Nonplanar shocks in a warm electronegative plasma with electron nonextensivity effects

By employing the reductive perturbation technique, nonlinear cylindrical and spherical Korteweg–de Vries Burgers (KdVB) equation is derived for ion acoustic shock waves in an unmagnetized electronegative plasma. The latter is composed of warm positive and warm negative ions as well as q-distributed nonextensive electrons. Numerically, the modified KdVB equation is solved to examine the impact of nonthermal electrons on the profiles of nonplanar fast ion acoustic shocks. With the help of experimental parameters, it is found that the variations of different quantities, like q (nonextensive parameter), α (the negative-to-positive ion mass ratio), μ (the electron-to-positive ion density ratio) and θ _i (the positive ion-to-electron temperature ratio), η _i0,n0 (the positive/negative ion viscosities) significantly modify the propagation characteristics of nonplanar shocks in electronegative plasmas. The relevance to a laboratory experiment is highlighted, where positive and negative ions are present.     

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.     

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.     

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.     

Overtaking collision of two ion acoustic soliton in a plasma with a q-nonextensive electron and thermal positrons

Theoretically the propagation of two ion acoustic soliton interaction in a three component collisionless unmagnetized plasma which consists of electrons, positrons and cold ions, has been investigated here by employing reductive perturbation technique. In this study, q distributed electrons and Maxwell-Boltzmann distributed positrons are considered and Korteweged-de Vries (KdV) equation is derived. The KdV equation is solved to get two soliton solution by using Hirota bilinear method. The effects of the q distributed electrons on the profiles of two soliton structures and the corresponding phase shifts are investigated. It is observed that both the nonextensive parameter (q) and the ratio of positrons density and electron density (p=n _p0/n _e0), play a significant role in the formation and existence of two soliton and also in the nature of their phase shifts.     

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.     

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.     

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.     

Diffusion of a multi-component plasma

Diffusion in a weakly ionized plasma composed of negative ions as well as positive ions is examined using appropriate linearized fluid equations. For initial, electrically neutral, density perturbations of the form exp(ikx) the diffusion process is characterized by electrical non-neutrality and by three stages or time scales. For equal positive and negative ion diffusion coefficients these stages are in general (1) equilibration of the electron gas so that pressure gradient and electric forces are balanced (2) ambipolar-like diffusion of all three species, and concluding with (3) free ion diffusion. The details of the process are governed by the product kλ_e (wave number times electron Debye length) and the ambient ratio of negative ion to electron number density. Numerical and analytic results for separate positive and negative diffusion coefficients show added complexity which is briefly described. These results or the more complete numerical solutions find application to the lower D region of the ionosphere.     

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.     

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.     

Dust ion acoustic (DIA) solitary waves in plasmas with weak relativistic effects in electrons and ions

In the new investigation of dust-ion acoustic (DIA) waves with negative dust charges and weakly relativistic ions and electrons in the plasma, compressive and rarefactive DIA solitons of interesting characters are established through the Korteweg-de Vries (KdV) equation. Eventually, the amplitudes of the compressive DIA solitons are found to be constant at some critical temperature ratio α _c (electron to ion temperature ratio) identifying some critical dust charge Z _dc . It is predicted, that the reception of dust charges by the plasma particles at the variation of temperature starts functioning to the growth of compressive soliton’s constant stage of amplitude after the state of critical α _c . The identification of critical dust charge (Z _dc ) which is found to be very great for solitons of constant amplitudes becomes feasible for very small dust to ion density ratio (σ). But it can be achieved, we observe, due to the relativistic increase in ion-density as in mass, which is also a salient feature of this investigation.     

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.     

KP Burgers shocks in a warm electronegative plasma with q-nonextensive distributed electrons

Nonlinear properties of ion-acoustic (IA) shock are studied by incorporating the effects of electron nonextensivity in a warm electronegative plasma, whose constituents are the inertial positive/negative ions and q-distributed electrons. For this purpose, the evolution equations are solved to obtain Kadomtsev-Petviashvili (KP) Burgers equation by using the reductive perturbation technique and its solution by the tanh method. Furthermore, the conditions for the existence of oscillatory and monotonic shocks are discussed. Numerically, it is found that IA shock propagation characteristics are significantly modified by the variation of plasma parameters, such as, the effects of electron nonextensivity, the positive and negative ion-to-electron temperature ratios (θ _i ,θ _n ), respectively. The former also affect the dispersion, dissipation and nonlinearity coefficients of the KPB equation involving the IA shocks. The present analyses could be useful for understanding the nonlinear shock wave excitations in space and laboratory plasmas, where two distinct groups of ions are present.     

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.     

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.     

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.     

Ion-acoustic double layers in magnetized positive-negative ion plasmas with nonthermal electrons

The nonlinear ion-acoustic double layers (IADLs) in a warm magnetoplasma with positive-negative ions and nonthermal electrons are investigated. For this purpose, the hydrodynamic equations for the positive-negative ions, nonthermal electron density distribution, and the Poisson equation are used to derive a modified Zakharov–Kuznetsov (MZK) equation, in the small amplitude regime. It is found that compressive and rarefactive IADLs strongly depend on the mass and density ratios of the negative-to-positive ions as well as the nonthermal electron parameter. Also, it is shown that there are one critical value for the density ratio of the negative-to-positive ions (ν), the ratio between unperturbed electron-to-positive ion density (μ), and the nonthermal electron parameter (β), which decide the existence of positive and negative IADLs. The present study is applied to examine the small amplitude nonlinear IADL excitations for the (H⁺, O₂^-)(\mathrm{H}^{+}, \mathrm{O}_{2}^{-}) and (H⁺,H⁻) plasmas, where they are found in the D- and F-regions of the Earth’s ionosphere. This investigation should be helpful in understanding the salient features of the nonlinear IADLs in either space or laboratory plasmas where two distinct groups of ions and non-Boltzmann distributed electrons are present.     

Winter anomalous D-region over Sardinia (40°N)

A simplified D-region model consisting of O₂⁺, NO⁺ and their respective cluster ions grouped as Z_o2⁺ and Z_NO⁺ is used to reproduce the available rocket data on positive ion relative composition and effective clustering rates for the height range 70–90 km. The results of this analysis for a winter anomalous day (Sardinia, 40°N) are in good agreement with the presently known ideas on NO densities, O₂⁺ production rates, mesospheric temperature, negative ion to electron density ratio and effective loss coefficient for electrons. Mesospheric nitric oxide density and temperature profiles from this study are in excellent agreement with the findings of Zbinden et al. (1975) and Hidalgo (1977) for the anomalous day at Sardinia.     

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.