Unmagnetized Dusty Plasma Research Articles

Effect of combined Kappa-Cairns distributed electrons on modulational instability and envelope soliton of ion-acoustic waves in electron-ion dusty plasma

Abstract Theoretical and numerical investigations are performed to study the amplitude modulation of ion-acoustic waves in an unmagnetized collisionless dusty plasma system whose components are warm ions (adiabatic), charged (negative) dust particles and Combined Kappa-Cairns distributed electrons. Modulational instability of ion-acoustic waves is analyzed through derivation of the nonlinear Schrödinger equation using the reductive perturbation technique by implementing hydrodynamic equations for this system. The conditions for modulational instability for this electron-ion dusty plasma system have been developed, and the impacts of the relevant physical parameters on the instability region along with the maximum growth rate of instability are demonstrated. Bright and dark envelope solitons are presented, and it is observed that the profiles of envelope solitons are significantly influenced by the existence of high-energy Combined Kappa-Cairns distributed electrons.

Effect of combined Kappa-Cairns distributed electrons on modulational instability and envelope soliton of ion-acoustic waves in electron-ion dusty plasma

Abstract Theoretical and numerical investigations are performed to study the amplitude modulation of ion-acoustic waves in an unmagnetized collisionless dusty plasma system whose components are warm ions (adiabatic), charged (negative) dust particles and Combined Kappa-Cairns distributed electrons. Modulational instability of ion-acoustic waves is analyzed through derivation of the nonlinear Schr{"o}dinger equation using the reductive perturbation technique by implementing hydrodynamic equations for this system. The conditions for modulational instability for this electron-ion dusty plasma system have been developed, and the impacts of the relevant physical parameters on the instability region along with the maximum growth rate of instability are demonstrated. Bright and dark envelope solitons are presented, and it is observed that the profiles of envelope solitons are significantly influenced by the existence of high-energy Combined Kappa-Cairns distributed electrons.

Variable dust charge generates multi solitons, breather soliton structures in Saturn’s ring

In this study, we have investigated nonlinear wave structures that are localized along with the exact stationary wave solutions with oscillating, i.e. the breather structures in an unmagnetized dusty plasma with variable dust charge concentration with two temperatures of ions. We have derived GE from the normalized governing equations employing the reductive perturbative technique (RPT). The GE is the extended Korteweg–de Vries (KdV) equation that includes the united effect of quadratic and cubic nonlinearities. Employing the Hirota bilinear method (HBM), multi-soliton solutions and the breather soliton solutions have been obtained. Breathers (oscillating wave packets) play a significant role in hydrodynamics and optics, and their interaction can change the dynamics of the wave fields. It is also important to propagate finite-amplitude waves in the astrophysical atmosphere, plasma dynamics, ocean, optic fibers, signal processing, etc. In the circumstances of Saturn’s ring, it is noticed that the breather soliton structures are modified significantly with variations in dust charge concentration, ion temperature ratio, and other physical parameters.

Role of polarized force on dust-acoustic structures in the presence of suprathermal electrons

The modulational instability (MI) of dust-acoustic wave (DAW) in an unmagnetized dusty plasma including dust, ions, and electrons is studied. Electrons are kappa-distributed, ions follow a Maxwellian distribution, and negatively charged dust particles display dynamic behavior. A nonlinear Schrödinger equation (NLSE) is generated using the Krylov–Bogoliubov–Mitropolsky approach to explore MI. Using the essential physical characteristics, the steady and unstable portions of the modulated wave packets are properly characterized. The impact of polarization force, suprathermal index (κ), effective temperature of electron to ion temperature ratios, and other physical factors in stable and unstable DAW zones is numerically studied. In unstable zones, unpredictable amplitude perturbations cause freak/rogue waves for which the essential studies on the localized solutions of the NLSE are done extensively.

Landau damping effects on dust ion-acoustic solitary waves in a nonthermal pair-ion plasma

The Landau damping effects on the nonlinear propagation of dust ion-acoustic solitary waves (DIASWs) are studied in an electron-free unmagnetized collisionless dusty pair-ion plasma. The two species of nonthermal ions (positive and negative) are described by the kinetic Vlasov equations, whereas the massive charged dust grains form only the background plasma. Using the multi-scale reductive perturbation technique generalized for the applications to the Vlasov equation, we derive a modified Korteweg–de Vries (KdV) equation that governs the evolution of DIASWs with the effects of linear resonance, in particular, linear Landau damping. The properties of the phase velocity and the Landau damping rate of DIASWs are studied with the effects of positive and negative-ion nonthermality parameters ( α p , α n ), the ratios of the positive to negative ion masses (m) and temperatures (T) as well as the dust to negative-ion number density ratio (δ). It is found that, depend on the degree of positive to negative ion mass ratios (m), both of damped and growing oscillations occur in a collisionless dusty pair-ion plasma due to the resonance phenomena between the wave and the nonthermal particles of the system. The properties of the decay rates of the amplitude of the KdV soliton with a small effect of Landau damping are also studied with the above system of parameters. The results may be useful for understanding the localization of solitary pulses and associated resonance damping and/or growing oscillations of the wave in laboratory and space plasmas, in which the number density of free electrons is much smaller than that of ions and highly charged heavy, micron seized dust grains.

Nonlinear dust-ion acoustic solitary waves for collisional electronegative dusty plasma in the presence of trapped electron distribution

We have investigated the characteristics of nonlinear propagation of dust-ion acoustic solitary waves in collisional electronegative unmagnetized dusty plasma, which consists of trapped electrons, Boltzmann negative ions, mobile positive ions, mobile negative dust particulates, and a uniform background of neutral particles. In account of ion-neutral collisions, the modified Korteweg–de Vries relation has been derived by employing the standard reductive perturbation method. Analytical and numerical solutions of the damped Korteweg–de Vries equation has been presented in which finite difference method is used for numerical solution. On the other hand, the dust charging equation has been solved by using Newton’s Raphson method. It is found that the temperature ratio of free to trapped electrons, ion-neutral collision, concentration of negative ions, dust number density, and dust density perturbation modify the basic properties of the dust-ion acoustic solitary waves. The temporal evolution of dust-ion acoustic solitary waves is crucial as it affects the amplitude and width of wave structure. In addition, the analytical and numerical solutions are compared, and their deviation is graphically illustrated.

Effect of nonthermal electron distributions on dust acoustic solitons in cometary plasmas

We investigate the effect of nonthermal electrons modeled by two non-Maxwellian distribution functions, i.e., the (r, q) and Cairn’s distributions on the formation of dust acoustic (DA) solitons in an un-magnetized dusty plasma by incorporating the effect of dust streaming. We adopt the pseudopotential technique to obtain solitary wave solutions from fluid equations. It is seen that only rarefactive soliton can be obtained in such plasmas where ions are considered Boltzmannian and electrons non-Maxwellian. We find that soliton characteristics are strongly dependent on the nonthermal spectral indices r, q, and α and dust temperature Td. For (r, q) distribution, it is found that soliton amplitude increases but width decreases when the positive (negative) value of r decreases (increases). For Cairn’s distribution, we find that with the increase in α, soliton amplitude decreases. In space environments, such as cometary tails, solar wind, and Earth’s magnetosphere, where non-Maxwellian populations of electrons are present, our theoretical results show that the amplitude of soliton remains smaller than the Maxwellian case. Thus, Maxwellian distribution overestimates the soliton amplitude in such space environments. Therefore, we feel that our results will better interpret the results of observations, from cometary tails, and other space plasmas where nonlinear DA structures are likely to be observed.

Consequence of head‐on collision and double‐layer soliton with linear analysis in multi‐component dusty plasmas

AbstractThe unmagnetized multicomponent collisional dusty plasmas have been considered to investigate the consequence of head‐on collision of dust‐ion‐acoustic waves (DIAWs) with nonlinear characteristic analysis of DIAWs and collisionless plasmas have been considered for studying the production of double layer (DL). The plasma system consists of positively charged ion fluid, negatively charged cold dust fluid, thermal electrons, q‐nonextensive electrons, and immobile background neutral particles. The extended Poincaré‐Lighthill‐Kuo (ePLK) method has been used to derive two‐sided damped Korteweg–De Vries (dKdV) equations and the reductive perturbation method has been used to derive modified KdV (mKdV) equation and the standard Gardner equation (SGE). Linear dispersion relation is derived using linear perturbation technique. The nonlinear propagation of DIA Gardner solitons (DIAGSs) and double layers (DLs) as well as phase shifts have been investigated for the effects of the concerned parameters. It is found that the DIA soliton structures are significantly modified by the species densities, dust mass, and superextensive parameter. The rarefactive dip shape solitary Gardner solitons become produced for the effects of concerned parameters and the positive (negative) DLs become produced in the range of () for the effect of temperatures on the species. The superextensive and the subextensive parameters of electrons significantly affect the DL soliton structures.

On massive photons in unmagnetized dusty plasmas

On massive photons in unmagnetized dusty plasmas

The separation of one-soliton-shock to multi-soliton-shock of dust-ion acoustic wave using Lax pair and Darboux transformation of Burgers’ equation

Properties of dust-ion acoustic waves (DIAWs) in an unmagnetized dusty plasma consisting of mobile ions, superthermal electrons, and negatively charged dust clouds with charge fluctuation are investigated. Burgers’ equation is derived from the fluid equation of the plasmas by considering the reductive perturbation technique. The Lax pair of the evolution equation is obtained, and the characteristics of the DIAWs are investigated by employing the Darboux transformation. Some new waves (one-soliton, two-soliton-shocks, etc.) other than usual shocks are observed as the Darboux transformation is used through the Lax pair. It is also shown that all the physical plasma parameters have a significant effect on the structure of the nonlinear waves.

Three-Dimensional Cylindrical Dust-Acoustic Solitary Pulses in Warm Nonthermal Plasma

The nonlinear propagation of 3-D cylindrical dust-acoustic (DA) solitary waves in an unmagnetized dusty plasma system consisting of mobile adiabatic positively charged dust (PCD) grains, nonthermal ions, and electrons is investigated. The basic properties of nonlinear DA solitary structures, which exist in such a warm dusty plasma medium, are studied. The ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3+1$</tex-math> </inline-formula> )-dimensional cylindrical Kadomstev–Petviashvili equation (cKPE) (also known as cylindrical Korteweg-de Vries (KdV) equation) is derived by using the reductive perturbation method (RPM). The possible region of the formation of solitons is shown. The effects of different plasma parameters (viz., the nonthermal parameter, the dust-to-ion temperature ratio, the ion-to-dust number density ratio, etc.) on the characteristics of the DA solitary waves are studied, and also the graphical representation of the cylindrical DA solitary structures is presented. The polarity of DA solitary waves changes with different plasma parameters (viz., the ion-to-electron temperature ratio, the nonthermality of ions and electrons, the ion-to-dust number density, etc.). These results may improve our understanding of DA solitary structures in space and laboratory plasma devices where nonthermal dusty plasma occurs.

Effects of trapped electrons on the sheath at the boundary of a dusty plasma

In the present paper, the characteristic behaviors of the sheath in an unmagnetized dusty plasma that contained trapped electrons, cold ions, and variable-charged dusts are investigated, based on the Sagdeev potential approach. The result shows that both the formation and structure of the sheath are modified by the trapped electrons. At the sheath edge, the critical ion Mach number decreases as the trapping parameter β increases. It is noted that the effect of electron trapping on the ion-entering-sheath-velocity is indirect, and closely related to the dust charge variation. In the sheath, the increased β leads to the enlargement of the sheath thickness and the absolute value of electrostatic potential, which results in the redistribution of particle densities. Moreover, the results of the Maxwellian case are essentially recovered when β = 1. As expected, the present results can give more insight into the interaction processes that happened on the plasma-wall interface.

On charged photons in unmagnetized dusty plasma instabilities

Motivated by the expanding interest in complex plasmas, we discuss the equivalent photon charge in dusty electron-ion plasmas. Particularly, we investigate the dusty plasma response in terms of the electron density perturbation driven by electromagnetic waves. The resulting polarization of this plasma medium caused by the photon ponderomotive force of the electromagnetic radiation pressure gives rise to an effective photon electric charge. We determine the acquired photon charge in terms of the involved characteristic parameters. More precisely, here we derive an explicit expression of the photon charge which is found to depend strongly on the free electron density and the photon frequency. Such a photonic charge is relevant for dealing with the photon–plasma couplings in most plasma mediums, namely of the early Universe.

Quantum Effects on Cylindrical Dust-ion Acoustic Waves in a Semiclassical Dense Dusty Plasma

The nonlinear cylindrical dust ion acoustic waves are studied in a collisional unmagnetized dense dusty plasma medium containing inertialess degenerated electrons and positrons, fluid ions, negatively charged dust fluid and neutrals in the background, including exchange-correlation effects of both electrons and positrons. Employing the reductive perturbation method, the damped Kadomstev–Petviashvili equation is derived in the framework of two-dimensional cylindrical geometry. An approximate analytical solution of this equation is also discussed. The quantum and geometrical effects on the dust ion acoustic waves have been investigated. It is found that the dust ion acoustic wave is modified by quantum diffraction, Fermi statistics and exchange-correlation potential. Moreover, it has been found that the nebulon structures of quantum dust ions acoustic wave are formed due to the Cartesian geometry and the transverse perturbation. It is also observed that the nebulon structure is significantly modified by the exchange-correlation effects.

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 a Nonextensive Dust Charge Variation on an Oblique Collision of Dust Acoustic Solitons in a Dusty plasma

In the current study, two-dimensional collision of two dust acoustic solitons in an unmagnetized nonextensive dusty plasma is investigated, including the effect of non-extensive dust charge variation. By using the extended Poincar-Lighthill-Kuo (PLK) method, two Korteweg-de Vries equations that describe the two dust acoustic solitons propagating in two different directions are derived. The phase shifts after a two-dimensional collision of dust acoustic solitons are obtained as well. The effects of parameters of the ratio of ion temperature to electron temperature, the ratio of ion density to electron density and nonextensive parameter of electrons/ions on the phase shifts are discussed with and without dust charge variation. The results show that the phase shift has been significantly influenced by these parameters. Furthermore, the non-extensive dust charge variation has a significant effect on the amplitude, width of a new nonlinear wave, which generates during the oblique collision.

Singular solitons interaction of dust ion acoustic waves in the framework of Korteweg de Vries and Modified Korteweg‐de Vries equations with (r,q) distributed electrons

AbstractTwo nonlinear evolution equations (NLEEs), namely, Korteweg‐de Vries (KdV) and modified Korteweg‐de Vries (MKdV) are derived from the dust hydrodynamic model of collisionless, unmagnetized dusty plasma with electrons following double spectral velocity distribution, that is, (r,q) distribution. Regular as well as singular analytic solutions of derived KdV equations and MKdV equations are obtained separately with the aid of the Hirota Bilinear method. Two singular soliton solutions of both KdV and MKdV equations are obtained separately. The efficiency and interactive approach of the heuristic Hirota Bilinear method leads to multiple singular soliton solutions for its beautiful algebraic technique which generates solitons solutions as well as singular solitons explicitly. Then the significance of multi singular soliton interaction has been studied for KdV singular solitons and for MKdV singular solitons in the critical parameter set.

Dust-acoustic solitary and periodic waves in a plasma with ion distribution with trapped particles

The nonlinear propagation of electrostatic dust-acoustic waves is studied in an unmagnetized three-component dusty plasma consisting of negatively charged dust, free as well as a small percentage of trapped ions and Maxwellian electrons. By using the reductive perturbation technique, a Korteweg de Vries type equation, which governs the dynamics of the small-amplitude solitary and periodic waves of the dusty plasma under consideration, is derived. The traveling soliton (shown to be only of the rarefactive type) and periodic solutions of the KdV type equation are obtained. Bifurcation analysis for the obtained nonlinear KdV type equation is used to describe the qualitative phase portrait for the corresponding dynamical system, which is found to be controlled by the plasma system parameters. The effects of trapped ions and free electrons on the dust-acoustic solitons and periodic waves are discussed. The present investigation may be useful in understanding some nonlinear features of the dust-acoustic waves, which have been observed in astrophysical plasmas such as Saturn's moon Enceladus.

Propagation characteristics of (2 + 1) dimensional dust acoustic solitary waves in hot dusty plasma

The propagation characteristics of (2 + 1) dimensional nonlinear dust acoustic solitary wave in an unmagnetized hot dusty plasma composed of dust particles, electrons and nonthermal ions are studied in the paper. Firstly, the Kadomtsev-Petviashvili (KP) equation, which is used to describe the (2 + 1) dimensional nonlinear dust acoustic solitary wave, is derived by the reduced perturbation method, and the phase diagram and the Sagdeev potential equation of the system are obtained by using the traveling wave solution method. Then, the effects of different parameters in the hot dusty plasma system on the nonlinear coefficient, dispersion coefficient of the KP equation, system phase diagrams, Sagdeev potential function and the solitary wave solution in isothermal and adiabatic states are discussed by using numerical simulation and analysis method of mathematical software. Finally, the results show that the mass of dust particles, temperature, number density and distribution state of electrons and nonthermal ions have important effects on the amplitude, width and waveform of the nonlinear dust acoustic solitary wave under isothermal and adiabatic conditions.

Dust-ion acoustic solitons in superthermal dusty plasmas

In this research, the properties of dust- ion-acoustic (DIA) solitons in an unmagnetized dusty plasma, whose constituents are inertial ions, superthermal electrons, and stationary dust particles, are studied by using the Pseudopotential method. As an important result it is shown that DIA solitons are accepted beyond a certain critical value of the electron-to-ion density ratio (μ) as well as the superthermal parameter of electrons. We show that Mach permissible numbers shift to lower values in supethermal dusty plasmas. The results of this study help to gain a better understanding of the dust-ion wave behavior propagated in various spaces such as the Earth's atmosphere, Venus ionosphere and solar winds.