge Macro Particles

The results on shock waves in plasmas containing variable-charge dust grains are reviewed. The problems where the shock waves in dusty plasmas can be important are formulated. The dusty plasma is presented as an open, highly dissipative system where there is a tendency to self-organization. An anomalous dissipation originating from the charging processes results in a possibility of existence of a new kind of shock waves. The shock waves related to this dissipation can be important for description of star formation, shocks in supernova explosions, particle acceleration in shocks, formation of dusty crystals, etc.