Electron-acoustic supernonlinear waves and their multistability in the framework of the nonlinear Schrödinger equation

Finite-amplitude supernonlinear electron-acoustic waves (EAWs) are investigated under the nonlinear Schrödinger (NLS) equation in a plasma system that is composed of cold electron fluid, immobile ions and q-nonextensive hot electrons. Using the wave transfiguration, the NLS equation is deduced in a dynamical system. The presence of finite-amplitude nonlinear and supernonlinear EAWs is shown by phase plane analysis. The effects of the nonextensive parameter (q) and the speed of waves (v) on different traveling wave solutions of EAWs are presented. Furthermore, by introducing a small external periodic force in the dynamical system, multistability behaviors of EAWs under the NLS equation are shown for the first time in classical plasmas.     

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

The 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)     

Envelope excitations in nonextensive plasmas with warm-ions

In this work we study the modulational instability of plasmas with q-entropy electrons and warm ions, using the hydrodynamic approach. A nonlinear Schrödinger 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$\sigma \ne 0$, a new region of modulational instability appears, indicating that the study of modulation instability in the cold-ion limit (σ=0$\sigma =0$) 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$q>1$ and q<1$q<1$.     

Effect of nonextensivity on the characteristics of supersolitons in a two-temperature electron plasma

Ion-acoustic supersolitons are investigated in an unmagnetized two-temperature electron plasma comprising cold fluid ions, hot nonextensive electrons, and cool Maxwellian electrons by using the Sagdeev pseudopotential technique. Existence domain of positive polarity supersolitons in terms of Mach number is computed, which is found to exist for Mach numbers beyond the existence of positive double layers. The domain of existence of supersolitons diminishes with the decrease of the nonextensive parameter (q ). The amplitude and width of the supersolitons are dependent on the cool-to-hot electron temperature ratio (τ ), cool electron density (f ), and nonextensive parameter (q ). The increase of cool electron density increases the amplitude of the supersolitons. For fixed values of f , q _, and Mach numbers, the decrease of τ exhibits more distinct wiggles in the electric fields of supersolitons. The present work may be helpful for further study of supersolitons in the auroral plasma.     

Modulation instability of ion-acoustic waves in a multi-ion plasma

A nonlinear Schrödinger equation for ion-acoustic waves in a collision-free plasma, consisting of a mixture of two cold ion species and hot isothermal electrons is derived using the KBM method. It is used to discuss the modulation instability in which the effect of the light-on concentration is analysed. We find that the unstable region depends sensitively upon the fraction of light-ion concentration (α) and the ion-mass ratio. An approximate relation for α_critical is derived for a given ion species in terms of the ion-mass ratio, which governs the minimum wave number, below which the carrier wave is stable against the modulational instability.     

Dust-acoustic solitons in quantum plasma with kappa-distributed ions

Arbitrary amplitude dust-acoustic (DA) solitary waves in an unmagnetized and collisionless quantum dusty plasma comprising cold dust particles, kappa (κ)-distributed ions and degenerate electrons are investigated. The influence of suprathermality and quantum effects on the linear dispersion relation of DA waves is investigated. Then, the effect of κ-distributed ions and degenerate electrons on the existence domain of solitons is discussed in the space of (M, f). The comparison of the existence domain for higher and lower values of κ shows that suprathermality results in propagation of solitons with lower Mach number, and the quantum effects, lead to a higher values of Mach number. The existence domain of solitons for nondegenerate κ-distributed electrons is considered for comparison with effect of degenerate electrons. Also, we found that the Sagdeev potential well becomes deeper and wider as ε _F???i decreases, as for lower κ values, the influence of quantum effects on the Sagdeev pseudopotential profile is smaller.     

Dispersion properties of electron acoustic waves in degenerate and non‐degenerate quantum plasmas

The longitudinal response functions are used to generalize the dispersion properties of electron acoustic waves (EAWs) in the presence of quantum recoil, for isotropic, non‐relativistic, degenerate/non‐degenerate plasmas. In order to study the EAWs, the constituents of non‐degenerate (thermal) plasma are considered to be of two groups of electrons having different number density and temperature, namely the cold electrons and the hot electrons. Similarly in degenerate (Fermi) plasma the two population of electrons are considered to be the thinly populated and the thickly populated electrons. The sparsely populated electrons are termed as cold electrons while the densely populated ones are termed as hot electrons. The ions are stationary which form the neutralizing background. The absorption coefficients for Landau damping with the inclusion of the quantum recoil in both plasmas are calculated and discussed. The results are discussed in the context of laser‐produced plasma.     

Ion sound wave excitation in a plasma under a Langmuir turbulence regime

Ion sound wave excitation in a warm non-relativistic (W_b ≤ 400 eV) electron beam unmagnetized plasma system is studied experimentally. The spectrum of these waves shows two peaks at frequencies of 70 and 230 kHz respectively. The origin of these waves is connected with modulational instability and cavity collapse. We show that the energy of bulk accelerated electrons can explain the measured value of kr_De for high-frequency sound waves. The energy of ion sound waves is not high enough to have an influence on the Langmuir turbulence dynamics.     

Non-linear behaviour of electron acoustic wave dynamics in a magnetized plasma with non-thermal hot electrons

Non-linear dynamical behaviour of electron acoustic waves (EAWs) is studied in a magnetized non-thermal plasma (containing inertial cold electrons, inertialess hot electrons following non-thermal distribution function, and static ions) via a fluid dynamical approach. A linear dispersion relation is derived and the propagation of two possible modes and their evolution are studied through the different plasma configuration parameters, such as non-thermality and external magnetic field strength. In a non-linear perturbation regime, a reductive perturbation technique is employed to derive the non-linear evolution equation and the analysis is executed for travelling plane waves in terms of a non-linear dynamical system to enlighten the numerous aspects of the phase space dynamics. The results of numerical simulation predict the existence of a wide class of non-linear structures, namely solitonic, periodic, quasiperiodic, and chaotic depending upon different controlling plasma parameters. Also, Poincaré return map analysis confirms these non-linear structures of the EAWs.     

Modulational Instability of Ion-Acoustic Waves in a Warm Plasma with a Relativistic Electron Beam

The modulational instability of ion-acoustic wave in a collisionless, unmagnetized plasma consisting ofwarm ions, hot isothermal electrons, and relativistic electron beam is studied. A modified nonlinear Schrodinger equationincluding one additional term that comes from the effect of relativistic electron beam is derived. It is found that theinclusion of a relativistic electron beam would modify the modulational instability of the wave packet and could notadmit any stationary soliton waves.     

Modulational instability,rogue waves,and envelope solitons in opposite polarity dusty plasmas

Dust-acoustic (DA) waves (DAWs) and their modulational instability (MI) have been investigated theoretically in a plasma system consisting of inertial opposite polarity (positively and negatively) warm adiabatic charged dust grains as well as inertialess non-extensive $q?$distributed electrons and non-thermal ions. A nonlinear Schrödinger equation (NLSE) is derived by using the reductive perturbation method. It has been observed from the analysis of NLSE that the modulationally stable solitary DAWs give rise to the existence of dark envelope solitons, and that the modulationally unstable solitary DAWs give rise to the existence of bright envelope solitons or rogue structures. It is also observed for the fast mode of DAWs that the basic features (viz. stability of the DAWs, MI, growth rate, amplitude, and width of the DA rogue waves, etc.) are significantly modified by the related plasma parameters (viz. dust masses, dust charge state, non-extensive parameter q, and non-thermal parameter α). The results of our present investigation might be useful for understanding different nonlinear electrostatic phenomena in both space (viz. ionosphere and mesosphere) and laboratory plasmas (viz. high intensity laser irradiation and hot cathode discharge).     

Jeans' gravitational instability of a thermally conducting plasma

The gravitational instability of an infinitely extending homogenous plasma endowed with several physical mechanisms, namely Hall currents, finite conductivity, ion viscosity and thermal conductivity is considered. The main result is that the various parameters play different physical roles in the perturbed problem. Jeans' criterion is analyzed in the framework of Tsallis' statistics for possible modifications due to the presence of nonextensive effects. A simple generalization of the Jeans' criterion is obtained and the standard values are obtained in the limiting case q=1, q being the nonextensive parameter.     

Effects of adiabaticity of electrons and ions on dust-ion-acoustic solitary waves

The nonlinear propagation of dust-ion-acoustic (DIA) waves in an adiabatic dusty plasma (containing adiabatic inertial-less electrons, adiabatic inertial ions, and negatively charged static dust) is investigated by the pseudo-potential approach. The combined effects of adiabatic electrons and negatively charged static dust on the basic properties (critical Mach number, amplitude, and width) of small as well as arbitrary amplitude DIA solitary waves are explicitly examined. It is found that the combined effects of adiabatic electrons and negatively charged static dust significantly modify the basic properties (critical Mach number, amplitude, and width) of the DIA solitary waves. It is also found that due to the effect of adiabaticity of electrons, negative DIA solitary waves [which are found to exist in a dusty plasma (containing isothermal electrons, cold ions, and negatively charged static dust) for α=zdnd0/ni0>2/3, where zd is the number of electrons residing onto a dust grain surface, nd0 is the constant (static) dust number density and ni0 is the equilibrium ion number density] disappears, i.e. due to the effect of adiabatic electrons, one cannot have negative DIA solitary waves for any possible set of dusty plasma parameters [0?α<1 and 0?σ=Ti0/Te0?1, where Ti0 (Te0) is electron (ion) temperature at equilibrium].     

Unstable mode of ion-acoustic waves with two temperature q-nonextensive distributed electrons

The linear characteristics of the unstable mode of ion-acoustic waves are examined in an electrostatic electron-ion plasma composed of streaming hot electrons, non-streaming cold electrons and dynamical positive ions. The plasma under consideration is modeled by using a non-gyrotropic nonextensive q-distribution function in which the free energy source for wave excitation is provided by the relative directed motion of streaming hot electrons with respect to the other plasma species. In the frame work of kinetic model, a linearized set of Vlasov–Poisson's equations are solved to obtain the analytical expressions for dispersion relation and Landau damping rate. The threshold condition for the unstable ionacoustic wave is derived to assess the stability of the wave in the presence of nonextensive effects. Growth in the wave spectrum and nontrivial effects of q-nonextensive parameter on the ion-acoustic waves can be of interest for the readers in the regions of Saturns' s magnetosphere.     

The effect of negative ions on the dust acoustic wave in dusty electronegative plasma with positively charged dust grains

The effect of negative ions on the modulational instability properties of nonlinear dust acoustic (DA) waves in the electronegative dusty plasmas was investigated by considering Boltzmann-distributed electrons, negative ions, positive ions as well as positively charged dust grain under the ultraviolet irradiation. It is shown that the modulational instability properties of the DA waves were strongly affected by the temperature and proportion of negative ions. The modulational instability can occur only if the proportion of negative ions was smaller than critical value. The instability growth rate has a maximum value when the proportion of negative ions was a critical one in the unstable region. The effect of photoelectron generated by ultraviolet irradiation on the modulational instability of dust acoustic waves was also discussed by numerical method.     

Parametric study of cylindrical and spherical dust ion acoustic shock waves with two temperature electrons in dusty plasma relevant to Saturn's E ring

We have performed numerical analysis of the one-dimensional dynamics of the cylindrical/spherical dust ion acoustic shock waves in unmagnetized dusty plasma consisting of positive ions, immobile dust particles, and nonextensive distributed cold and hot electrons. A multiple-scale expansion method is used to derive Burgers Equation (BE) and modified Burgers equation (MBE) by including higher order nonlinearity. The basic characteristics of the shock waves have been analysed numerically and graphically for different physical parameters relevant to Saturn' E ring through 2D figures. The parametric dependence of dust ion acoustic shock waves on some plasma parameters nonextensive index, density, and temperature of cold and hot electrons, concentration of dust particles, thermal effects and kinematic viscosity of ions is explored. Furthermore, it is found that the nonplanar geometry effects have an important impact on the establishment of shock waves. The amplitude of the wave decreases faster as one departs away from the axis of the cylinder or centre of the sphere. Such decaying behaviour continues as time progresses. It is also found that an increasing dust concentration decreases the amplitude of the dust ion acoustic shock waves.     

Structural and morphological characterization of CdSe:Mn thin films

The nonlinear propagation of cylindrical and spherical dust-ion-acoustic (DIA) envelope solitary waves in unmagnetized dusty plasma consisting of dust particles with opposite polarity and non-extensive distribution of electron is investigated. By using the reductive perturbation method, the modified nonlinear Schrödinger (NLS) equation in cylindrical and spherical geometry is obtained. The modulational instability (MI) of DIA waves governed by the NLS equation is also presented. The effects of different ranges of the non-extensive parameter q on the MI are studied. The growth rate of the MI is also given for different values of q. It is found that the basic features of the DIA waves are significantly modified by non-extensive electron distribution, polarity of the net dust-charge number density and non-planar geometry.     

Filamentation and modulational instabilities of laser radiation in magnetoactive piezoelectric semiconductors

Following the fluid model for the nonlinear response of electrons, a theoretical investigation has been made on the filamentation and modulational instabilities of high power laser radiation in magnetoactive piezoelectric semiconductors. The ponderomotive force on electrons is responsible for the parametric amplification of the low frequency electrostatic perturbation which may cause the filamentation or modulational instability of the incident laser beam depending upon the direction of propagation of the perturbation. For typical parameters in n-InSb: ?_L = 16 at 77°K, ω_p = 10¹³radsec^?1, v₀ = 10¹¹radsec^?1,K² = 10^?3, ω_c = 10¹²radsec^?1,k = 5 × 10²cm^?1, and when the power density of the 10.6 microm CO₂ laser is 2.37 MW cm^?2 ($\text{|?}{}_{\mathrm{0x}}\text{C| = 10}{}^{\mathrm{?3}}$), the growth rate of the filamentation instability is ~ 10⁴ rad sec^?1 and the growth rate of the modulational instability is ~ 10³ rad sec^?1. It is observed that the external static magnetic field decreases the growth rate of the filamentation instability, whereas it has insignificant effect on the modulational instability of laser beams in piezoelectric semiconductors.     

On the Nonlinear Processes During Generation of Current Drive

The manifestations of the induced scattering effects in the generation process of current driven by lower-hybrid (LH) waves are studied taking into account the radiative-resonant interactions. The influence extent of the LH wave modulational instability on current drive is estimated. It is shown that the induced scattering of LH waves on plasma particles leads to a change of the LH waves spectrum and through this leads to an essential influence on fast electrons generation rate and the steady-state current drive. The modulational instability of LH waves can provide a “spectral gap” filling in the case of sufficiently strong LH wave pumping.     

Landau damping of longitudinal oscillation in ultra- relativistic plasmas with nonextensive distribution

The generalized dispersion equation for longitudinal oscillation in an unmagnetized, collisionless, isotropic and relativistic plasma is derived in the context of nonextensive q-distribution. An analytical expression for the Landau damping is obtained in an ultra-relativistic regime, which is related to q-parameter. In the limit q → 1, the result based on the relativistic Maxwellian distribution is recovered. It is shown that the interactions between the wave and particles are stronger and the waves are more strongly damped for lower values of q-parameter. The results are explained by the increased number of superthermal particles or low velocity particles contained in the plasma with the nonextensive distribution.