Cylindrical and spherical dust ion-acoustic solitary waves in quantum plasmas

Dust ion-acoustic solitary waves in unmagnetized quantum plasmas are studied in spherical and cylindrical geometries. Using quantum hydrodynamic model, the electrostatic waves are investigated in the weakly nonlinear limit. A deformed Korteweg-de Vries (dKdV) equation is derived by using the reductive perturbation method and its numerical solutions are also presented. The quantum diffraction and quantum statistical effects incorporated in the system modifies the characteristics of dust ion-acoustic waves in cylindrical and spherical geometries. The role of stationary dust particles in quantum plasmas are also discussed. It is shown that the cylindrical and spherical dust ion-acoustic solitary waves behave quite differently from one-dimensional planar solitary waves in quantum plasmas.     

Effect of excavated trapped electron distributions on ion-acoustic solitary structures in an electron-positron-ion plasma

Fully nonlinear propagation of ion-acoustic solitary waves in an unmagnetized electron-positron-ion plasma is investigated. A more realistic situation is considered in which electrons interact with the wave potential during its evolution and, follow the vortex-like excavated trapped distribution. The basic properties of large amplitude solitary waves are studied by deriving an energy integral equation involving Sagdeev potential. It is shown that effects of such electron behavior and positron concentration change the maximum values of the Mach number and amplitude for which solitary waves can exist. The small amplitude limit is also investigated by expanding the Sagdeev potential to include third-order nonlinearity of electric potential. In this case, exact analytical solution is obtained which is related to the contribution of the resonant electron to the electron density. It is shown from both highly and weakly nonlinear analysis that the plasma system under consideration supports only compressive solitary waves.     

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.     

Nonplanar Ion-Acoustic Solitons in Electron-Positron-Ion Quantum Plasmas

The propagation of nonplanar quantum ion-acoustic solitary waves in a dense, unmagnetized electron-positronion （e-p-i） plasma are studied by using the Korteweg-de Vries （KdV） model. The quantum hydrodynamic （QHD） equations are used taking into account the quantum diffraction and quantum statistics corrections. The analytical and numerical solutions of KdV equation reveal that the nonplanar ion-acoustic solitons arc modified significantly with quantum corrections and positron concentration, and behave differently in different geometries.     

Ion-acoustic solitary waves in a dense pair-ion plasma containing degenerate electrons and positrons

Fully nonlinear propagation of ion-acoustic solitary waves in a collisionless dense/quantum electron–positron–ion plasma is investigated. The electrons and positrons are assumed to follow the Thomas–Fermi density distribution and the ions are described by the hydrodynamic equations. An energy balance-like equation involving a Sagdeev-type pseudo-potential is derived. Finite amplitude solutions are obtained numerically and their characteristics are discussed. The small-but finite-amplitude limit is also considered and an exact analytical solution is obtained. The present studies might be helpful to understand the excitation of nonlinear ion-acoustic solitary waves in a degenerate plasma such as in superdense white dwarfs.     

Head-on collision of ion-acoustic solitary waves in a Thomas-Fermi plasma containing degenerate electrons and positrons

Head-on collision between two ion acoustic solitary waves in a Thomas-Fermi plasma containing degenerate electrons and positrons is investigated using the extended Poincaré-Lighthill-Kuo (PLK) method. The results show that the phase shifts due to the collision are strongly dependent on the positron-to-electron number density ratio, the electron-to-positron Fermi temperature ratio and the ion-to-electron Fermi temperature ratio. The present study might be helpful to understand the excitation of nonlinear ion-acoustic solitary waves in a degenerate plasma such as in superdense white dwarfs.     

Head-on collision of ion-acoustic solitary waves in an unmagnetized electron-positron-ion plasma

The head-on collision between two ion-acoustic solitary waves in an unmagnetized electron-positron-ion plasma has been investigated. By using the extended Poincaré-Lighthill-Kuo perturbation method, we obtain the KdV equation and the analytical phase shift after the head-on collision of two solitary waves in this three-component plasma. The effects of the ratio of electron temperature to positron temperature, and the ratio of the number density of positrons to that of electrons on the phase shift are studied. It is found that these parameters can significantly influence the phase shifts of the solitons. Moreover, the compressive solitary wave can propagate in this system.     

Effect of deviations from isothermality of ions on the propagation of localized dust-acoustic waves

The effect of deviations from isothermality of ions on arbitrary amplitude dust-acoustic solitary structures is studied in an unmagnetized dusty plasma which consists of a negative charged dust fluid, free electrons and hot ions obeying a trapped distribution. For the finite deviation from isothermality of ions, the basic properties of large amplitude solitary waves are studied by employing pseudo-potential approach. It is shown that the effect of such ion behavior changes the maximum values of the Mach number and the amplitude for which solitary wave can exist. For the case that the deviation from isothermality due to nonlinear resonant particle effects is small, calculations by reductive perturbation method leads to a generalized Korteweg-de Vries equation with mixed nonlinearity. The latter admits a stationary dust-acoustic solitary solution with similar width and qualitatively different amplitude in comparison to the case that deviations from isothermality are finite. Furthermore, effects of the equilibrium free electron density and such trapped ions on the amplitude of solitary structures imply a non-uniform transition from the Boltzmann ion distribution to the trapped ion one.     

Electrostatic Nonlinear Structures in Dissipative Electron--Positron--Ion Quantum Plasmas

Low frequency （in comparison to ion plasma frequency） ion-acoustic shocks and solitons in superdense electronpositron-ion quantum plasmas are studied. The quantum hydrodynamic model is used incorporating quantum Bohm forces and Fermi-Dirac statistical corrections to derive the deformed Korteweg de Vries-Burgers （dKdVB） equation in weakly nonlinear limit. The travelling wave solution of dKdVB equation is presented and results are discussed in different limits. It is found that shock height increases with increase of quantum pressure, positron concentration and dissipation. Further, it is seen that the width of soliton decreases with increase of quantum pressure     

Speed and shape of solitary waves in relativistic warm plasma

Large-amplitude solitary waves are investigated in a relativistic plasma with finite ion-temperature. The mass of electron is also considered. The Sagdeev’s pseudopotential is determined in terms ofu, the ion speed. It is found that there exists a critical value ofu ₀, the value ofu at which (u′)²=0, beyond which the solitary waves cease to exist. The critical value also depends on the parameters likeν, the soliton velocity;μ, the electronion mass ratio orσ, the temperature ratio of ion to electron. This result reproduces our previous result [Czech. J. Phys., Vol. 54 (2004), No. 4, 489–496] when the ion temperature is neglected.     

Exact electrostatic solitons in a magnetoplasma with degenerate electrons

Fully nonlinear planar ion-acoustic solitary waves (IASWs) moving obliquely to an external magnetic field are studied in a collisionless magnetoplasma with degenerate electrons. The features of the nonlinear IASWs are investigated through the derivation of an energy balance-like equation involving the Sagdeev-type potential as well as the nonlinear dispersion relation.     

Rarefactive ion-acoustic electrostatic solitary structures in nonthermal plasmas

An investigation has been made of ion-acoustic solitary waves in an unmagnetized nonthermal plasma whose constituents are an inertial ion fluid and nonthermally distributed electrons. The properties of stationary solitary structures are briefly studied by the pseudo-potential approach, which is valid for arbitrary amplitude waves, and by the reductive perturbation method which is valid for small but finite amplitude limit. The time evolution of both compressive and rarefactive solitary waves, which are found to coexist in this nonthermal plasma model, is also examined by solving numerically the full set of fluid equations. The temporal behaviour of positive (compressive) solitary waves is found to be typical, i.e., the positive initial disturbance breaks up into a series of solitary waves with the largest in front. However, the behaviour of negative (rarefactive) solitary waves is quite different. These waves appear to be unstable and produce positive solitary waves at a later time. The relevancy of this investigation to observations in the magnetosphere of density depressions is briefly pointed out. Received 12 October 1999     

Ion-acoustic dressed solitons in electron-positron-ion plasmas

Expanding the Sagdeev potential to include fourth-order nonlinearities of electric potential and integrating the resulting energy equation, an exact soliton solution is determined for ion-acoustic waves in an electron-positron-ion (e-p-i) plasma system. This exact solution reduces to the dressed soliton solution obtained for the system using renormalization procedure in the reductive perturbation method (RPM), when Mach number (M) is expanded in terms of soliton velocity (λ) and terms up to order of λ² are retained in the analysis. Variation of shape, velocity, width and product (P) of amplitude (A) and square of width (W²) for the KdV soliton, core structure, dressed soliton, and exact soliton are graphically represented for different values of fractional positron concentration (p). It is found that for a given value of the fractional positron concentration (p) and amplitude of soliton, the velocity of the dressed soliton is faster and width is narrower than the KdV or exact soliton, and agrees qualitatively with the experimental observations of Ikezi et al. for small amplitude solitons in the plasma free from positron component. Among all these structures, the product P(AW²) is found to be lowest for the dressed soliton and it decreases as Mach number of soliton or fractional positron concentration in the plasma increases.     

Nonlinear generation of zonal flows by ion-acoustic waves in a uniform magnetoplasma

It is shown that large-scale zonal flows (ZFs) can be excited by Reynolds stress of nonlinearly interacting random phase ion-acoustic waves (EIAWs) in a uniform magnetoplasma. Since ZFs are associated with poloidal sheared flows, they can tear apart short scale EIAW turbulence eddies, and hence contribute to the reduction of the cross-field turbulent transport in a magnetized plasma.     

Ion acoustic shock waves in a relativistic electron-positron-ion plasmas

The Korteweg-de Vries-Burger (KdVB) equation is derived for ion acoustic shock waves in a weakly relativistic electron-positron-ion plasma. Electrons, positrons are considered isothermal and ions are relativistic. The travelling wave solution has been acquired by employing the tangent hyperbolic method. The vivid display of the graphical results is presented and analyzed. It is observed that amplitude and steepness of the shock wave decrease with increase of the relativistic streaming factor, the positron concentration and they increase with the increase of the coefficient of kinematic viscosity and vice versa. It is determined that at low temperature the shock wave propagates, whereas at very high temperature the solitary wave propagates in the system. The results may have relevance in astrophysical plasmas as well as in inertial confinement fusion plasmas.     

Excitation of the dust ion-acoustic and dust acoustic-like perturbations by plasma density ripples

It is shown that the dust ion-acoustic (DIA) and dust acoustic (DA)-like perturbations can be excited by the electron density and ion density ripples, respectively. For this purpose, we use the relevant equations for the DIA and DA-like disturbances and derive the standard Mathieu equation. The latter admits unstable solutions, demonstrating that both the DIA and DA-like mode can be driven on account of the free energy in the plasma density ripples.     

Formation of dust-acoustic shock waves in a strongly coupled cryogenic dusty plasma

The nonlinear propagation of ultra-low-frequency dust-acoustic (DA) waves in a strongly coupled cryogenic dusty plasma has been investigated, by using the Boltzmann distributed electrons and ions, as well as modified hydrodynamic equations for strongly coupled charged dust grains. The reductive perturbation technique is used to derive the Burger equation. It is shown that strong correlations among negatively charged dust particles acts like a dissipation, which is responsible for the formation of the DA shock waves. The latter are associated with the negative potential, i.e. with the compression of negatively charged cryogenic dust particle density. It is also found that the effective dust-temperature, which arises from electrostatic interactions among negatively charged dust particles, significantly affects the height of the DA shock structures. New laboratory experiments at cryogenic temperature should be conducted to verify our theoretical prediction.     

Dust-acoustic solitary waves in an adiabatic hot dusty plasma

An adiabatic hot dusty plasma (containing non-inertial adiabatic electron and ion fluids, and negatively charged inertial adiabatic dust fluid) is considered. The basic properties of arbitrary amplitude dust-acoustic (DA) solitary waves, which exist in such an adiabatic hot dusty plasma, are explicitly examined by the pseudo-potential approach. To compare the basic properties (critical Mach number, amplitude and width) of the DA solitary waves observed in a dusty plasma containing adiabatic electron, ion and dust fluids with those observed in a dusty plasma containing isothermal electron and ion fluids and adiabatic dust fluid, it has been found that the adiabatic effect of inertia-less electron and ion fluids has significantly modified the basic properties of the DA solitary waves, and that on the basic properties of the DA solitary waves, the adiabatic effect of electron and ion fluids is much more significant than that of the dust fluid.     

Quantum ion acoustic solitary waves in electron-ion plasmas: A Sagdeev potential approach

Linear and nonlinear ion acoustic waves are studied in unmagnetized electron-ion quantum plasmas. Sagdeev potential approach is employed to describe the nonlinear quantum ion acoustic waves. It is found that density dips structures are formed in the subsonic region in a electron-ion quantum plasma case. The amplitude of the nonlinear structures remains constant and the width is broadened with the increase in the quantization of the system. However, the nonlinear wave amplitude is reduced with the increase in the wave Mach number. The numerical results are also presented.     

Periodic, solitary and rational wave solutions of the 3D extended quantum Zakharov-Kuznetsov equation in dense quantum plasmas

The three-dimensional extended quantum Zakharov-Kuznetsov (ZK) equation was investigated in dense quantum plasmas which arises from the dimensionless hydrodynamics equations describing the nonlinear propagation of the quantum ion-acoustic waves. With the aid of symbolic computation, many types of new analytical solutions of the extended quantum ZK equation are constructed in terms of some powerful ansatze, which include new doubly periodic wave, solitary wave, shock wave, rational wave, and singular wave solutions. Moreover, we analyze the nonlinear wave propagation of the obtained solutions for some chosen parameters.