Ion-acoustic Waves In Plasma Research Articles

Soliton Molecules, Asymmetric Solitons and Hybrid Solutions for (2+1)-Dimensional Fifth-Order KdV Equation**Supported by the National Natural Science Foundation of China under Grant Nos 11775121, 11805106 and 11435005, and K.C. Wong Magna Fund in Ningbo University.

Soliton molecules were first discovered in optical systems and are currently a hot topic of research. We obtain soliton molecules of the (2+1)-dimensional fifth-order KdV system under a new resonance condition called velocity resonance in theory. On the basis of soliton molecules, asymmetric solitons can be obtained by selecting appropriate parameters. Based on the N-soliton solution, we obtain hybrid solutions consisting of soliton molecules, lump waves and breather waves by partial velocity resonance and partial long wave limits. Soliton molecules, and some types of special soliton resonance solutions, are stable under the meaning that the interactions among soliton molecules are elastic. Both soliton molecules and asymmetric solitons obtained may be observed in fluid systems because the fifth-order KdV equation describes the ion-acoustic waves in plasmas, shallow water waves in channels and oceans.

Optical soliton solutions to the (2+1)-dimensional Chaffee\u2013Infante equation and the dimensionless form of the Zakharov equation

The (2+1)-dimensional Chaffee–Infante equation and the dimensionless form of the Zakharov equation have widespread scopes of function in science and engineering fields, such as in nonlinear fiber optics, the waves of electromagnetic field, plasma physics, the signal processing through optical fibers, fluid dynamics, coastal engineering and remarkable to model of the ion-acoustic waves in plasma, the sound waves. In this article, the first integral method has been assigned to search closed form solitary wave solutions to the previously proposed nonlinear evolution equations (NLEEs). We have constructed abundant soliton solutions and discussed the physical significance of the obtained solutions of its definite values of the included parameters through depicting figures and interpreted the physical phenomena. It has been shown that the first integral method is powerful, convenient, straightforward and provides further general wave solutions to diverse NLEEs in mathematical physics.

Obliquely propagating ion-acoustic solitary and shock waves in magnetized quantum degenerate multi-ions plasma in the presence of trapped electrons

The properties of obliquely propagating ion-acoustic waves have been investigated in multi-ions magnetized plasma comprising of inertial, positively and negatively charged ion fluids, trapped electrons, and negatively charged stationary heavy ions. The propagation of the waves is oblique to the ambient magnetic field which is along the z-direction. Only fast type of modes exists in the linear regime. The reductive perturbation method was adopted to derive the Korteweg– de Vries (KdV) and Burger equations, as well as the solitary and shock wave solutions of the evolved equations, have been used to analyze the properties of the small but finite amplitude waves. The effects of the constituent plasma parameters, namely, the trapping effect of electrons, the electron degenerate temperature and the viscosity coefficient on the dynamics of the small amplitude solitary and shock waves have been examined. The influence of the magnetic field and the obliquity parameter on the propagation characteristics of ion-acoustic waves are discussed.

Numerical simulation for solitary wave of Klein–Gordon–Zakharov equation based on the lattice Boltzmann model

This work reports a study of Klein–Gordon–Zakharov equation by using the lattice Boltzmann method. The Klein–Gordon–Zakharov equation describes the interaction of the Langmuir wave and the ion acoustic wave in plasma. Numerical simulations of the constructed lattice Boltzmann model for the Klein–Gordon–Zakharov equation show the propagation and the interaction of the (1+1) and (2+1) dimensional solitary waves. These simulation results are examined and compared by using different parameters and different schemes. This work indicates that the lattice Boltzmann method can be a very effective tool for the simulation of Klein–Gordon–Zakharov equation.

Ion-Acoustic Rogue Waves in Multi-ion Plasmas**Supported by the Bangladesh Ministry of Science and Technology Fellowship Award and the Alexander von Humboldt Foundation for a Postdoctoral Fellowship

The basic properties of nonlinear ion-acoustic (IA) waves (IAWs), particularly finite amplitude IA rogue waves (IARWs) in a plasma medium (containing pair ions, iso-thermal positrons, and non-thermal electrons) are theoretically investigated by deriving the nonlinear Schrödinger equation (NLSE). The criteria for the modulational instability of IAWs, and the basic features of finite amplitude IARWs are identified. The modulationally stable and unstable regions are determined by the sign of the ratio of the dispersive coefficient to the nonlinear coefficient of NLSE. The latter is analyzed to obtain the region for the existence of the IARWs, which corresponds to the unstable region. The shape of the profile of the rogue waves depends on the non-thermal parameter α and the ratio of electron temperature to positron temperature. It is found that the increase in the value of the non-thermal parameter enhances both the amplitude and width of IARWs, and that the enhancement of electron (positron) temperature reduces (enhances) the amplitude and width of IARWs. It is worth to mention that our present investigation may be useful for understanding the salient features of IARWs in space (viz., upper region of Titan’s atmosphere, cometary comae, and Earth’s ionosphere, etc.) and laboratory (viz., plasma processing reactor and neutral beam sources, etc.) plasmas.

Resonant multi-soliton solutions to the (2 + 1)-dimensional Sawada–Kotera equations via the simplified form of the linear superposition principle

In this work, a simplified form of the linear superposition principle is proposed to facilitate the computational work and make the resonant multi-soliton solutions easily generated. The (2 + 1)-dimensional Sawada–Kotera (SK) equation, one of fifth-order KdV-like equations describing the nonlinear wave phenomena in shallow water, ion-acoustic waves in plasmas, etc., is investigated. Moreover, in order to demonstrate the power of the proposed method, a new version of the SK equation is further considered and examined. The general forms of resonant multi-soliton solutions are formally established. Furthermore, by taking about reverse engineering of the generated solutions, various versions of the (2 + 1)-dimensional SK equation can be derived that may make great contributions to real physical phenomena and enrich the related nonlinear sciences. Finally, the propagations of two- and three-soliton waves are presented.

Closed form wave solutions to the time fractional Boussinesq-type equation and the Zakharov-Kuznetsov equation

In this article, we have considered the time fractional Boussinesq-type equation and the (3, 3,.3) time fractional Zakharov-Kuznetsov (FZK) equation, as the model of fluid flow and heat transfer, temperature changes from one place to another, waves on a free-moving fluid surface, periodic and shallow water waves, conservation of mass, ion-acoustic waves in plasma, electromagnetic waves, traffic flow and signal processing waves of optical fibers, etc. Applying the generalised (G'/G)-expansion method and by means of fractional complex transformation, we have examined fresh, useful and further generalised exact travelling wave solutions to the above mentioned equations. We have shown that the method used in this article is a more generalised, straightforward and efficient technique that can be used to establish a large number of fresh solutions of the fractional nonlinear differential equations involved in mathematical physics. We have also discussed the physical explanation for its definite values of emerging parameters of the solutions, which are examined from these equations. Finally we have depicted the 3D and 2D figures to the sense of physical phenomena of the obtained solutions.

Dynamics of ion-acoustic waves in Thomas-Fermi plasmas with source term

Dynamics of ion acoustic waves are studied in Thomas-Fermi plasmas with source term consisting of electrons, positrons and positive ions, where electrons and positrons follow zero-temperature Fermi-gas statistics, but ions behave as classical fluid. Using RPT (reductive perturbation technique) the forced KdV and modified KdV equations are obtained. Employing the concept of planar dynamical systems, periodic, quasiperiodic and chaotic features of ion-acoustic waves are studied in Thomas-Fermi plasmas with space debris depending on positron concentration (α), speed (vd) of the space debris and strength (f0) of source perturbation. The results of this work may have relevance in the Thomas-Fermi plasma environments with space debris.

Low-Frequency Kinetic Waves in Plasmas of Magnetic Loops at the Early Stage of a Flare Process in an Active Region

The process of the rise and development of low-frequency instability of kinetic Alfven waves (KAW) and kinetic ion-acoustic waves (KIAW) in preflare solar plasma near the footpoints of magnetic loops, i.e., in the area that corresponds to the height of low-middle chromosphere, has been studied. The observational data obtained in the framework of international missions Hinode, SDO, and IRIS demonstrate that a magnetic field’s amplitude can vary in the interval from a few dozen up to few hundred gausses. The existence of large-scale weak electric fields (“sub-Dreicer” in generally accepted terminology) during a long enough time (with respect to the time of instability development) can be considered in the framework of the used concept as the main source of the wave generation. One more source of instability is slow drift motions of plasma, which are the result of spatial inhomogeneties of temperature and density of a medium. Our former investigations of the obtained solutions of dispersive relation for low-frequency kinetic waves, which are generated due to the development of correspond instabilities, have established an important fact: for some semiempirical models of the solar atmosphere, the kinetic waves generated during the linear stage of the development are members of the family of kinetic Alfven waves and the family of kinetic ion-acoustic waves. It has been proven that the considered wave generation can take place in plasma with pure Coulomb conductivity as well as in plasma with saturated, small-scale Bernstein turbulence. The latter can appear in the investigated area as result of natural evolution of instability of the first harmonics of quasi-Bernstein modes. This mode has much lower threshold with respect to the amplitude of a sub-Dreicer field than low-frequency kinetic waves. Besides this fact, the waves considered have a low enough degree of plasma nonisothermality, which is needed for the appearance of instability. The principal possibility for excitation of nondamped kinetic waves with small amplitudes in the area under investigation has also been proven. It is very important for the increase in the probability for realization of the process of three-wave interaction and appearance of the spikes of microwave emission in the preflare state of the active region and, correspondingly, for making the combined short-term prediction of a flare in it.

Obliquely propagating nonlinear ion-acoustic solitary and cnoidal waves in nonrelativistic magnetized pair-ion plasma with superthermal electrons

The nonlinear propagation of ion-acoustic waves is considered in a magnetized system of collisionless and dissipative pair-ion plasma, composed of cold positively and negatively charged nonrelativistic ions, with superthermal electrons. obliquely propagating ion-acoustic solitary and cnoidal waves are investigated via a mechanical-motion analog Korteweg de Vries (KdV) approach. The characteristics of the emerged nonlinear magnetized waves are significantly modified by the effects of plasma parameters like the obliquity angle, superthermality parameter, negative to positive ions density ratio, electron density and it is also affected by the electron temperature. The obtained results can be generalized to be used to investigate the plasma waves nature in neutron stars, Saturn’s and Pulsars magnetospheres in addition to the laboratory plasmas.

Nonlinear ion flux caused by dust ion-acoustic nonlinear periodic waves in non-thermal plasmas

The propagation of dust ion-acoustic nonlinear periodic (cnoidal) waves is investigated in an unmagnetised dusty plasma characterised by a non-thermal electron population. The equations describing the dynamics of the wave potential in the first and second orders of perturbation theory are derived, and their non-secular periodic solutions are found. The average nonlinear ion flux caused by the propagation of a cnoidal wave is determined. The nonlinear ion flux is found to depend significantly on dust concentration and non-thermality parameter.

Acceleration and Trapping of Ions upon Collision of Ion-Acoustic Solitary Waves in Plasma with Negative Ions

The phenomena occurring under head-on collision of ion-acoustic solitary waves in collisionless plasma consisting of positive and negative ions and electrons obeying the Boltzmann distribution are considered. Using particle-in-cell simulations, it is shown that large-amplitude compressive ion-acoustic solitary waves do not preserve their identity after the collision. Their amplitudes decrease and their shapes change. It is shown that the collision is accompanied by the generation of fast positive ions the velocity of which can exceed more than threefold the speed of sound. In addition, the collision is accompanied by the trapping of negative ions by the field of ion-acoustic solitary waves formed after the collision.

Kinetic theory derivation of exchange-correlation in quantum plasma hydrodynamics

A quantum kinetic equation containing exchange-correlation described by an effective potential is derived, in a non-relativistic electrostatic quantum plasma. The velocity moments of the kinetic equation produce quantum fluid equations modified by the exchange-correlation potential. Closure of the hydrodynamic equations is achieved by expressing the pressure dyad in terms of the number density, using a quantum corrected local velocity displaced Wigner function equilibrium. The propagation of ion-acoustic waves in a quantum electron-ion plasma is analyzed, in the case of a completely degenerate electron gas. The fluid and kinetic approaches are compared and shown to agree in the long wavelength limit. A discussion on the equation of state and the role of the exchange-correlation and quantum diffraction effects is provided. Possible experimental parameters for the verification of the predictions are identified.

An efficient analytical technique for fractional partial differential equations occurring in ion acoustic waves in plasma

In this work, we apply an efficient analytical algorithm namely homotopy perturbation Sumudu transform method (HPSTM) to find the exact and approximate solutions of linear and nonlinear time-fractional regularized long wave (RLW) equations. The RLW equations describe the nature of ion acoustic waves in plasma and shallow water waves in oceans. The derived results are very significant and imperative for explaining various physical phenomenons. The suggested method basically demonstrates how two efficient techniques, the Sumudu transform scheme and the homotopy perturbation technique can be integrated and applied to find exact and approximate solutions of linear and nonlinear time-fractional RLW equations. The nonlinear expressions can be simply managed by application of He's polynomials. The result shows that the HPSTM is very powerful, efficient, and simple and it eliminates the round-off errors. It has been observed that the proposed technique can be widely employed to examine other real world problems.

Numerical simulation on modulational instability of ion-acoustic waves in plasma**Project supported by the National Natural Science Foundation of China (Grant No. 11675014).

In this paper, the one-dimensional (1D) particle-in-cell (PIC) simulation is used to study the modulation instability of ion acoustic waves in electron–ion plasmas. The ion acoustic wave is described by using a nonlinear Schrödinger equation (NLSE) derived from the reductive perturbation method. Form our numerical simulations, we are able to demonstrate that, after the modulation, the amplitude increases steadily over time. Furthermore, by comparing the numerical results with traditional analytical solutions, we acquire the application scope for the reductive perturbation method to obtain the NLSE. We also find this method can also be extended to other fields such as fluid dynamics, nonlinear optics, solid state physics, and the Bose–Einstein condensate to validate the application scope of the results from the traditional perturbation method.

Effects of positive ion temperature and negative ion number density on arbitrary amplitude ion-acoustic solitary waves in nonextensive electronegative plasma

The formation and the basic features of arbitrary amplitude ion-acoustic solitary waves (IASWs) in an electronegative plasma containing cold negative ion fluid, warm positive ion fluid and nonextensive electrons are theoretically investigated by using the pseudo-potential technique. The pseudo-potential is analytically and numerically analyzed and the conditions for the formation of the arbitrary amplitude IASWs and their basic features (viz. polarity, amplitude, width etc.) are identified. It is observed that the electronegative plasma under consideration supports the coexistence of compressive and rarefactive IASWs, and that the temperatures and number density of positive ion fluid significantly modify not only the basic features of compressive and rarefactive IASWs, but also the parametric regime of their coexistence. The implications of our results in some space and laboratory electronegative plasma situations are finally pinpointed.

On Amplification of Ion-Acoustic Mode in Burning Plasma in Presence of Drift Wave Turbulence

Generation of high frequency ion-acoustic wave in burning plasmas is investigated in presence of drift wave turbulence field. Drift wave turbulence is supported by plasma inhomogeneity of a burning plasma. This low frequency wave phenomenon is playing a crucial role in energy exchange process with alpha particles of fusion reactors. Frequency of ion-acoustic wave in burning plasma may be amplified when the accelerated plasma particles transfer their energy to ion-acoustic wave nonlinearly through a modulated field. Considering an ion distribution function for inhomogeneous plasma, we have evaluated fluctuating parts of distribution function due to drift wave turbulence using Vlasov equation. We have also obtained nonlinear fluctuating parts of ion distribution function due to modulated wave as well as nonlinear ion-acoustic wave. We have estimated the growth rate of ion-acoustic wave using nonlinear dispersion relation for ion-acoustic wave.

A kinetic description of ion-acoustic waves in collisional dusty plasma: Effects of grain charge fluctuations

The dispersion relation for ion-acoustic waves in collisional weakly ionized dusty (complex) plasma is formulated with due regard to the grain charge fluctuations. Calculations of the dielectric response function are performed using the Bhatnagar-Gross-Krook kinetic equation. The grain charging currents are described by the Khrapak-Morfill interpolation formula [S. A. Khrapak and G. E. Morfill, Phys. Plasmas 15, 114503 (2008)]. The dependencies of the charging frequencies and effective collision frequencies on dusty plasma parameters are studied in detail. The analysis of the ion-acoustic wave spectrum is presented for the wide range of the ion collisionality for both nonisothermal and isothermal plasmas.

On the Exact Soliton Solutions of Some Nonlinear PDE by Tan-Cot Method

For many solitary wave applications, various approximate models have been proposed. Certainly, the most famous solitary wave equations are the K-dV, BBM and Boussinesq equations. The K-dV equation was originally derived to describe shallow water waves in a rectangular channel. Surprisingly, the equation also models ion-acoustic waves and magneto-hydrodynamic waves in plasmas, waves in elastic rods, equatorial planetary waves, acoustic waves on a crystal lattice, and more. If we describe all of the above situation, we must be needed a solution function of their governing equations. The Tan-cot method is applied to obtain exact travelling wave solutions to the generalized Korteweg-de Vries (gK-dV) equation and generalized Benjamin-Bona- Mahony (BBM) equation which are important equations to evaluate wide variety of physical applications. In this paper we described the soliton behavior of gK-dV and BBM equations by analytical system especially using Tan-cot method and shown in graphically.
 GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 5(1), Dec 2018 P 31-36

The structure of ion-acoustic waves in a low-frequency three-component electron–ion space plasma with two-electron populations

Low-frequency ion-acoustic waves are analysed on the ion time-scale, in a three-component electron–ion space plasma. The solitary waves propagate in the positive x direction relative to an ambient magnetic field $$\vec {B}_0$$ which forms static background for a configuration consisting of cool fluid ions and both warm and hot Boltzmann-distributed electrons with temperatures $$T_{ic},$$ $$T_{ew}$$ and $$T_{eh},$$ respectively. We derive linear dispersion relation for the waves by introducing first-order density, pressure and velocity perturbations into the ion fluid equations. Additionally, the variation in the nonlinear structure of the waves are investigated by carrying out a full parametric analysis utilising our numerical code. Our results reveal that ion-acoustic waves exhibit well-defined nonlinear spikes at speeds of $$M\ge 2.25$$ and an electric field amplitude of $$E_0=0.85.$$ It is also shown that low wave speeds $$(M\le 2),$$ higher densities of the hot electrons, antiparallel drifting of the cool fluid ions, and increased ion temperatures all lead to significant dispersive effects. The ion-acoustic plasma waves featured in this paper have forms that are consistent with those classified as the type-A and type-B broadband electrostatic noise (BEN) observed in the data obtained from earlier satellite missions.