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.     

Head-on collision of ion-acoustic solitary waves in magnetized plasmas with nonextensive electrons and positrons

This article presents the first study of the head-on collision of two ion-acoustic solitary waves (IASWs) in magnetized plasmas with nonextensive electrons and positrons using the extended Poincaré-Lighthill-Kuo (PLK) method. The effects of the ion gyro-frequency to ion plasma frequency ratio, the positron to ion number density ratio, the electrons temperature to positrons temperature ratio, and the nonextensive parameter q on the phase shifts are investigated. It is shown that these factors significantly modify the phase shifts.     

Head-on collision of electron acoustic solitary waves in a plasma with nonextensive hot electrons

The head-on collision between two electron-acoustic solitary waves (EASWs) in an unmagnetized plasma is investigated, including a cold electrons fluid, hot electrons, obeying a nonextensive distribution and stationary ions. By using the extended Poincaré-Lighthill–Kuo (PLK) perturbation method, the analytical phase shifts following the head-on collision are derived. The effects of the ratio of the number density of hot electrons to the number density of cold electrons α, and the nonextensive parameter q on the phase shifts are studied. It is found that q and the hot-to-cold electron density ratio significantly modify the phase shifts.     

Investigation on spectral character of ELF electromagnetic radiations during Leonid 2009 meteor shower

The problem of solitary electron acoustic (EA) wave propagation in a plasma with nonthermal hot electrons featuring the Tsallis distribution is addressed. A physically meaningful nonextensive nonthermal velocity distribution is outlined. It is shown that the effect of the nonthermal electron nonextensivity on EA waves can be quite important. Interestingly, we found that the phase speed of the linear EA mode increases as the entropic index q decreases. This enhancement is weak for q>1, and significant for q<1. For a given nonthermal state, the minimum value of the allowable Mach numbers is lowered as the nonextensive nature of the electrons becomes important. This critical limit is shifted towards higher values as the nonthermal character of the plasma is increased. Moreover, our plasma model supports rarefactive EA solitary waves the main quantities of which depend sensitively on q. This dependency (for q>1) becomes less noticeable as the nonthermal parameter decreases. Nevertheless, decreasing α yields for q<0 a different result, a trend which may be attributed to the functional form of the nonthermal nonextensive distribution. Our study (which is not aimed at putting the ad hoc Cairns distribution onto a more rigorous foundation) suggests that a background electron nonextensivity may influence the EA solitons.     

Effect of <Emphasis Type="Italic">q</Emphasis>-nonextensive distribution of electrons on ion acoustic shock waves in dissipative plasma

Ion acoustic shock waves (IASWs) are studied in a plasma consisting of nonextensive electrons and ions. The dissipation is taken into account the kinematic viscosity among the plasma constituents. The Korteweg-de Vries-Burgers (KdV-Burgers) equation is derived by reductive perturbation method. Shock waves are solutions of KdV-Burgers equation. It is shown that acceptable values of q-parameter (where q stands for the electron nonextensive parameter) are more than 3 in a weakly nonlinear analysis. We have found that the amplitude of shock waves decreases by an increasing q-parameter.     

Effect of q-nonextensive distribution of electrons on dust-ion acoustic solitons

Properties of dust-ion acoustic solitary waves (DIASWs) in dusty plasmas composed of nonextensive electrons, cold fluid ions and stationary dust particles are investigated. The possibility of soliton formation and the effect of nonextensivity of the electron distribution on the soliton characters are studied using the pseudo-potential method. Regions of parameters in which a solitary wave can be propagated in the plasma is analyzed too. It is found that the solitary excitations strongly depend on the electron-ion density ratio (μ), Mach numbers (M) as well as the nonextensive parameter (q). It is shown that the domain of allowed Mach numbers depends drastically on the plasma parameters and especially on the electron nonextensivity. It is found that beyond a threshold value of the nonextensive parameter (q), dust-ion acoustic solitons are admitted.     

Dust ion acoustic instability with q-distribution in nonextensive statistics

The instability of dust ion acoustic waves (DIAWs) driven by ions and electrons with different drift velocities in an unmagnetized, collisionless, isotropic dusty plasma was investigated. The electrons, ions and dust particles are assumed to be the generalized q-nonextensive distributions. The spectral indices of the q-distributions for the three plasma components are different from each other. Based on kinetic theory, the dispersion relation and the instability growth rate of DIAWs are obtained. It is found that the presence of the nonextensive distribution electrons and ions significantly modify the domain of the instability growth rate, as well as the ion-electron density ratio (ρ) and drifting-thermal velocity ratio (u _i0/v _Te ). In reverse, the index of dust grains has nearly no any effect on the instability growth rate. Furthermore, the effects of these parameters on the growth rate have also been discussed in detail.     

Obliquely propagating solitary wave structures in nonextensive magneto-rotating plasmas

The propagation of the nonlinear electrostatic ion acoustic solitary wave structures in two component, non relativistic, homogenous, magneto rotating plasma are studied. The inertialess electrons are assumed to follow nonextensive q velocity distribution. Small amplitude reductive perturbation technique is applied to derive Korteweg de Vries (KdV) equation and its analytical solution is presented. The effects of variation of different plasma parameters on propagation characteristics of solitary wave structure in the presence of the Coriolis force are discussed. It is observed that nonextensive parameter q modifies the structure of solitary wave structures in rotating plasmas.     

Ion acoustic solitons in a nonextensive plasma with multi-temperature electrons

The properties of propagation of small amplitude ion acoustic solitary waves (IASWs) are studied in a plasma containing cold fluid ions and multi-temperature electrons (cool and hot electrons) with nonextensive distribution. Korteweg-de Vries (KdV) equation with finite amplitude is derived using a reductive perturbation method. From the solitary solutions of KdV equation, the combined effects of nonextensivity and density ratio are studied on characteristics of ion acoustic (IA) solitary waves. Positive as well as negative polarity solitons exist. Since singularity exists for A=0 so we have also derived modified Korteweg de Vries (mKdV) equation to study the solitonic solution for critical values of physical parameters (q,f,σ). The nonextensivity of electrons (via q) and density ratio of electrons and ions (via f) and temperature ratio (σ) significantly influence the characteristics of ion acoustic solitary structures.     

Arbitrary amplitude electron acoustic waves in a magnetized nonextensive plasma

Arbitrary amplitude electron acoustic (EA) solitary waves in a magnetized nonextensive plasma comprising of cool fluid electrons, hot nonextensive electrons, and immobile ions are investigated. The linear dispersion properties of EA waves are discussed. We find that the electron nonextensivity reduces the phase velocities of both modes in the linear regime: similarly the nonextensive electron population leads to decrease of the EA wave frequency. The Sagdeev pseudopotential analysis shows that an energy-like equation describes the nonlinear evolution of EA solitary waves in the present model. The effects of the obliqueness, electron nonextensivity, hot electron temperature, and electron population are incorporated in the study of the existence domain of solitary waves and the soliton characteristics. It is shown that the boundary values of the permitted Mach number decreases with the nonextensive electron population, as well as with the electron nonextensivity index, q. It is also found that an increase in the electron nonextensivity index results in an increase of the soliton amplitude. A comparison with the Vikong Satellite observations in the dayside auroral zone is also taken into account.     

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.     

Dust-acoustic solitary waves and double layers with two temperature ions in a nonextensive dusty plasma

Small amplitude dust-acoustic solitary waves in an unmagnetized dusty plasma consisting of electrons and two temperature ions obeying the q-nonextensive distribution are investigated. Employing reductive perturbation method, the Korteweg-de Vries (KdV) equation is derived. From the solitonic solutions of KdV equation, the influence of nonextensivity of electrons as well as ions and dust concentration on the amplitude and width of dust-acoustic solitary waves has been studied. It is observed that both positive and negative potential dust acoustic solitary waves occur in this case. The modified KdV (mKdV) equation is derived in order to examine the solitonic solutions for the critical plasma parameters for which KdV theory fails. The parametric regimes for the existence of mKdV solitons and double layers (DLs) have also been determined. Positive potential double layers are found to occur in the present study.     

Astrophysical naturally moderated classical positron beam interaction with nonlinear waves in nonextensive astrophysical plasmas

The positron acoustic shock and solitary wave are explored in nonextensive electron-positron-ion plasma. The plasma system under-consideration, consists of a classical positron beam, q distributed electrons and positively charged bulky ions constitute a neutralizing background. The nonlinear Korteweg-de Vries and Burger equations are derived by employing the standard reductive perturbation method. The positron acoustic wave in linear limit is also discussed for dissipative as well as nondissipative cases of nonextensive plasmas. The plasma parameters such as, the concentration of neutralizing ions background, beam velocity, temperature and q parameter of the nonextensive electrons are noticed to significantly affect the positron acoustic shock and solitary waves. Our findings may be helpful in the understanding of laboratory beam plasma interaction experiments as well as the astrophysical nonextensive plasmas interacting with positron beam.     

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).     

Effect of ion temperature on arbitrary amplitude Kinetic Alfvén solitons in a plasma with a q-nonextensive electron velocity distribution

Taking into account of ion temperature effect, existence conditions of arbitrary amplitude solitary Kinetic Alfvén Waves (KAWs) in a plasma with q-nonextensive electrons are investigated by the conventional Sagdeev pseudo potential method. It is found that only solitons with density hump can exist, the amplitude of which depends sensitively on the parameter q, ion temperature ( \(\sigma= \frac{T_{i}}{T_{e}}\) ) and plasma β. There is an upper limit of solitary wave amplitude which decreases with increase of q, σ and β. The amplitude of solitary KAWs is found to increase with increase in ion temperature. The results obtained in the framework of Maxwellian distribution are reproduced when q→1.     

Ion-acoustic rogue waves in a plasma with a q-nonextensive electron velocity distribution

Ion-acoustic rogue waves (IARWs) are addressed in a two-component plasma with a q-nonextensive electron velocity distribution. A weakly nonlinear analysis is carried out to derive a Korteweg-de Vries (K-dV) equation with a particular emphasis on its application to the IARWs. This K-dV equation is transformed to a nonlinear Schr?dinger equation, provided that the frequency of the carrier wave is much smaller than the ion plasma frequency. Interestingly, it is found that the IARWs may be drastically affected by electron nonextensivity depending on whether the entropic index q is positive or negative. In view of the crucial importance of RWs in space environments, our results should be useful in understanding the basic features of the nonextensive IARGs that may occur in space plasmas.     

Bifurcations of dust acoustic solitary waves and periodic waves in an unmagnetized plasma with nonextensive ions

Bifurcations of dust acoustic solitary waves and periodic waves in an unmagnetized plasma with q-nonextensive velocity distributed ions are studied through non-perturbative approach. Basic equations are reduced to an ordinary differential equation involving electrostatic potential. After that by applying the bifurcation theory of planar dynamical systems to this equation, we have proved the existence of solitary wave solutions and periodic wave solutions. Two exact solutions of the above waves are derived depending on the parameters. From the solitary wave solution and periodic wave solution, the effect of the parameter (q) is studied on characteristics of dust acoustic solitary waves and periodic waves. The parameter (q) significantly influence the characteristics of dust acoustic solitary and periodic structures.     

Korteweg-de Vries equation for ion acoustic soliton with negative ions in the presence of nonextensive electrons

Korteweg-de Vries (KdV) equation for electrostatic ion acoustic wave in a three component plasma containing positive and negative ions along with the nonextensive electrons is derived. Fast and slow ion acoustic modes which propagate with different velocities are excited. The effects of variation of quantities like q (nonextensive parameter), Q (mass ratio of positive to negative ion), μ (electron to positive ion number density ratio), θ _i (positive ion to electron temperature ratio) and θ _n (negative ion to electron temperature ratio) have been presented for fast and slow ion acoustic modes. Both compressive and rarefactive solitons are observed. It is found that the solitary excitations strongly depend on the mass and density ratios of the positive and negative ions as well as on nonextensive electron parameter.     

On the head-on collision between two ion acoustic solitary waves in a weakly relativistic plasma containing nonextensive electrons and positrons

The head-on collision of two ion acoustic solitary waves propagating in opposite directions in a weakly relativistic electron-positron-ion plasma composed of weakly relativistic warm ion fluid and nonextensive electrons, positrons is investigated. Using extended Poincaré-Lighthill-Kuo method, the Korteweg-de Vries equations and the analytical phase shifts after the head-on collision of two solitary waves are derived. The effects of the nonextensive parameter, positron-to-electron density ratio, ion-to-electron temperature ratio, electron-to-positron temperature ratio and relativistic factor on the phase shifts are studied. It is found that these parameters can significantly influence the phase shifts of solitary waves.     

Effect of ion kinematic viscosity on large amplitude dust ion acoustic solitary waves

Nonlinear dust ion acoustic solitary waves (DIASW) in dusty plasma are studied incorporating kinematic viscosity, using Sagdeev’s pseudopotential approach. The effects of kinematic viscosity and the nonextensive parameter q on the features of DIASW are investigated in some detail.