Dust Ion-acoustic Shock Waves Research Articles

DIA Solitary and Shock Waves in Dusty Multi-Ion Dense Plasma with Arbitrary Charged Dust

The nonlinear propagation of the DIA (dust ion-acoustic) waves in multi-ion dense plasma system containing degener- ate electrons, both positive and negative ions, arbitrary charged dust grains has been investigated by employing the reductive perturbation method. The nonlinear waves (solitary and shock waves) have been observed to be formed in case of both positive and negative charged dust grains from the stationary solution of the Korteweg de-Vries (K-dV) equation and Burger’s equation. The fundamental properties of such nonlinear waves have been theoretically analyzed by comparing system potential for both positive and negative dust grains. It has been shown that the basic features of these waves are significantly modified by the positive and negative ions drift speed and polarities of dust grains. The implications of our results in space and laboratory plasmas are briefly discussed.

Dust ion-acoustic shock waves due to dust charge fluctuation in a superthermal dusty plasma

The nonlinear propagation of dust ion-acoustic (DIA) shock waves is studied in a charge varying dusty plasma with electrons having kappa velocity distribution. We use hot ions with equilibrium streaming speed and a fast superthermal electron charging current derived from orbit limited motion (OLM) theory. It is found that the presence of superthermal electrons does not only significantly modify the basic properties of shock waves, but also causes the existence of shock profile with only positive potential in such plasma with parameter ranges corresponding to Saturnʼs rings. It is also shown that the strength and steepness of the shock waves decrease with increase of the size of dust grains and ion temperature.

Effects of adiabaticity and non-adiabaticity of dust charge fluctuation on the propagation of the dust ion acoustic waves in inhomogeneous dusty plasma

A theoretical investigation has been made for adiabatic positive and negative dust charge fluctuations on the propagation of dust-ion acoustic waves (DIAWs) in a weakly inhomogeneous, collisionless, unmagnetized dusty plasmas consisting of cold positive ions, stationary positively and negatively charged dust particles and isothermal electrons. The reductive perturbation method is employed to reduce the basic set of fluid equations to the variable coefficients Korteweg–de Vries (KdV) equation. Either compressive or rarefactive solitons are shown to exist depending on the critical value of the ion density, which in turn, depends on the inhomogeneous distribution of the ion. The dissipative effects of non-adiabatic dust charge variation has been studied which cause generation of dust ion acoustic shock waves governed by KdV-Burger (KdVB) equation. The results of the present investigation may be applicable to some dusty plasma environments, such as dusty plasma existing in polar mesosphere region.

Dust ion-acoustic shock waves in charge varying dusty plasmas with electrons having vortexlike velocity distribution

A weakly nonlinear analysis is carried out to investigate the properties of dust ion-acoustic shock waves in a charge varying dusty plasma with vortexlike electron distribution. We use the ionization model, hot ions with equilibrium streaming speed and a trapped electron charging current derived from the well-known orbit limited motion theory. A new modified Burger equation is derived. Besides nonlinear trapping, this equation involves two kinds of dissipation (the anomalous one inherent to nonadiabatic dust charge fluctuation and the one due to the particle loss and ionization). These two kinds of dissipation can act concurrently. The traveling wave solution has been acquired by employing the modified extended tanh-function method. The shocklike solution is numerically analyzed based on the typical numerical data from laboratory dusty plasma devices. It is found that ion temperature, trapped particles, and weak dissipations significantly modify the shock structures.

Dust ion-acoustic solitary and shock waves due to dust charge fluctuation with vortexlike electrons

A rigorous theoretical investigation has been made of the dust ion-acoustic (DIA) solitary and shock waves in an unmagnetized dusty plasma (containing vortexlike electrons, mobile ions, and charge fluctuating static dust) by reductive perturbation method. The effects of dust grain charge fluctuation and vortexlike (trapped) electron are found to modify the properties of the DIA solitary and shock waves significantly. The implications of these results for some space and astrophysical dusty plasma systems, especially planetary ring systems, are briefly mentioned.

Effects of dust charge fluctuations and deviations from isothermality of electrons on nonlinear dust ion-acoustic waves

The effects of dust charge fluctuations and deviations from isothermality of electrons are incorporated in the study of nonlinear dust ion-acoustic waves. Deviations from isothermality of electrons are included in this model as a result of nonlinear resonant interaction of the electrostatic wave potential with electrons during its evolution. The basic properties of stationary structures are studied by employing the reductive perturbation method, and conditions for the formation of small but finite amplitude dust ion-acoustic solitary waves in the space dusty plasma situations are clearly explained. It is shown that a more depletion of the background free electrons owing to the attachment of these electrons to the surface of the dust grains during the charging process can lead to the formation of solitary waves with smaller amplitude. Furthermore, effects of the dust charge fluctuation and deviations from isothermality of electrons show a non-uniform behavior for the amplitude of solitary waves in transition from the Boltzmann electron distribution to a trapped electron one. It is also found that the dust charge fluctuation caused by trapped as well as free electrons is a source of dissipation, and is responsible for the formation of the dust ion-acoustic shock waves.

Dust ion-acoustic solitary and shock waves in a dusty plasma with non-thermal electrons

A theoretical investigation of the one dimensional dynamics of nonlinear electrostatic dust ion-acoustic (DIA) waves in an unmagnetized dusty plasma consisting of ion fluid, non-thermal electrons and fluctuating immobile dust particles has been made by the reductive perturbation technique. The basic features of DIA solitary and shock waves are studied by deriving the Korteweg-de Vries (KdV) and KdV Burger equations, respectively. It is shown that the special patterns of nonlinear electrostatic waves are significantly modified by the presence of the non-thermal electron component. In particular, the rarefactive solitary and shock structures are found with smaller amplitude in comparison to the isothermal case. The transition from DIA solitary to shock waves is also studied which is related to the contributions of the dispersive and dissipative terms. It is found that the dust charge fluctuation is a source of dissipation, and is responsible for the formation of the dust ion-acoustic shock waves. Furthermore, the dissipative effect becomes important and may prevail over that of dispersion as the population of non-thermal electrons present decreases. The present investigation may be of relevance to electrostatic solitary structures observed in many space dusty plasma, such as Saturn’s E-ring.

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 solitary and shock waves in a dusty plasma with electrons following a vortex-like distribution

Properties of nonplanar (viz. cylindrical and spherical) dust ion-acoustic (DIA) solitary and shock waves propagating in a dusty plasma containing charge fluctuating stationary dust, inertial warm ions, and non-isothermal electrons following a vortex-like distribution, are investigated by the reductive perturbation method. It has been shown that all the basic features of the DIA solitary and shock waves are significantly modified by the effects of vortex-like electron distribution, dust charge fluctuation, and nonplanar cylindrical and spherical geometries. The implications of our results in some space and laboratory dusty plasma environments are briefly discussed.

Weakly nonlinear dust ion-acoustic shock waves in a dusty plasma with nonthermal electrons

Weakly nonlinear dust ion-acoustic (DIA) shock waves are investigated in a dusty plasma with nonthermal electrons. A modified Korteweg–de Vries equation with a cubic nonlinearity is derived. Due to the net negative dust charge μZd and electron nonthermality, the present plasma model can admit compressive and rarefactive weak DIA shock waves. The effect of increasing μZd is to lower the critical nonthermal parameter βc above which only rarefactive DIA shock waves are admitted. Our investigation may help to understand the nonlinear structures observed in the auroral acceleration regions.

Propagation and stability of quantum dust-ion-acoustic shock waves in planar and nonplanar geometry

Dust-ion-acoustic (DIA) shock waves are studied in an unmagnetized quantum plasma consisting of electrons, ions, and dust by employing the quantum hydrodynamic (QHD) model. In this context, a Korteweg–deVries–Burger (KdVB) equation is derived by employing the small amplitude perturbation expansion method. The dissipation is introduced by taking into account the kinematic viscosity among the plasma constituents. It is found that the strength of the quantum DIA shock wave is maximum for spherical, intermediate for cylindrical, and minimum for the planar geometry. The effects of quantum Bohm potential, dust concentration, and kinematic viscosity on the quantum DIA shock structure are also investigated. The temporal evolution of DIA KdV solitons and Burger shocks are also studied by putting the dissipative and dispersive coefficients equal to zero, respectively. The effects of the quantum Bohm potential on the stability of the DIA shock is also investigated. The present investigation may be beneficial to understand the dissipative and dispersive processes that may occur in the quantum dusty plasmas found in microelectronic devices as well as in astrophysical plasmas.

Dust ion-acoustic shock waves in an adiabatic dusty plasma

The properties of dust ion-acoustic shock waves in an unmagnetized dusty plasma, whose constituents are adiabatic ion fluid, Boltzmann electrons, and static dust, are investigated by employing the reductive perturbation method. The Burgers equation is derived and its stationary analytical solution is numerically analyzed. It has been found that both the amplitude and the width decrease with the increase of the ion-fluid temperature. The implications of our results in space and laboratory dusty plasmas are briefly discussed.

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.

Ion Acoustic Shock Waves in a Dusty Plasma

A dispersive shock wave is generated in a plasma when wave breaking due to the nonlinearity is balanced by the combined action of dispersion and dissipation. In the absence of dissipation, the dispersive effect leads to the generation of solitons described by a KdV equation. On the other hand, when dissipation dominates, the shock front exhibits a monotonic transition of plasma density, while the shock transition is of oscillatory nature when the dissipation is weak. In a dusty plasma, when viscosity and Landau damping effects are not important, the nonadiabaticity of the dust charge variation provides shocks for which both monotonic and oscillatory structures are possible, and such shocks can be described by a K-dV Burger equation.In this paper the evolution of the Dust Ion Acoustic (DIA) shock waves is discussed. In addition, analytical studies of the propagation of DIA waves governed by K-dV Burger equation are presented.

Cylindrical and spherical dust–ion acoustic shock waves

The effect of the bounded nonplanar geometry on dust–ion acoustic shock wave (DIASW) in unmagnetized dusty plasmas is investigated for the first time. By using the standard reductive perturbation method, a cylindrical/spherical Korteweg–de Vries–Burgers (KdV–Burgers) equation is obtained. The change of the DIASW structure due to the effect of the geometry, dust density, and ion temperature is studied by numerical calculation of the cylindrical/spherical KdV–Burgers equation.

Nonlinear waves and structures in dusty plasmas

Recent laboratory observations conclusively reveal that coherent nonlinear waves and structures (viz., solitons, shocks, Mach cones, voids, vortices, etc.) can be produced in a dusty plasma. Our objective here is to describe the underlying physics, mathematical details, and salient features of dust ion-acoustic as well as dust acoustic solitary and shock waves, dust voids, and dust vortex flows. It is shown that the presence of charged dust grains introduces new features to the nonlinear electrostatic waves and structures. Consideration of the dust charge fluctuation dynamics causes a novel dissipation, which is responsible for the formation of dust ion-acoustic shock waves. Furthermore, the formation of a dust void is associated with double layers and ion holes arising from trapped ion effects. Finally, a nonlinear model for dust vortex flows is presented. It is shown that the dynamics of dust vortex flows in a plasma is governed by a modified Navier–Stokes equation (MNSE), and that possible stationary solutions of the MNSE can be represented as monopolar as well as a row of identical and a row of counter-rotating vortices. The implications of our theoretical results/models to experimental observations of solitary and shock waves as well as of voids and vortices are discussed.

The role of dust charge fluctuations on nonlinear dust ion-acoustic waves

The nonlinear propagation of the dust ion-acoustic waves has been investigated accounting for the charge fluctuation dynamics of stationary dust grains in an unmagnetized dusty plasma. The Korteweg-de Vries equation, as well as the Korteweg-de Vries-Burgers equation, are derived by employing the reductive perturbation method. It has been shown that dust charge fluctuations produce a dissipation which is responsible for shock waves. Conditions for the formation of dust ion-acoustic solitary and shock waves as well as their properties are clearly explained. The implications of our investigations to both space and laboratory dusty plasmas are discussed.

Experiments on ion-acoustic shock waves in a dusty plasma

Dust ion-acoustic shock waves have been investigated experimentally in a homogeneous unmagnetized dusty double-plasma device. An initial compressional wave with a ramp shape steepens to form oscillations at the leading part due to dispersion. The oscillation develops to a train of solitons when the plasma contains no dust grain. The wave becomes an oscillatory shock wave when the dust is mixed in the plasma and the density of the dust grains is smaller than a critical value. When the dust density is larger than the critical value, only steepening is observed at the leading part of the wave and a monotonic shock structure is observed. The velocity and width of the shock waves are measured and compared with results of numerical integrations of the modified Korteweg–de Vries–Burgers equation.

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)].

Small Amplitude Nonlinear Dust Ion Acoustic Waves in a Magnetized Dusty Plasma With Charge Fluctuation

A theoretical investigation of one dimensional dynamics of nonlinear electrostatic dust ion acoustic waves in a magnetized dusty plasma has been made by reductive perturbation technique. The effects of both the adiabatic and the nonadiabatic dust charge variation are incorporated. The most interesting feature is that the nonlinear evolution equation of the dust ion acoustic wave for nonadiabatic dust charge variation is the Korteweg-de Vries (KdV) Burger equation, whereas for adiabatic dust charge variation, the equation is the KdV equation. A nonadiabaticity generated anomalous dissipative effect causes generation of dust ion acoustic shock waves, a new mechanism for the generation of shock waves. Numerical integration of the KdV Burger equation shows that dust ion acoustic waves admit oscillatory (dispersion dominant) or monotone (dissipation dominant) shock solutions. It is also seen that the magnetic field and the dust charge variations significantly modify the wave amplitude.