Spherical Kadomtsev-Petviashvili Solitons in a Suprathermal Complex Plasma

The nonlinear aspects of nonplanar dust acoustic (DA) solitary waves are investigated in an unmagnetized complex plasma comprising of cold dust grains, kappa-distributed ions as well as electrons. The nonplanar DA solitons are studied based on the reductive perturbation technique. It is shown that the evolution of DA solitons is governed by a spherical Kadomtsev-Petviashvili (sKP) equation and then the impact of suprathermality on the spatial structure as well as the nature of DA soliton is studied. It seems that the properties of DA solitons in nonplanar geometry are quite different from that of the planar solitons.     

Spherical Kadomtsev-Petviashvili Solitons in a Suprathermal Complex Plasma

The nonlinear aspects of nonplanar dust acoustic (DA) solitary waves are investigated in an unmagnetized complex plasma comprising of cold dust grains,kappa-distributed ions as well as electrons.The nonplanar DA solitons are studied based on the reductive perturbation technique.It is shown that the evolution of DA solitons is governed by a spherical Kadomtsev-Petviashvili (sKP) equation and then the impact of suprathermality on the spatial structure as well as the nature of DA soliton is studied.It seems that the properties of DA solitons in nonplanar geometry are quite different from that of the planar solitons.     

K-P-Burgers equation in negative ion-rich relativistic dusty plasma including the effect of kinematic viscosity

The stationary solution is obtained for the K–P–Burgers equation that describes the nonlinear propagations of dust ion acoustic waves in a multi-component, collisionless, un-magnetized relativistic dusty plasma consisting of electrons, positive and negative ions in the presence of charged massive dust grains. Here, the Kadomtsev–Petviashvili(K–P) equation, threedimensional(3D) Burgers equation, and K–P–Burgers equations are derived by using the reductive perturbation method including the effects of viscosity of plasma fluid, thermal energy, ion density, and ion temperature on the structure of a dust ion acoustic shock wave(DIASW). The K–P equation predictes the existences of stationary small amplitude solitary wave,whereas the K–P–Burgers equation in the weakly relativistic regime describes the evolution of shock-like structures in such a multi-ion dusty plasma.     

Parametric Study of Nonplanar Dust Acoustic Solitons in Two‐Dimensional Superthermal Dusty Plasmas

The nonlinear properties of two dimensional low‐frequency electrostatic excitations of charged dust particles (or defects) are studied in a collisionless, unmagnetized dusty plasma. A fully ionized three‐component model plasma consisting of kappa distributed electrons, Maxwellian ions, and negatively charged massive dust grains is considered. In this regard, the well known reductive perturbation technique is used to the hydrodynamical equations and the Poisson equation, obtaining the cylindrical Kadomtsev–Petviashvili (CKP) equation. A parametric investigation indicates that the structural characteristics of these nonlinear excitations (width, amplitude) are significantly affected by the plasma nonthermality as well as by the relevant plasma parameters, such as dust concentration and dust temperature. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dust‐ion‐acoustic solitary waves in a magnetized dusty pair‐ion plasma with Cairns‐Gurevich electrons and opposite polarity dust particles

The nonlinear dust‐ion‐acoustic (DIA) solitary structures have been studied in a dusty plasma, including the Cairns‐Gurevich distribution for electrons, both negative and positive ions, and immobile opposite polarity dust grains. The external magnetic field directed along the z‐axis is considered. By using the standard reductive perturbation technique and the hydrodynamics model for the ion fluid, the modified Zakharov–Kuznetsov equation was derived for small but finite amplitude waves and was provided the solitary wave solution for the parameters relevant. Using the appropriate independent variable, we could find the modified Korteweg–de Vries equation. By plotting some figures, we have discussed and emphasized how the different plasma values, such as the trapping parameter, the positive (or negative) dust number density, the non‐thermal electron parameter, and the ion cyclotron frequency, can influence the solitary wave structures. In addition, using the bifurcation theory of planar dynamical systems, we have extracted the centre and saddle points and illustrated the phase portrait of such a system for some particular plasma parameters. Finally, we have graphically investigated the behaviour of the solitary energy wave by changing the plasma values as well as by calculating the instability criterion; we have also discussed the growth rate of the solitary waves. The results could be useful for studying the physical mechanism of nonlinear propagation of DIA solitary waves in laboratory and space plasmas where non‐thermal electrons, pair‐ions, and dust particles can exist.     

Nonplanar double layers in plasmas with opposite polarity dust

Nonplanar (cylindrical and spherical) double layers (DLs) in a four-component dusty plasma (composed of inertial positively and negatively charged dust, Boltzmann electrons and ions) are studied by employing the reductive perturbation method. The modified Gardner equation describing the nonlinear propagation of the dust-acoustic (DA) waves is derived, and its nonplanar double layer solutions are numerically analyzed. The parametric regimes for the existence of the DLs, which are found to be associated with positive potential only, are obtained. The basic features of nonplanar DA DLs, which are found to be different from planar ones, are also identified. The implications of our results to different space and laboratory dusty plasma situations, where opposite polarity dust are observed, are discussed.     

Nonlinear propagation of ultra-low-frequency electromagnetic modes in a magnetized dusty plasma

A theoretical investigation has been made of nonlinear propagation of ultra-low-frequency electromagnetic waves in a magnetized two fluid (negatively charged dust and positively charged ion fluids) dusty plasma. These are modified Alfvén waves for small value of and are modified magnetosonic waves for large , where is the angle between the directions of the external magnetic field and the wave propagation. A nonlinear evolution equation for the wave magnetic field, which is known as Korteweg de Vries (K-dV) equation and which admits a stationary solitary wave solution, is derived by the reductive perturbation method. The effects of external magnetic field and dust characteristics on the amplitude and the width of these solitary structures are examined. The implications of these results to some space and astrophysical plasma systems, especially to planetary ring-systems, are briefly mentioned. Received 8 July 1999 and Received in final form 11 October 1999     

Nonlinear pulse propagation and phase velocity of laser-driven plasma waves

Laser evolution and plasma wave excitation by a relativistically intense short-pulse laser in underdense plasma are investigated in the broad pulse limit, including the effects of pulse steepening, frequency redshifting, and energy depletion. The nonlinear plasma wave phase velocity is shown to be significantly lower than the laser group velocity and further decreases as the pulse propagates owing to laser evolution. This lowers the thresholds for trapping and wave breaking and reduces the energy gain and efficiency of laser-plasma accelerators that use a uniform plasma profile.     

Possibility of weakly charged nonlinear solitary dust clouds near the continuum threshold of dust population in a quasi-neutral dusty plasma

Considering the Boltzmann response of the plasma ions and electrons and inertial dynamics of the charged dust grains, the possibility of very weak compressive soliton near the continuum limit of the dust population has been inferred. It is concluded that the behaviour of such coherent structures could be well described by the numerical analysis of the derived nonlinear classical energy integral equation for bounded solutions. These seem to be higher order dispersive structures within acoustic limit of the nonlinear turbulence. It is observed that the dust density enhancement beyond the continuum threshold causes regular increment in width and amplitude of the soliton structures. It is found that the soliton amplitude sensitively depends on the massive impurity’s population. These coherent structures could be visualized as weakly charged solitary dust clouds of finite extension (∼ plasma Debye length) within Boltzmann environment of plasma particles in their local surroundings. The seeding mechanism of such clouds may be attributed to some plasma instabilities driven by either internal or external free energy sources. Numerical analysis of the problem concludes that the experimental observations of such clouds could be possible in low density plasma regime. It is deduced that for plasma density ∼ 10⁶ cm^-3 at temperatures of a few electron volts and for micron to l0nm sized dust grains, the observation of such structures could be possible within wide range variability of the dust population density.     

Effect of ion drag on a pulsational mode of gravitational collapse

The effect of ion drag on the pulsational mode of gravitational collapse(PMGC) is investigated within the partially charged dusty plasma model by fluid dynamics. It is found that the ion drag force significantly enhances the instability of the PMGC. In addition, it is shown that the instability of the PMGC is influenced by the ratio of the abundances of charged to neutral grains.These results can be relevant for the planetesimal formation in dark interstellar clouds.     

Kadomtsev–Petviashvili equation for dust ion-acoustic solitons in pair-ion plasmas

Using the reductive perturbation method, we have derived the Kadomtsev-Petviashvili (KP) equation to study the nonlinear properties of electrostatic collisionless dust ion-acoustic solitons in the pair-ion (p-i) plasmas. We have chosen the fluid model for the positive ions, the negative ions, and a fraction of static charged (both positively and negatively) dust particles. Numerical solutions of these dust ion-acoustic solitons are plotted and their characteristics are discussed. It is found that only the amplitudes of the electrostatic dust ion-acoustic solitons vary when the dust is introduced in the pair-ion plasma. It is also noticed that the amplitude and the width of these solitons both vary when the thermal energy of the positive or negative ions is varied. It is shown that potential hump structures are formed when the temperature of the negative ions is higher than that of the positive ions, and potential dip structures are observed when the temperature of the positive ions supersedes that of the negative ions. As the pair-ion plasma mimics the electron-positron plasma, thus our results might be helpful in understanding the nonlinear dust ion acoustic solitary waves in super dense astronomical bodies.     

Dust Self‐Organized Structures I. Role of Ion Drag and Ion Diffusion on Screened Grains

Self‐organized dust structures are investigated using a Gurevich‐Parker model for non‐linear dust screening. The non‐linear dust drag coefficients and non‐linear diffusion coefficients are calculated numerically as functions of nonlinear parameter for screening, dust density and ion flux drift velocity. Nonlinear ion dust drag inside the structures creates an electric field with potential well for ions at the structure center. The equilibrium dust structures confine both the dust grains and the plasma particles, have a finite size and have inside an enhanced dust and ion densities. The necessary conditions for existence of equilibrium dust structures are found. The equilibrium dust structures are determined by two global parameters related to the external plasma flux and to the power of ionization. The equilibrium exist only in a restricted phase space of these two parameters and depends on the the drag coefficient at the structure center. The equilibrium requirements are found using non‐linear drag coefficient calculated numerically. It is shown that this phase space area can be broad but it is systematically decreasing with an increase of the ionization rate. It is found that equilibrium exists for dust structures with large dust and ion density concentration at the center and that for these structures the ion diffusion is strongly suppressed by ion scattering on non‐linearly screened grains. The results of the theory can be used to interpret the recently observed compact dust structures in micro‐gravity experiments and can provide some recommendations for future micro‐gravity experiments in spherical chambers (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical Solution of the Two-Dimensional Vlasov Equation

The two-dimensional Vlasov equation is solved by direct integration in phase space. Two problems, namely the nonlinear evolution of the two-dimensional electrostatic two-stream instability, and the nonlinear evolution of a monochromatic wave in a two-dimensional Vlasov plasma, are studied. Comparison with previously available results is given.     

The Kadomtsev-Petviashvili equation for dust ion-acoustic solitons in pair-ion plasmas

Using the reductive perturbation method,we have derived the Kadomtsev-Petviashvili(KP) equation to study the nonlinear properties of electrostatic collisionless dust ion-acoustic solitons in pair-ion(p-i) plasmas.We have chosen the fluid model for the positive ions,the negative ions,and a fraction of static charged(both positively and negatively) dust particles.Numerical solutions of these dust ion-acoustic solitons are plotted and their characteristics are discussed.It is found that only the amplitudes of the electrostatic dust ion-acoustic solitons vary when the dust is introduced in the pair-ion plasma.It is also noticed that the amplitude and the width of these solitons both vary when the thermal energy of the positive or negative ions is varied.It is shown that potential hump structures are formed when the temperature of the negative ions is higher than that of the positive ions,and potential dip structures are observed when the temperature of the positive ions supersedes that of the negative ions.As the pair-ion plasma mimics the electron-positron plasma,thus our results might be helpful in understanding the nonlinear dust ion acoustic solitary waves in super dense astronomical bodies.     

Nonlinear Structures in an Ion-Beam Plasmas Including Dust Impurities with Nonthermal Nonextensive Electrons

The properties of dust ion acoustic waves are investigated in an unmagnetized multicomponent plasma system consisting of ion beam, charged positive and negative ions, electrons obeying nonthermal-Tsallis distribution and stationary negatively charged dust grains by the conventional Sagdeev pseudopotential method, through which the condition for existence of several nonlinear structures is analyzed theoretically. The dispersion relation for electrostatic waves is derived and analyzed and an expression of the energy integral equation is obtained. It is reported here that our plasma model supports solitions, double layers and supersoliton solutions for certain range of parameters. Finally, the effects of different physical plasma parameters on these nonlinear structures are studied numerically. The present theory should be helpful in understanding the salient features of the electrostatic waves in space and in laboratory plasmas where two distinct groups of ions and non-Maxwellian distributed electrons are present.     

Effect of Polynomial Expressed Distribution Dust Particles for Unmagnetized Two-Ion-Temperature Dusty Plasma

Linear dispersion relation for linear wave and a Kadomtsev-Petviashvili (KP) equation for nonlinear wave are given for the unmagnetized two-ion-temperature cold dusty plasma with many different dust grain species. The numerical results of variationsof linear dispersion with respect to the different dust size distribution are given. Moreover, how the amplitude, width, and propagation velocity of solitary wave vary vs different dust size distribution is also studied numerically in this paper.     

Nonlinear Dust Acoustic Waves in Dissipative Space Dusty Plasmas with Superthermal Electrons and Nonextensive Ions

The nonlinear characteristics of the dust acoustic(DA)waves are studied in a homogeneous,collisionless,unmagnetized,and dissipative dusty plasma composed of negatively charged dusty grains,superthermal electrons,and nonextensive ions.Sagdeev pseudopotential technique has been employed to study the large amplitude DA waves.It(Sagdeev pseudopotential)has an evidence for the existence of compressive and rarefractive solitons.The global features of the phase portrait are investigated to understand the possible types of solutions of the Sagdeev form.On the other hand,the reductive perturbation technique has been used to study small amplitude DA waves and yields the Korteweg-de Vries-Burgers(Kd V-Burgers)equation that exhibits both soliton and shock waves.The behavior of the obtained results of both large and small amplitude is investigated graphically in terms of the plasma parameters like dust kinematic viscosity,superthermal and nonextensive parameters.     

New physical concept of the formation of dust crystals

A clear physical model is proposed for phase transitions in a dusty plasma. According to this model, the formation of plasma dust crystals is associated with the nonlinear effect of the collective attraction of dust particles. The nonlinear collective attraction between negatively charged dust particles corresponds to large charges of dust particles used in the available experiments. This concept provides a new physical model of crystallization that is attributable to the capture of dust particles in an attractive potential well rather than to the strong interaction between them. Calculation using this model yields the depth of the attractive potential well and the critical coupling constant in good agreement with the available experimental data.     

Quantum phase distribution and the number—phase Wigner function of the generalized squeezed vacuum states associated with solvable quantum systems

The quantum phase properties of the generalized squeezed vacuum states associated with solvable quantum systems are studied by using the Pegg-Barnett formalism.Then,two nonclassical features,i.e.,squeezing in the number and phase operators,as well as the number-phase Wigner function of the generalized squeezed states are investigated.Due to some actual physical situations,the present approach is applied to two classes of generalized squeezed states:solvable quantum systems with discrete spectra and nonlinear squeezed states with particular nonlinear functions.Finally,the time evolution of the nonclassical properties of the considered systems has been numerically investigated.