Landau damping of longitudinal oscillation in ultra-relativistic plasmas by analytic function of nonextensive distribution

The analytic function of relativistic nonextensive distribution is given, and employed to solve the Landau damping of longitudinal oscillation in ultra-relativistic plasmas. The unified expression of Landau damping which reduces to the result in relativistic Maxwellian distributed plasmas in the extensive limit is obtained, and find that Landau damping is relevant to both the number and energy of resonant particles, which described by temperature and nonextensive parameters in relativistic nonextensive distribution.     

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-acoustic wave modulation in the presence of q-nonextensive electrons and/or ions in dusty plasma

A study is presented of the nonlinear self-modulation of low-frequency electrostatic dust acoustic waves (DAWs) propagating in a dusty plasma, within the theoretical framework of the nonextensive statistics proposed by Tsallis. Using the reductive perturbation method (RPM), the nonlinear Schrödinger equation (NLSE) which governs the modulational instability (MI) of the DAWs is obtained. The presence of the nonextensive electron/ion distribution is shown to influence the MI of the waves. Furthermore it is observed that nonextensive distributed ions has more effect on the MI of the DAW than electrons.     

What Does the Nonextensive Parameter Stand for in Self-Gravitating Systems?

It is natural important question for us to ask what the nonextensive parameter stands for when Tsallis statistics is applied to the self-gravitating systems. In this paper, some properties of the nonextensive parameter and Tsallis’ equilibrium distribution for the self-gravitating system are discussed in the framework of nonextensive kinetic theory. On the basis of the solid mathematical foundation, the nonextensive parameter can be expressed by a formula with temperature gradient and the gravitational potential and it can be related to the non-isothermal (nonequilibrium stationary state) nature of the systems with long-range interactions. We come to the conclusion that Tsallis’ equilibrium distribution is corresponding to the physical state of self-gravitating system at the hydrostatic equilibrium. PACS numbers 05.20.-y, 95.30.Lz     

The effect of q-distributed ions during the head-on collision of dust acoustic solitary waves

The head-on collision of dust acoustic solitary waves are studied in a dusty plasma composed of dust and nonextensive distributed ions by using the extended version of Poincaré-Lighthill-Kuo (PLK) method. The effect of the nonextensivity on the phase shift is studied. It is found that the presence of nonextensive distributed ions plays a significant role on the collision of dust acoustic solitary waves.     

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.     

Nonlinear propagation of ion-acoustic waves in an electron-positron-ion plasma

A theoretical investigation has been made of electrostatic solitary structures in an electron-positron-ion (e-p-i) plasma, taking nonextensive electrons and nonextensive positrons. By employing the reductive perturbation method, the basic characteristics of ion-acoustic (IA) solitary waves (SWs) in a three-component e-p-i plasma (consisting of negatively charged nonextensive electrons, positively charged nonextensive positrons, and ions) have been addressed. The Korteweg-de Vries (K-dV), modified K-dV (mK-dV), and Gardner equations are derived and their numerical solutions are obtained. It has been shown that the combined effects of electron nonextensivity, positron nonextensivity, and ions significantly modify the behavior of these electrostatic solitary structures that have been found to exist with positive and negative potential in this plasma model. The present analysis may be useful to understand and demonstrate the dynamical properties of IA SWs in different astrophysical and cosmological scenarios (viz. stellar polytropes, hadronic matter and quark-gluon plasma, protoneutron stars, dark-matter halos, etc.).     

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 waves modulation in dusty plasmas with nonextensive electrons

The nonlinear amplitude modulation of dust-ion acoustic wave (DIAW) is studied in the presence of nonextensive distributed electrons in dusty plasmas with stationary dust particles. Using the reductive perturbation method (RPM), the nonlinear Schrödinger equation (NLSE) which governs the modulational instability (MI) of the DIAWs is obtained. Modulational instability regions and the growth rate of nonlinear waves are discussed. It is shown that the wave characters are affected by the value of nonextensive parameter and also relative density of plasma constituents.     

Nonextensive collisioneless dust-acoustic shock waves in a charge varying dusty plasma

Nonlinear dust-acoustic (DA) shock waves are addressed in a nonextensive dusty plasma exhibiting self-consistent nonadiabatic charge variation. Our results reveal that the amplitude, strength and nature of the DA shock waves are extremely sensitive to the degree of ion nonextensivity. Significant differences in the potential function occur for very small changes in the value of the nonextensive parameter. Stronger is the ions correlation, more important is the charge variation induced nonlinear wave damping.     

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.     

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.     

Ion acoustic solitary waves in a weakly relativistic plasma with <Emphasis Type="Italic">q</Emphasis>-nonextensive electrons and thermal positrons

Nonlinear ion acoustic solitary waves (IASWs) are addressed in a weakly relativistic plasma consisting of cold ion fluid, q-nonextensive electron velocity distribution and Boltzmann distributed positron. The Korteweg-de Vries- (KdV) equation is derived by reductive perturbation method. We investigate the effect of nonextensive electrons on solitary waves in this medium. It is found that only compressive solitons can be appeared in the existence of nonextensive electrons. It is shown that the structure of soliton depend sensitively on the q-nonextensive 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.     

Shock waves in a dusty plasma having q-nonextensive electron velocity distribution

The dust-acoustic shock waves have been theoretically investigated using reductive perturbation technique. An unmagnetized four-component dusty plasma system consisting of nonextensive q-distributed electrons, Boltzmann distributed ions, and negatively as well as positively charged dust particles has been considered. The solution of Burgers equation in planar geometry is numerically analyzed. It has been observed that the nonextensive q-distribution of electrons has a significant role in the formation of shock waves. The relevance of our results to astrophysics as well as laboratory plasmas are briefly discussed.     

Effect of nonextensive electron and ion on dust acoustic rogue waves in dusty plasma of opposite polarity

Propagation of nonlinear dust-acoustic waves in a magnetized collisionless plasma having positively, negatively charged dust grains and nonextensive distributed electrons and ions has been investigated. A reductive perturbation method is used to obtain a nonlinear Korteweg-de Vries (KdV) equation describing the model. The dynamics of the modulational instability gives rise to the formation of rogue waves that is described by a nonlinear Schrödinger equation. The dependence of rogue waves profiles on positive and negative charged dust cyclotron frequencies, nonextensive parameters of electrons and ions is investigated numerically. The result of the present investigation may be applicable to some plasma environments, such as cometary tails and upper mesosphere.     

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.     

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.     

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.