Ion acoustic solitary and shock waves with nonextensive electrons and thermal positrons in nonplanar geometry

The nonlinear wave structures of ion acoustic waves (IAWs) in an unmagnetized plasma consisting of nonextensive electrons and thermal positrons are studied in bounded nonplanar geometry. Using reductive perturbation technique we have derived cylindrical and spherical Korteweg-de Vries-Burgers’ (KdVB) equations for IAWs. The presence of nonextensive q-distributed electrons is shown to influence the solitary and shock waves. Furthermore, in the existence of ion kinematic viscosity, the shock wave structure appears. Also, the effects of nonextensivity of electrons, ion kinematic viscosities, positron concentration on the properties of ion acoustic shock waves (IASWs) are discussed in nonplanar geometry. It is found that both compressive and rarefactive type solitons or shock waves are obtained depending on the plasma parameter.     

Ion acoustic solitary waves in bi-ion plasma with superthermal electrons

Weak ion-acoustic solitary waves (IASWs) in unmagnetized plasmas having two-fluid ions and kappa-distributed electrons are considered. The effects of electron suprathermality, warm ion temperature and polarity on the nonlinear properties of these IASWs are analyzed. It is found that our present plasma model may support compressive as well as rarefactive solitary structures.     

Effect of electron nonextensivity on oblique propagation of arbitrary ion acoustic waves in a magnetized plasma

The combined effects of the obliqueness and nonextensive electrons are incorporated in the study of ion acoustic (IA) waves in a magnetized plasma. The propagation properties of two possible modes (in the linear regime) are investigated. It is found that the electron nonextensivity decreases the phase velocities of both two modes. Also obliqueness leads to increase of separation between two modes. The nonlinear evolution of IA solitary waves is governed by an energy-like equation. The influence of electron nonextensivity, obliqueness and electron population on the existence domain of solitary waves and the soliton characteristics are examined. It is shown that the existence domain of the IA soliton and its profile is significantly depended on the deviation of electrons from thermodynamic equilibrium and obliqueness. Interestingly, the present model supports compressive as well as rarefactive IA solitary waves. Our finding should elucidate the nonlinear electrostatic structures that propagate in astrophysical and cosmological plasma scenarios where nonextensive and magnetized plasma can exist; like instellar plasma stellar polytropes, solar neutrino problem, peculiar velocities of galaxy clusters, dark-matter halos, protoneutron stars, hadronic matter, quark-gluon plasma, and magnetosphere, etc.     

Nonplanar ion-acoustic Gardner solitons in a pair-ion plasma with nonextensive electrons and positrons

The properties of nonplanar (cylindrical and spherical) ion-acoustic solitary waves (IA SWs) in an unmagnetized, collisionless electron-positron-ion (e-p-i) plasma, whose constituents are q-distributed electrons and positrons and inertial ions, are investigated by deriving the modified Gardner (MG) equation. The well known reductive perturbation method is employed to derive the MG equation. The basic features of nonplanar IA Gardner solitons (GSs) are discussed. It is found that the properties of nonplanar IA GSs (rarefactive and compressive) are significantly affected by the particle nonextensivity.     

Higher-order corrections to ion acoustic waves in degenerate electron-positron-ion plasmas

The nonlinear propagation of ion acoustic waves in ideal plasmas consisting of degenerate electrons and positrons, and isothermal ions is investigated. The Korteweg de Vries (K-dV) equation that contains the lowest order nonlinearity and dispersion is derived from the lowest order of perturbation and a linear inhomogeneous (K-dV type) equation that accounts for the higher order nonlinearity and the dispersion relation is obtained. The stationary wave solution for these equations has been found using the renormalization method. Also, the effects of electrons and positrons densities and ion temperature on the amplitude and width of solitary waves are investigated, numerically. It is seen that higher order corrections significantly change the properties of the K-dV solitons. Also, it is found that both compressive and rarefactive solitary waves can be propagated in such plasma system.     

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.     

Fully nonlinear ion-acoustic solitary waves in a warm magnetized plasma with electron inertia

Ion-acoustic solitary waves in a warm, magnetized plasma with electron inertia have been investigated through Sagdeev pseudopotential method. It has been established the existence of both compressive supersonic solitons, and rarefactive subsonic and supersonic solitons within the parametric domains. The effect of the external magnetic field for generation of the supersonic compressive solitons of constant amplitudes appears to be passive after some critical direction of propagation of the wave. However, up to the critical direction of propagation, the magnetic resistance is found to be quite active to drastically reduce the soliton amplitudes. The generation of rarefactive solitons in this warm magnetized plasma is rather more feasible to be supersonic without electron inertia.     

Detection of ionospheric perturbation due to a soft gamma ray repeater SGR J1550-5418 by very low frequency radio waves

The properties of cylindrical and spherical dust acoustic (DA) solitary and shock waves in an unmagnetized electron depleted dusty plasma consisting of inertial dust fluid and ions featuring Tsallis statistics are investigated by employing the reductive perturbation technique. A Korteweg-de Vries Burgers (KdVB) equation is derived and its numerical solution is obtained. The effects of ion nonextensivity and dust kinematic viscosity on the basic features of DA solitary and shock waves are discussed in nonplanar geometry. It is found that nonextensive nonplanar DA waves behave quite differently from their one-dimensional planar counterpart.     

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 double layers in non-uniform plasma with $$-nonextensive distributed electrons

Electrostatic solitary waves and double layers (DLs) formed by the coupled ion acoustic (IA) and drift waves have been investigated in non-uniform plasma using \(q\)-nonextensive distribution function for the electrons and assuming ions to be cold \(T_{i}< T_{e}\). It is found that both compressive and rarefactive nonlinear structures (solitary waves and DLs) are possible in such a system. The steeper gradients are supportive for compressive solitary (and double layers) and destructive for rarefactive ones. The \(q\)-nonextensivity parameter \(q\) and the magnitudes of gradient scale lengths of density and temperature have significant effects on the amplitude of the double layers (and double layers) as well as on the speed of these structures. This theoretical model is general which has been applied here to the \(F\)-region ionosphere for illustration.     

Characteristic of ion acoustic shock waves in a dissipative quantum pair plasma with dust particulates

The behavior of quantum dust ion-acoustic (QDIA) shocks in a plasma including inertialess quantum electrons and positrons, classical cold ions and stationary negative dust grains are studied, using a quantum hydrodynamic model (QHD). The effect of dissipation due to the viscosity of ions is taken into account. The propagation of small but finite amplitude QDIA shocks is governed by the Kortoweg-de Vries-Burgers (KdVB) equation. The existence regions of oscillatory and monotonic shocks will depend on the quantum diffraction parameter (H) and dust density (d) as well as dissipation parameter (η ₀). The effect of plasma parameters (d,H,η ₀), on these structures is investigated. Results indicate that the thickness and height of monotonic shocks; oscillation amplitude of the oscillatory shock wave and it’s wavelength effectively are affected by these parameters. Additionally, the possibility of propagation of both compressive and rarefactive shocks is investigated. It is found that depending on some critical value of dust density (d _c ), which is a function of H, compressive and rarefactive shock waves can’t propagate in model plasma. The present theory is applicable to analyze the formation of nonlinear structures at quantum scales in dense astrophysical objects.     

Critical density solitary waves structures in a hot dusty plasma with vortex-like ion distribution in phase space

The nonlinear properties of solitary waves structure in a hot dusty plasma consisting of isothermal hot electrons, non isothermal ions and high negatively charged massive dust grains, are reported. A modified Korteweg-de Vries equation (modified KdV), which admits a solitary waves solution for small but finite amplitude, is derived using a reductive perturbation theory. A nonisothermal ions distribution provides the possibility of coexistence of amplitude rarefactive as well as compressive solitary waves. On the other hand, consideration of a critical ions density gives a stationary solution of solitary waves and the dynamics of small but finite amplitude of solitary waves is governed by Korteweg-de Vries equation (KdV). The properties of solitary waves in the two cases are discussed.     

Effects of the non-extensive parameter on the propagation of ion acoustic waves in five-component cometary plasma system

Some important evolution nonlinear partial differential equations are derived using the reductive perturbation method for unmagnetized collisionless system of five component plasma. This plasma system is a multi-ion contains negatively and positively charged Oxygen ions (heavy ions), positive Hydrogen ions (lighter ions), hot electrons from solar origin and colder electrons from cometary origin. The positive Hydrogen ion and the two types of electrons obey \(q\)-non-extensive distributions. The derived equations have three types of ion acoustic waves, which are soliton waves, shock waves and kink waves. The effects of the non-extensive parameters for the hot electrons, the colder electrons and the Hydrogen ions on the propagation of the envelope waves are studied. The compressive and rarefactive shapes of the three envelope waves appear in this system for the first order of the power of the nonlinearity strength with different values of non-extensive parameters. For the second order, the strength of nonlinearity will increase and the compressive type of the envelope wave only appears.     

Nonplanar dust ion-acoustic solitary and shock excitations in electronegative plasmas with trapped electrons

It is shown that the three-dimensional cylindrical Kadomtsev-Petviashvili (CKP) and the extended cylindrical Kadomtsev-Petviashvili (ECKP) equations can describe the propagation of nonplanar dust ion-acoustic excitations in a dusty plasma composed of positive ions, negative ions, stationary dust particles, as well as trapped electrons or a small percentage of trapped electrons. It is found that the solution of the CKP equation supports only solitary pulses, while the ECKP equation describes the propagation of both solitary and shock excitations. The effects of physical parameters, namely negative ions density, dust grains density, positive-to-negative mass ratio, direction cosine of the wave propagation on the pulses profile are examined. Furthermore, the existence regions of either localized or shock pulses are investigated. The relevance of nonlinear structures in the Earth’s ionosphere and plasma experiment is discussed.     

Planar and nonplanar ion acoustic shock waves with nonthermal electrons and positrons

The nonlinear propagation of ion acoustic shock waves (IASWs) are studied in an unmagnetized plasma consisting of nonthermal electrons, nonthermal positrons, and singly charged adiabatically hot positive ions, whose dynamics is governed by the two dimensional nonplanar Kadomstev-Petviashvili-Burgers (KPB) equation. The shock solution of the KPB equations is obtained numerically. The effects of several parameters and ion kinematic viscosities on the properties of ion acoustic shock waves are discussed in planar and nonplanar geometry. It is shown that the ion acoustic shock wave propagating in cylindrical/spherical geometry with transverse perturbation will be deformed as time goes on. Also, it is seen that the strength and the steepness of the IASWs increases with increasing β, the nonthermal parameter.     

Non-linear localized ion-acoustic waves in electron–positron–ion plasmas with trapped and non-thermal electrons

For an unmagnetized collisionless electron–positron–ion plasma, the effects of trapped and non-thermal electron distributions are incorporated in the study of arbitrary amplitude ion-acoustic solitary structures. Both highly and weakly analyses are examined by deriving an energy integral equation involving the Sagdeev potential for the large amplitude limit, and obtaining the non-linear partial-differential equations for the small but finite amplitude limit. It is shown that there exist ion-acoustic solitary waves with qualitatively different structures in a way that depend on the population of trapped and non-thermal electrons. In the presence of trapped electrons, fully non-linear analyses show that plasma can support only arbitrary amplitude compressive solitary waves. On the other hand, a consideration of the fast or non-thermal electron distribution provides the possibility of the coexistence of large amplitude compressive and rarefactive solitary waves, whereas both of them are decoupled in the small amplitude limit. It is found that the effects of such electron distributions and positron concentration change the maximum values of the Mach number and the amplitude for which solitary waves can exist. Furthermore, the non-thermally distributed electrons provide a KdV equation in the small amplitude limit, whereas the trapped electrons give rise to a modified KdV equation which exhibits a stronger non-linearity.     

Arbitrary Amplitude Ion Acoustic Solitary Waves in An Unmagnetized Two Electron Population Ultra-Relativistic Dense Plasmas

The nonlinear wave structure of arbitrary amplitude ion acoustic solitary waves (IASWs) are studied in the Sagdeev’s pseudopotential framework for an ultra-relativistic degenerate dense plasma comprising cold and hot electrons and inertial ultra-cold ions. By employing standard normal-mode analysis the dispersion relation for linear waves is studied. The numerical results are presented to understand the features of ion acoustic solitary wave structures. It is shown that the present plasma model supports IASWs having positive potential well. Also, it is found that the small amplitude rarefactive double layer solution can exist in such a plasma system in some parametric region. It is shown that solitary structures and double layers are affected by relevant plasma parameters.     

Nonplanar solitons in a warm electronegative plasma with electron nonextensivity effects

The nonlinear propagation of ion-acoustic waves is studied in an unmagnetized collissionless electronegative plasma, whose constituents are the inertial warm positive/negative ions and q-distributed nonextensive electrons. The latter have strong impact on the linear dispersion relation. However, for nonlinear analysis, a reductive perturbation technique is employed to derive a Korteweg-de Vries (KdV) equation accounting for nonthermal electrons in nonplanar geometries. Numerically, the effects of various plasma parameters, such as, the nonextensive parameter (q), the negative-to-positive ion mass ratio (α), the electron-to-positive ion number density ratio (μ), the positive ion-to-electron temperature ratio (θ _i ) and negative ion-to-electron temperature ratio (θ _n ), have been examined on the nonplanar compressive/rarefactive fast ion-acoustic solitons (where the wave phase speed is taken as λ>1). The relevance of our findings involving plasma wave excitations should be useful both for space and laboratory plasmas, where two distinct groups of ions besides the electrons, are present.     

Planar and nonplanar quantum dust ion-acoustic Gardner double layers in multi-ion dusty plasma

The longitudinal fast solitary waves induced by weakly relativistic positron showers of astrophysical origin are studied in a plasma system contaminated with some massive impurities in presence of superthermal effects. The superthermal effects are due to the high energy electrons. The impurities are dust corpuscles with positive and negative charges. It is noticed that increase in the kappa parameter of electrons and relativistic streaming factor of weakly relativistic positron shower, negative dust concentration invoke an enhancement in the strength of solitary wave. On the other hand increase in the shower’s temperature as well as positive dust concentration diminish the solitary hump strength. It is worth to mention that only hump type compressive fast solitary waves are predicted by our model, for the given set of plasma parameters, because the convective coefficient of the nonlinear governing equation for solitary wave remains positive in considered regime of interaction for plasma and positron shower. Our calculations in linear regime predict both the fast and slow positron shower induced longitudinal, electrostatic perturbations. Our results may be of importance in understanding the nonlinear propagation of waves in doped astrophysical superthermal plasmas with relativistic positron showers.     

Nonlinear propagation of dust ion-acoustic waves in dusty multi-ion dense plasma

We have studied the nonlinear propagation of dust ion-acoustic (DIA) waves in a dusty multi-ion dense plasma (with the constituents being degenerate, either non-relativistic or ultra-relativistic) and the propagation of such waves have been investigated by the reductive perturbation method. From the stationary solution of the Korteweg de-Vries (K-dV) equation and Burgers’ equation the nonlinear waves (specially, solitary and shock waves) have been found to be formed in the dusty plasma system under consideration. It has shown that the basic features of these waves are significantly modified by both the positive and negative ions and dust number densities, the degenerate of the constituents. The implications of our results have been briefly discussed.