Arbitrary amplitude dust acoustic waves in a nonextensive dusty plasma

Making use of the Sagdeev pseudo-potential approach, we derive the energy like equation for dust-acoustic (DA) solitary waves in a complex plasma having negatively charged cold dust, and electrons/ions featuring the Tsallis distribution. The effects of electron and ion nonextensivity on the DA soliton profile are examined. It is shown that depending on the strength of particle nonextensivity, our plasma model may admit compressive as well as rarefactive DA solitary waves. Our results complement previously published results on this problem.     

Compressive and rarefactive dust-acoustic Gardner solitons beyond the K-dV limit with two-temperature ions dusty plasma

The Gardner equation is derived and numerically solved. This equation shows the existence of compressive and rarefactive dust-acoustic (DA) solitons with two-temperature ions beyond the K-dV (Korteweg–de Vries) limit. These may be referred to as DA Gardner solitons (DA-GSs). Here we deal with a dusty plasma, composed of negatively charged cold mobile dust fluids, inertialess Boltzmann electrons and ions with two distinctive temperatures. The basic features of the compressive and rarefactive DA solitons are identified. These solitons are found to exist beyond the K-dV limit, i.e. they exist for μ _i1～μ _c. Here μ _i1=n _i10/Z _d n _d0, Z _d is the number of electrons residing upon the dust grain surface, and n _i0 (n _d0) is the lower temperature ion (dust) number density at equilibrium. These DA-GSs are completely different from the K-dV solitons, because μ _c (the critical value) corresponds to vanishing of the nonlinear coefficient of the K-dV equation, and μ _i1～μ _c corresponds to K-dV solitons, with extremely large amplitude, for which the validity of the reductive perturbation method breaks down. It has been found that, depending on whether the parameter μ _i1 is less than or greater than the critical value, the DA-GSs exhibit compression for μ _i1>μ _c and rarefaction for μ _i1<μ _c. The basic features of double layers with arbitrary amplitude are also briefly discussed, employing the pseudo-potential approach. The present investigation might be relevant to the electrostatic solitary structures observed in various cosmic dust-laden plasmas, such as supernova shells, Saturn’s F-ring, the ionopause of Halley’s comet, etc.     

Formation of dust ion-acoustic solitary waves in a dusty plasma with two-temperature trapped electrons

We look for particular solutions to the restricted three-body problem where the bodies are allowed to either lose or gain mass to or from a static atmosphere. In the case that all the masses are proportional to the same function of time, we find analogous solution to the five stationary solutions of the usual restricted problem of constant masses: the three collinear and the two triangular solutions, but now the relative distance of the bodies changes with time at the same rate. Under some restrictions, there are also coplanar, infinitely remote and ring solutions.     

Large amplitude acoustic solitons in a warm electronegative dusty plasma with q-nonextensive distributed electrons

Linear and nonlinear analysis are presented for an electronegative dusty plasma system. Linear analysis shows that the dispersive nature of the plasma system changes considerably due to the presence of nonthermal q-nonextensive distributed electrons. The presence of both compressive and rarefactive Sagdeev solitons is investigated and shown that the addition of even a small population of dust particles will significantly modify the large amplitude Sagdeev solitons. The coexistence of both compressive and rarefactive solitons for a certain set of parameters is also noticed in such system. The effect of variation of entropic index q, θ _i (ratio of positive ion temperature to electron temperature), θ _n (ratio of negative ion temperature to electron temperature) and dust particles concentration (R) is elaborated with the help of suitable parameters.     

Small amplitude double-layers in an electron depleted dusty plasma with ions featuring the Tsallis distribution

The properties of dust acoustic double-layers (DA-DLs) in an unmagnetized electron depleted dusty plasma consisting of inertial dust fluid and ions featuring Tsallis statistics are investigated. It is found that our plasma model can admit compressive as well as rarefactive DA-DLs depending on the value of nonextensive parameter q. As the value of q increases, the negative DA-DL shrinks and, beyond a certain critical value, develops into a positive structure allowing therefore the existence of compressive DA-DLs.     

Gardner solitons in dusty plasmas with nonextensive ions and two-temperature superthermal electrons

Nonlinear propagation of dust-acoustic waves in an unmagnetized dusty plasma consisting of negatively charged mobile dust, nonextensive ions following nonextensive q-distribution and two distinct temperature superthermal electrons following superthermal kappa distribution each, is investigated by employing lower and higher order nonlinear equations, namely the Korteweg-de-Vries (K-dV), the modified Korteweg-de-Vries (mK-dV) and the Gardner equations. The characteristic features of the hump (positive potential) and dip (negative potential) shaped dust-acoustic (DA) Gardner solitons are found to exist beyond the K-dV limit. The effects of two superthermal temperature electrons and ions nonextensivity on the basic characteristics of DA K-dV, mK-dV and Gardner solitons have also been investigated. It has been found that the DA Gardner solitons exhibit either negative or positive potential solitons only for q<q _c where, q _c is the critical value of the nonextensive parameter q. The possible applications of our results in understanding the localized nonlinear electrostatic structures existing in solar atmosphere, Saturn’s magnetosphere etc. (where the tails of the high energetic particles at different temperatures follow power-law like distribution) are also briefly discussed.     

Dust acoustic shock waves in a suprathermal dusty plasma with dust charge fluctuation

The properties of small but finite amplitude dust acoustic (DA) shock waves are studied in a charge varying dusty plasma with ions and electrons having kappa velocity distribution. We obtain the global Debye length including the influence of suprathermality effects and dust charge fluctuations. It is shown that the effects of suprathermality of ions/electrons and dust charge fluctuation significantly modify the basic properties of DA shock wave. We observe that only negative DA shock waves will be excited in this model. The amplitude of DA shock wave increases with deviation of electrons or ions from Maxwellian distribution via decrease of spectral index, κ _j (j=i,e denotes, ions and electrons, respectively). Also, it is indicated that the amplitude and steepness of the shock front decreases with an increase in the ion temperature.     

Solitary waves in a dusty plasma with negatively (positively) charged dust grains and non-thermal electrons

For an unmagnetized multicomponent dusty plasma, the effects of non-thermal electron distribution, ion temperature and two oppositely charged dust grains are incorporated in the study of arbitrary amplitude solitary waves. An energy-like integral equation involving Sagdeev potential is derived, and the existence, formation and basic properties of solitons are studied. It is also found a definite interval for the Mach number for which solitary waves exist and depends sensitively upon the population of fast or non-thermal electrons present. Our results should be useful to understand the properties of localized electrostatic disturbances that may occur in space dusty plasma.     

Dust-acoustic solitary waves in a magnetized dusty plasmas with nonthermal ions and two-temperature nonextensive electrons

A rigorous theoretical investigation has been made on the obliquely propagating dust-acoustic (DA) waves in a magnetized dusty plasmas consisting of distinct temperature q-distributed electrons with distinct strength of nonextensivities, nonthermal ions and negatively charged mobile dust grains, and analyzed by deriving the Zakharov-Kuznetsov equation. It is found that the characteristics and the properties of the DA solitary waves (DASWs) are significantly modified by the external magnetic field, relative temperature ratio of ions, relative number densities of electrons as well as ions, the nonextensivity of electrons, nonthermality of ions and the obliqueness of the system. The possible implications of the results obtained from this analysis in space and laboratory dusty plasmas are briefly addressed.     

Arbitrary amplitude dust acoustic solitary waves in an electron-depleted dusty plasma with two high energy-tail ion distributions

Arbitrary amplitude dust acoustic waves (DAW’s) in two high energy-tail ion distributions are investigated. The electron number density has been assumed sufficiently depleted during the charging of the dust grains, on account of the attachment of the background plasma electrons on the surface of the dust grains. Our results reveal that under certain conditions, DA solitary waves with either negative or positive potential may be admitted. The high degree of suprathermalization of the relatively low temperature ion component favors the development of compressive localized structures. This behavior is preserved to a large extent in the small but finite amplitude regime. This means that the presence of additional relatively low temperature suprathermal ions does not only significantly modify the basic properties of DA structures, but also causes the existence of positive solitary potentials. This feature is completely new in a dusty plasma with two suprathermal ion components with widely disparate temperatures. Our results may be relevant to a number of space dusty plasma systems, particularly, the Saturn’s F-ring where electron depletion and suprathermality are thought to come into play.     

Effects of two-temperature electrons, external oblique magnetic field, and higher-order nonlinearity on dust acoustic solitary waves in a dusty plasma with vortex-like ion distribution

Nonlinear properties of the dust acoustic (DA) solitary waves in a dusty plasma consisting of negatively variable-charged dust particles, vortex-like distributed ions and two-temperature isothermal electrons are reported. A reductive perturbation theory has been used to derive a modified Korteweg-de Vries (mKdV) equation for the first-order perturbed potential and a linear inhomogeneous mKdV-type equation for the second-order perturbed potential. The renormalization method is used to obtain stationary solutions of these coupled equations. The modifications in the amplitude and width of the solitary wave structure due to the inclusion of two different types of isothermal electrons, external oblique magnetic field, higher-order nonlinearity, and vortex-like distributed ions are investigated. Also a method based on energy consideration was used to obtain the stability condition. Moreover, the numerical results are applied to investigate some nonlinear characteristics of the DA solitary waves.     

Arbitrary amplitude double layers in a four component dusty plasma with kappa distributed electron

Dust acoustic double layers are studied in a four component dusty plasma comprising positively and negatively charged dust grains, Boltzmann distributed ions and kappa distributed electrons. The conditions for existence of double layers are studied in detail using Sagdeev’s method. Large amplitude double layers are obtained for a range of values of the plasma parameters.     

Large amplitude double layers in a dusty plasma with nonthermal electrons featuring Tsallis distribution

The problems of large amplitude double layers are discussed using Sagdeev’s pseudo-potential technique for a dusty plasma comprising two temperature isothermal ions and nonextensive nonthermal velocity distributed electron. For different sets of plasma parameter values, the Sagdeev potential V(?) has been plotted. It is found that nonextensive q parameter plays a significant role in determining the shape and size of large amplitude double layers. Also, it is observed that the existence of large amplitude double layers depends on different plasma parameters.     

Weakly nonlinear dust ion- acoustic double- layers in a dusty plasma with nonextensive electrons

Weak dust ion-acoustic (DIA) double- layers (DLs) in a dusty plasma with nonextensive electrons are addressed. A generalized Korteweg-de Vries equation with a cubic nonlinearity is derived. It is shown that under certain conditions, the effect of electron nonextensivity can be quite important. In particular, it may be noted that due to the net negative dust charge and electron nonextensivity, the present dusty plasma model may admit compressive as well as rarefactive weak DIA-DLS. Considering the wide relevance of nonlinear oscillations in space dusty plasmas, our investigation may be taken as a prerequisite for the understanding of the nonlinear structures observed in the ionosphere and the auroral acceleration regions.     

Dust ion-acoustic solitary waves in a dusty plasma with arbitrarily charged dust and flat-trapped electrons

The properties of arbitrary amplitude dust ion-acoustic (DIA) solitary waves (SWs) in a dusty plasma containing warm adiabatic ions, electrons following flat-topped velocity distribution, and arbitrarily (positively or negatively) charged immobile dust is studied by the pseudo-potential approach. The effects of ion temperature, resonant electrons, and dust number density are found to significantly modify the basic features of the DIA-SWs as well modify the parametric regime for the existence of compressive DIA-SWs. The pseudo-potential for small but finite amplitude limit is also analytically analyzed.     

Propagation and interaction of dust acoustic multi-soliton in dusty plasmas with q-nonextensive electrons and ions

The nonlinear propagation and interaction of dust acoustic multi-soliton in a four component dusty plasma which consists of negatively and positively charged cold dust fluids, q-nonextensive velocity distributed electrons and ions, have been studied. Applying reductive perturbation technique (RPT), we have derived Korteweged-de Vries (KdV) equation for our model. By using Hirota bilinear method, we have obtained two-soliton and three-soliton solutions of the obtained KdV equation. Phase shifts of two-soliton and three-soliton have been presented. It has been observed that the parameters α ₁, α ₂, nonextensive parameter q, temperature ratio of ion to electron (σ), and μ play a crucial role in the formation of two-soliton and three-soliton. The implications of our results in understanding the localized nonlinear electrostatic perturbations observed in double-plasma machines, Cometary tails, Jupiter’s magnetosphere etc., where population of q-nonextensive velocity distributed electrons and ions can significantly dominate the wave dynamics, are also briefly discussed.     

Envelope solitons and their modulational instability in dusty plasmas with two-temperature superthermal electrons

The modified ion-acoustic envelope solitons and their modulational instability in a multi-component unmagnetized plasma (consisting of negatively charged immobile dusts, inertial ions and superthermal electrons of two distinct temperatures) are theoretically investigated. A multiple scale (in space and time) perturbation technique is used to derive the cubic nonlinear Schrödinger equation (which describes the evolution of a slowly varying wave envelope with space and time). It is observed that the plasma system under consideration supports two types (bright and dark) envelope solitons. It is also found that the dark (bright) envelope solitons are modulationally stable (unstable). The variation of the growth rate of the unstable bright envelope solitons with various plasma parameters (e.g. wave number, temperature of superthermal electrons, etc.) are found to be significant. The modulational instability criterions of the modified ion-acoustic envelope solitons are also seen to be influenced due to the variation of the intrinsic plasma parameters. The implications of the results of this theoretical investigations in some space plasma systems (viz. Saturn’s magnetosphere) are briefly mentioned.     

Dust acoustic shock waves in suprathermal dusty plasma in the presence of ion streaming with dust charge fluctuations

Dust acoustic (DA) shock waves are investigated in a dusty plasma having a high-energy-tail electron distribution. The effects of ion streaming, charge variation and electron deviation from the Maxwellian distribution on the DA shock wave are then considered. It is shown that as the suprathermal character of the plasma is increased, the potential amplitude enhances. It is also found that the ion temperature may be destructive for the formation of DA shock waves. Their strength decreases with increasing ion streaming speed. Our results may be useful in understanding the basic nonlinear features of the DA wave propagation that may occur in space dusty plasmas, especially those including a relative motion between species (comet tails, solar wind streams, etc.).     

K-dV solitons in a magnetized dusty plasma with two distinct temperature nonextensive electrons and Maxwellian ions

Nonlinear propagation of dust-acoustic (DA) waves in a magnetized dusty plasma, consisting of negatively charged mobile dust, Maxwellian ions and two distinct temperature nonextensive electrons (following nonextensive q-distribution each), has been studied and analyzed by deriving and solving the Korteweg-de-Vries (K-dV) equation. According to the outcomes of the investigation, the basic characteristics of the DA solitary profiles are found to be strongly modified by the external magnetic field, nonextensivity of the electrons and the respective number densities of the two species of electrons. The results of this investigation can be applied in both laboratory and astrophysical plasma scenarios for understanding the basic features of the localized electrostatic dust-acoustic solitary waves (DASWs).