Nonextensive Plasma Research Articles

Nonlinear Dynamics of Circularly Polarized Laser Pulse Propagating in a Magnetized Plasma with q ‐Nonextensive Velocity Distributions

AbstractThe nonlinear dynamics of a circularly polarized laser pulse propagating in magnetized plasma contains hot nonextensive q ‐distributed electrons and ions is studied theoretically. A nonlinear equation which describes the dynamics of the slowly varying amplitude electromagnetic wave is obtained using the relativistic two‐fluids model. Some nonlinear phenomena include modulational instability, self‐focusing, soliton formation, and longitudinal and transversal evolutions of laser pulse in nonextensive plasma medium are investigated. Results show that the nonextensivity of particles can substantially change the nonlinearity of medium. The external magnetic field enhances the modulation instability growth rate of right‐hand polarization wave but for the left‐hand polarization the growth rate decreases. The spot size of the laser pulse is strongly affected by the plasma nonextensivity. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Ion-acoustic Gardner solitons in a four-component nonextensive multi-ion plasma

The nonlinear propagation of ion-acoustic (IA) solitary waves (SWs) in a four-component non-extensive multi-ion plasma system containing inertial positively charged light ions, negatively charged heavy ions, as well as noninertial nonextensive electrons and positrons has been theoretically investigated. The reductive perturbation method has been employed to derive the nonlinear equations, namely, Korteweg−deVries (KdV), modified KdV (mKdV), and Gardner equations. The basic features (viz. polarity, amplitude, width, etc.) of Gardner solitons are found to exist beyond the KdV limit and these IA Gardner solitons are qualitatively different from the KdV and mKdV solitons. It is observed that the basic features of IA SWs are modified by various plasma parameters (viz. electron and positron nonextensivity, electron number density to ion number density, and electron temperature to positron temperature, etc.) of the considered plasma system. The results obtained from this theoretical investigation may be useful in understanding the basic features of IA SWs propagating in both space and laboratory plasmas.

Optical properties of nonextensive inhomogeneous plasma sheath

Propagation of electromagnetic wave through an inhomogeneous magnetized nonextensive plasma sheath is numerically examined for a realistic density profile of a reentry problem around a hypersonic vehicle. The effect of nonextensivity and inhomogeneity on radio wave communication is studied parametrically. Variation of reflection and transmission coefficients, total attenuation, and total phase shift over the plasma sheath with respect to the strength of applied magnetic field are derived and compared for different values of q-nonextensive parameter. The obtained results for inhomogeneous plasma sheath are compared with previously obtained results of authors for homogeneous plasma sheath. The comparison shows that radio communication in the inhomogeneous plasma sheath is more advantageous than that in the homogeneous case. The transmission coefficient of a plasma sheath with superthermal electrons (13<q<1) has larger value compared to that with q > 1. Moreover, for ωce>ω, the minimum value of total attenuation corresponds to the range 13<q<1. An interesting result is that nonextensivity effect on wave propagation in plasma sheath depends on the strength of the ambient magnetic field. The effect of nonextensivity on attenuation coefficient is found to be negligible for ωce<ω while it is significant for ωce>ω.

Nonextensivity effect on radio-wave transmission in plasma sheath

In this paper, new theoretical findings on the application of magnetic field in effective transmission of electromagnetic (EM) waves through a plasma sheath around a hypersonic vehicle are reported. The results are obtained by assuming the plasma sheath to consist of nonextensive electrons and thermal ions. The expressions for the electric field and effective collision frequency are derived analytically in the framework of nonextensive statistics. Examination of the reflection, transmission, and absorption coefficients regarding the strength of the ambient magnetic field shows the significance of q-nonextensive parameter effect on these entities. For small values of the magnetic field, the transmission coefficient increases to unity only in the range of −1<q<1. It is also found that the EM wave transmission through the nonextensive plasma sheath can take place using lower magnetic field strengths in the presence of superthermal electrons compared with that of Maxwellian ones. It is observed that superthermal electrons, with nonextensive parameter, q < 1, play a dominant role in overcoming the radio blackout for hypersonic flights.

Dust-acoustic shock waves in an electron depleted nonextensive dusty plasma

A theoretical study of dust-acoustic (DA) shock waves has been carried out in an unmagnetized electron depleted dusty plasma containing inertial negatively charged dust grains and nonextensive positively charged ions. The normal mode analysis is used to examine the linear properties of DA waves. The reductive perturbation technique is employed in order to derive the nonlinear Burgers equation. The basic features (viz. polarity, amplitude, width, etc.) of the DA shock waves are investigated. Both polarity (positive and negative potential) shock waves are found to exists in the plasma under consideration in this manuscript. The findings of this investigation may be used in understanding the wave propagation in laboratory and space plasmas.

Nonplanar dynamics of variable size dust grains in nonextensive dusty plasma

The nonplanar propagation of variable size dust grains in an unmagnetized, collisionless nonplanar (cylindrical) dusty plasma is investigated. The plasma is composed of cold positive and negative dust fluids and nonextensively distributed ions and electrons. The dust size distribution (DSD) is proposed to obey a power law distribution function which is widely applicable in space plasmas. The reductive perturbation technique is employed, and a cylindrical Kadomtsev-Petviashvili equation, describing the nonlinear propagation of dust acoustic waves (DAWs), is obtained. New solutions of this evolution equation (hyperbolic, trigeometrical, and rational) are obtained using G′/G-expansion method. In addition, the proposed model permits the two soliton types, i.e., the rarefactive and compressive solitons. It is found that the DSD and nonextensive distributions have drastic effects on the basic properties of the nonlinear cylindrical DAWs; the phase velocity, the amplitude, and the width. The applications of the present findings in certain astrophysics environments (such as Jupiter's magnetosphere and Earth's mesosphere), where both of the DSD and the geometrical effects are important, are discussed.

Ion-Acoustic Shock Waves in Nonextensive Multi-Ion Plasmas

The nonlinear propagation of ion-acoustic (IA) shock waves (SHWs) in a nonextensive multi-ion plasma system (consisting of inertial positive light ions as well as negative heavy ions, noninertial nonextensive electrons and positrons) has been studied. The reductive perturbation technique has been employed to derive the Burgers equation. The basic properties (polarity, amplitude, width, etc.) of the IA SHWs are found to be significantly modified by the effects of nonextensivity of electrons and positrons, ion kinematic viscosity, temperature ratio of electrons and positrons, etc. It has been observed that SHWs with positive and negative potential are formed depending on the plasma parameters. The findings of our results obtained from this theoretical investigation may be useful in understanding the characteristics of IA SHWs both in laboratory and space plasmas.

Dispersion relation of dust electrostatic oscillations in a nonextensive plasma

The generalized dispersion equation for longitudinal oscillation in an unmagnetized, collisionless and isotropic dusty plasma composed of nonextensive distributed electrons, ions and dust grains is derived based on kinetic theory. The analytical dispersion relation of dust acoustic waves which is related to nonextensive parameters () is obtained. In the limit , the result based on the Maxwellian distribution is recovered. Using the numerical method, we obtain the complete numerical dispersion curve of longitudinal oscillation which is in good agreement with the analytical result of dust acoustic wave at .

Modulation of ion-acoustic waves in a nonextensive plasma with two-temperature electrons

We study the amplitude modulation of ion-acoustic wave (IAW) packets in an unmagnetized electron-ion plasma with two-temperature (cool and hot) electrons in the context of the Tsallis' nonextensive statistics. Using the multiple-scale technique, a nonlinear Schrödinger (NLS) equation is derived, which governs the dynamics of modulated wave packets. It is shown that in nonextensive plasmas, the IAW envelope is always stable for long-wavelength modes (k→0) and unstable for short-wavelengths with k≳1. However, the envelope can be unstable at an intermediate scale of perturbations with 0<k<1. Thus, the modulated IAW packets can propagate in the form of bright envelope solitons or rogons (at small- and medium scale perturbations) as well as dark envelope solitons (at large scale). The stable and unstable regions are obtained for different values of temperature and density ratios, as well as the nonextensive parameters qc and qh for cool and hot electrons. It is found that the more (less) the population of superthermal cool (hot) electrons, the smaller is the growth rate of instability with cutoffs at smaller wave numbers of modulation.

Solitonic, periodic, quasiperiodic and chaotic structures of dust ion acoustic waves in nonextensive dusty plasmas

The solitonic, periodic, quasiperiodic and chaotic structures of dust ion acoustic waves in an unmagnetized dusty plasma with q-nonextensive electrons are studied using the bifurcation theory of planar dynamical systems through direct approach. Using Galilean transformation, model equations are transformed to a planar dynamical system. We obtain all possible phase portraits of the planar dynamical system and corresponding solitary and periodic wave solutions depending on parameters q and μ. Considering an external periodic perturbation, the quasiperiodic and chaotic behaviors of dust ion acoustic waves are presented. The effect of q, the nonextensive parameter is found to have significant effect on quasiperiodic and chaotic motions of dust ion acoustic waves. To show these we study the behavior of dust ion acoustic waves for several values of q, keeping the other plasma parameters like μ and v fixed. It is seen that the unperturbed dynamical system has the solitary and periodic wave solutions, but the perturbed dynamical system has quasiperiodic and chaotic motions for same values of parameters q,μ and v.

Nonplanar ion-acoustic shock waves in a multi-ion plasma with nonextensive electrons and positrons

The basic features of ion-acoustic shock waves (IASHWs) in a multi-ion nonextensive plasma (containing positive light ions, negative heavy ions, as well as nonextensive electrons and positrons) have been rigorously investigated in a nonplanar geometry. The standard reductive perturbation method has been employed to derive the Modified Burgers (MB) equation. The combined effects of the electron and positron nonextensivity, and the ion kinematic viscosity significantly have been found to modify the basic properties of these electrostatic shock structures. The properties of the cylindrical and the spherical IASHWs are observed to differ significantly from those of onedimensional planar waves. The findings obtained from this theoretical investigation may be useful in understanding the characteristics of IASHWs both in space and laboratory plasmas.

Nonlinear nature of composite structure induced by the interaction of nonplanar solitons in a nonextensive plasma

The nonlinear properties of composite structure induced by the head-on collision of electron-acoustic solitons in a general plasma composed of cold fluid electrons, hot nonextensive distributed electron, and stationary ions are studied. We have made a detailed investigation on the time-evolution process of this merged wave structure. It is found that the structure survives during some time interval, and there are obviously different for the properties of the composite structures which are induced in cylindrical and spherical geometries. Moreover, it is shown that there are both positive and negative phase shifts for each colliding soliton after the interaction. For fixed plasma parameters, the soliton received the largest phase shift in spherical geometry, followed by the cylindrical and one-dimensional planar geometries.

Effect of nonextensive velocity distribution on the filamentation instability in a current-driven dusty plasma

The evolution of filamentation instability in a current-driven dusty plasma with nonextensive distribution has been investigated in the dust acoustic frequency range. Using the dielectric permittivity functions of the nonextensive dusty plasma and the Lorentz transformation formulas, the generalized dispersion relation and growth rate of the filamentation instability are achieved. The results show that the possibility and development of the filamentation instability depend on the nonextensive parameters and drift velocity. It is found that by increasing the nonextensive parameter of electrons, the growth rate of instability declines slowly. Nevertheless, the development of filamentation instability is salient with the increase of nonextensive parameter and drift velocity of plasma ions. Moreover, the wavelength region in which the instability occurs is more stretched in the presence of higher values of ions nonextensive parameter and drift velocity. As compared to the electrons, the ions play a dominant role in the evolution of the filamentation instability.

Electromagnetic plasma waves in the nonextensive statistics

This paper presents theoretical findings of new electromagnetic plasma waves in nonextensive and Maxwellian plasma below and above plasma frequency. The new waves are observed among the solutions of general and exact nonextensive dispersion relations for electromagnetic waves in unmagnetized collisionless plasma. The solutions for all values of nonextensive q parameter are also containing a light mode. The exact dispersion relations are obtained via calculation of kinetic dispersion integral using nonextensive distributions and hypergeometric function properties. Finally the effects of q parameter on the oscillation modes and damps are discussed.

Self-similar and diffusive expansion of nonextensive plasmas

Exact analytical self-similar solution is presented for free collisionless expansion of a two-component plasma of inertial ions and nonextensive electrons into vacuum, using the generalized nonextensive velocity distribution for electrons. Furthermore, a hydrodynamic model of plasma expansion in the presence of the ambipolar diffusion caused by collisions among the plasma species, such as electrons and ions, is developed and a Fokker-Planck-like generalized diffusion equation for steady-state expansion of a nonextensive electron-ion plasma is derived. For the case of generalized statistics and in the absence of particle diffusion, the density, velocity, electric potential, and field of expansion profiles are exactly obtained and studied in terms of the self-similar parameter. It is found that superthermal electrons lead to an accelerated expansion of plasma compared to that of Maxwellian electrons. It is also revealed that the nonextensivity parameter plays a fundamental role on the density, velocity, electric potential, and field configuration of the expansion. Therefore, one is able to distinguish three different regimes q < 1, q = 1, and q > 1 for expansion corresponding to sub-nonextensive, extensive, and super-nonextensive statistical profiles for electrons, respectively. Current research can provide useful information and suggests techniques for investigation of the involved statistical mechanism on the role of the energetic electron fluid in the expansion of plasma in strong pulsed laser-matter interaction experiments. It is also shown that the particle diffusion expansion mechanism becomes more dominant for relatively large values of the nonextensivity parameter, q.

Nonplanar Solitary Waves and Shock Waves in a Nonextensive Plasma

Nonplanar Solitary Waves and Shock Waves in a Nonextensive Plasma

Electrostatic Shock Structures in Nonextensive Plasma with Two Distinct Temperature Electrons

The nonlinear dynamics of the dust-acoustic shock waves in a dusty plasma containing negatively charged mobile dust, nonextensive electrons with two distinct temperatures, and Maxwellian ions have been investigated by deriving the Burgers equation. The normal mode analysis is used to examine the linear properties of dust-acoustic (DA) waves. It has been observed that the properties of the DA shock waves (SHWs) are significantly modified by nonextensivity of the electrons, electron temperature ratios, and the respective number densities of two species of electrons. A critical value of nonextensivity is found for which shock structures transit from positive to negative potential. The shock waves with positive and negative potential are obtained depending on the plasma parameters. The entailments of our results may be useful to understand the structures and the characteristics of DASHWs both in laboratory and astrophysical plasma systems.

Filamentation instability of nonextensive current-driven plasma in the ion acoustic frequency range

The filamentation and ion acoustic instabilities of nonextensive current-driven plasma in the ion acoustic frequency range have been studied using the Lorentz transformation formulas. Based on the kinetic theory, the possibility of filamentation instability and its growth rate as well as the ion acoustic instability have been investigated. The results of the research show that the possibility and growth rate of these instabilities are significantly dependent on the electron nonextensive parameter and drift velocity. Besides, the increase of electrons nonextensive parameter and drift velocity lead to the increase of the growth rates of both instabilities. In addition, the wavelength region in which the filamentation instability occurs is more stretched in the presence of higher values of drift velocity and nonextensive parameter. Finally, the results of filamentation and ion acoustic instabilities have been compared and the conditions for filamentation instability to be dominant mode of instability have been presented.

Envelope excitations in nonextensive plasmas with warm-ions

Abstract In this work we study the modulational instability of plasmas with q-entropy electrons and warm ions, using the hydrodynamic approach. A nonlinear Schrodinger equation (NLSE), governing the dynamics of envelope excitations in the plasma, is obtained by using the conventional multiscales method. Investigation of the modulational instability of the nonextensive plasmas reveals that the criteria for propagation of bright/dark envelope excitations in such plasmas are significantly affected by value of the nonextensivity parameter, q, and the fractional ion-temperature, σ. In particular, by setting σ ≠ 0 , a new region of modulational instability appears, indicating that the study of modulation instability in the cold-ion limit ( σ = 0 ) is completely different from that of warm ions. The study of the growth-rate and rogue-wave amplitudes in terms of different plasma parameters, reveals that their magnitude is of different scales for two ranges of the nonextensivity parameters, q > 1 and q 1 .

Theoretical description based on general and exact nonextensive dispersion relations of plasma oscillation data and verification of new acoustic plasma waves

In this paper, first we represent the differences between spatial and temporal dispersions and their dependence on the measurement techniques for electrostatic waves in unmagnetized collisionless plasma. Then, three different experimental data are compared to the solutions of exact nonextensive dispersion relations for electron-ion and pair plasma. The results confirm the existence of new acoustic plasma waves. Furthermore, these comparisons yield a Maxwellian and a nonextensive plasma with nonextensive parameter q larger than one, and a Maxwellian plasma with some abnormal dispersion properties.