Ion-acoustic Research Articles

Head-on collision of ion-acoustic multi-solitons and study of rogue waves in electron-beam superthermal plasma

In this investigation, head-on collision of ion-acoustic (IA) multi-solitons and study of characteristics of ion acoustic rogue waves in an unmagnetized plasma which includes ion fluid, superthermal hot electrons, and penetrated by electron beam have been presented. The Korteweg-de Vries equation have been derived by employing the extended Poincaré-Lighthill-Kuo (PLK) method. Further, multi-solitons of different KdV equations have also been determined by following the Hirota bilinear method. The combined effects of electron beam parameters and variation of different physical parameters on the characteristics of IA solitons and phase shifts of multi-solitons have been analyzed. It is remarked that electron beam components and other plasma parameters significantly influence the phase shifts and other properties of ion-acoustic solitons (IASs). Furthermore, the nonlinear Schrodinger equation (NLSE) has been derived from the KdV equation by using appropriate transformation. The characteristics of different orders rogue waves have also been studied from the different solutions of NLSE. The results of this study may be of great importance to understand the characteristics properties of various kinds of nonlinear solitary structures in different kinds of plasma systems.

Solitary and periodic waves in magneto–rotating plasmas: Effect of the Kappa–Cairns distributed electrons

The nonlinear propagation of ion–acoustic (IA) waves in a magneto–rotating plasma is studied by considering the Kappa-Cairns electron distribution. Employing the perturbation scheme, Korteweg–de Vries equation is derived. It is seen that both positive and negative potential solitons can be supported in the present plasma model. The numerical results reveal that the Kappa-Cairns distributed electrons modify features of the electrostatic waves significantly. The effects of non–thermal parameters, plasma rotation frequency, ion temperature, and the wave propagation angle on electrostatic solitary wave structures are also discussed here. It is found that the plasma parameters considerably influence the propagation of IA waves in rotating plasmas. Furthermore, using the bifurcation theory of planar dynamical systems to the K-dV equation, we have presented the existence of solitary and periodic traveling waves. Our study may be helpful to understand the behavior of ion–acoustic wave in the rotating plasma.

Roles of positively charged dust in the formation of ion‐acoustic subsonic solitary waves in electron‐ion‐positively charged dust plasmas

AbstractThe electron‐ion‐positively charged dust plasma system containing Boltzmann distributed electron species, cold inertial ion species, and stationary positively charged dust (pcd) species are considered. The roles of pcd species in the formation of ion‐acoustic (IA) subsonic solitary waves (SWs) are investigated by the pseudo‐potential approach, which is valid for arbitrary amplitude time‐independent subsonic SWs, as well as by the reductive perturbation method, which is valid for the time‐dependent small amplitude subsonic SWs. It is observed that the presence of the pcd species reduces the phase speed of the IA waves, and consequently supports the IA subsonic SWs with the positive wave potential in such electron‐ion‐pcd plasmas. This is due to the reduction of the space charge electric field by the presence of the pcd species. The applications of the work in space environments (viz. Earth's mesosphere, cometary tails, Jupiter's magnetosphere, etc.), where pcd species have been detected, are briefly discussed.

Investigation of Shock Waves in Nonextensive Electron–Positron–Ion Plasma with Relativistic Ions

Nonlinear propagation of ion-acoustic (IA) shock wave in a nonextensive and relativistic plasma is investigated by deriving space fractional Korteweg–de Vries–Burgers (SFKB) equation. This unmagnetized and collisionless plasma contains relativistic thermal ions, q-distributed electrons, and positrons. A modified tanh-function method is presented to solve the obtained SFKB equation taking space fractional and relativistic parameters, electrons nonextensivity, positrons nonextensivity, and electron-to-positron temperature ratio. It is observed that the structure of the IA shock wave can be modified by space fractional parameters. On the other hand, the IA shock wave shape can be modulated using the space fractional parameter. Our results can help understand the astrophysical environments such as pulsar magnetospheres, quasars, and collimated jets.

Bifurcation analysis of ion-acoustic waves for Schrödinger equation in nonextensive Solar wind plasma

Bifurcation analysis of ion-acoustic wave (IAWs) solutions of the nonlinear Schrödinger equation (NLSE) is explored for the first time in an electron-ion (e-i) magnetized solar wind plasma. The existence of ion-acoustic (IA) periodic, superperiodic, kink, antikink, compressive and rarefactive solitary wave solutions are revealed. Special values of Solar wind plasma parameters at a normalized distance from the Sun are considered for numerical simulation. The IA wave solutions are derived analytically. These solutions are analyzed numerically considering the influence of parameters, namely, wave number (k), velocity (V) of traveling wave and nonextensive parameter (q). Computational simulation reveals that only IA periodic wave grows in amplitude as waves moves from the Sun.

Ion-acoustic dipolar vortex in degenerate magnetoplasma with ions/electrons thermal corrections.

Nonlinear evolution and propagation characteristics of an ion-acoustic (IA) dipolar vortex are examined in a magnetoplasma that comprises partially degenerate electrons and dynamic ions. The adiabatic ions reduce the quantum magnetohydrodynamic equations to a modified momentum equation. The latter admits a new solution and leads to an evolution equation for the description of a coherent IA dipolar vortex. Numerical analysis reveals that variations in the relevant plasma parameters alter the evolution condition for a stable vortex. The electron exchange-correlation enhances excitation of the vortex as it extends the parametric regime associated with the stable vortex solution. On the contrary, the ion temperature lessens the nonlinear evolution of the vortex. Importantly, a degree of enhancement in the exchange-correlation potential leads to the wave dispersion and-in return-widens the vortex potential spatially. The novel nature of the derived results stresses upon the comprehension of the ordered structures in the compact stars, the magnetic mirrors, the ionosphere, the pinch devices, etc., where thermal corrections significantly impact the waves dynamics.

Nonlinear ion acoustic waves in dissipative and dispersive magneto‐rotating relativistic plasmas with two temperature superthermal electrons

AbstractA study has been presented for the nonlinear features of ion‐acoustic (IA) shock waves in a magnetorotating plasma consisting of warm viscous streaming ions along with kappa‐distributed electrons having two different temperatures. In this regard, we have employed the reductive perturbation technique to derive the Zakharov‐Kuznetsov‐Burgers (ZKB) equation that governs the dynamics of IA shock waves. The solution obtained by the hyperbolic tangent method has been shown to depend on various plasma parameters such as spectral index (κc), density fraction (f), effective rotation frequency (Ωc), ion kinematic viscosity (ηo), and temperature ratio (σ). In the limiting case when dissipative coefficient D → 0, we have also examined the solitary potential distributions, which are the solutions of Zakharov Kuznetsov (ZK) equation. It is found that both rarefactive and compressive structures exist for the system under consideration. The transition in the nature of such profiles is due to the enhancement in the density of cold electrons. The importance of present theoretical investigations has been carried out with regard to Saturn's magnetosphere, where two temperature superthermal electron populations have been observed by various satellite missions.

Dynamics of ion-acoustic waves in nonrelativistic magnetized multi-ion quantum plasma: the role of trapped electrons

The presented work provides a new perspective of quantum nonlinear propagation of ion-acoustic (IA) waves in a magnetized collisionless and dissipative multi-ion plasma system, composed of cold positive and negative charged nonrelativistic ions, negatively charged immobile heavy ions and trapped electrons; all existed in a quantizing magnetic field. We address the reductive perturbation method to derive the Korteweg-de Vries- Burgers (KdV-Burgers) and modified KdV-Burgers equations. The bifurcation theory of planar dynamical systems is applied to investigate the existence of the solitary wave and the periodic traveling wave solutions of the resulting mKdV-Burgers equation. Accordingly, the phase portrait topology is illustrated for this equation. To study the nonlinear waves in case of mKdV- Burgers, we obtain some interesting physical solutions for mKdV- Burgers. These solutions are in the form of soliton, a combination between the shock and the soliton, and finally monotonic and oscillatory shock waves. Only rarefactive IA waves are obtained for the slow mode of phase velocity. It is found that the IA solitons, IA shocks are affected by the plasma system parameters. The presented theoretical research can be successfully implemented to understanding the solitary and shocks structures in dense magnetized quantum plasmas such as those existing in white dwarfs and in the intense-laser plasma interactions.

Nonlinear Wave Interaction with Positron Beam in a Relativistic Plasma: Evaluation of Hypersonic Dust Ion Acoustic Waves

We studied the propagation of small-amplitude dust ion acoustic (DIA) solitary waves in four-component relativistic plasma comprised of nonthermal electrons, mobile positively charged ions, positron beam and negatively charged massive dust particles. By using the reductive perturbation method, the Korteweg–de-Vries (KdV) nonlinear wave equation is derived numerically. In this work, we have elucidated the role of energetic positron beam in the relativistic plasma and analyzed the existence region for ion-acoustic (IA) solitary wave formation. It is found that for certain plasma parameters, the propagation of both compressive and rarefactive solitary waves is possible. Here, the injecting streaming positron beam in plasma gives rise to the increase in the phase velocity (Mach number) and reaches up to the hypersonic regime of flow velocity. It is observed that the initial increase in relativistic factor of positron beam $${{\gamma }_{{{\text{br}}}}}$$, as well as temperature ratio of the positron beam to electrons $${{\sigma }_{{\text{b}}}}$$ decrease the characteristic features (the amplitude) of the compressive solitary wave potential profiles. On the other hand, on increasing dust grain charge $${{Z}_{{{\text{d0}}}}}$$, positron beam concentration ratio $${{\mu }_{{\text{b}}}}$$ as well as nonthermal electrons concentration result in enhancement of the amplitudes of IA solitary wave potential profiles. The findings of this work can be more helpful in understanding the Earth’s upper atmosphere (Aurora region of the ionosphere) as well as the space plasmas.

Ion-acoustic shocklets in F-region of ionosphere with non-Maxwellian electrons

The evolution and propagation characteristics of ion-acoustic (IA) shocklets are examined in an unmagnetized collisionless plasma, comprised of warm ions and non-Maxwellian (Kappa/Cairns) electrons. Solving the fluid equations and using the frameworks of diagonalized-matrix/changing variable techniques, a nonlinear set of two characteristic wave equations is obtained, which admits dispersionless/dissipationless evolution of IA shocklets. Numerical analyses have also confirmed the excitation/deformation of IA shocklets and the wave overtaking/breaking effects at time τ>0 for nonlinear coupling of potential field. It is found that superthermal (Kappa distributed) electrons can enhance the overtaking/breaking of IA perturbations in comparison with nonthermal Cairns distributed electrons that lead to less steepened potential field to stabilize IA excitations against the nonlinear steepening. Finite ion temperature has significant impact on the wave coupling to lead the profiles of IA shocklets ahead. This study is important to understand the physical mechanism for excitation and deformation of IA shocklets relevant to the F-region of Ionosphere.

Evidence for neutrals carrying ion-acoustic wave momentum in a partially ionized plasma

An experimental study of Ion Acoustic (IA) wave propagation is performed to investigate the effect of neutral density for Argon plasma in an unmagnetized linear plasma device. The neutral density is varied by changing the neutral pressure, which, in turn, allows the change in ion-neutral, and the electron-neutral collision mean free path. The collisions of plasma species with neutrals are found to modify the IA wave characteristics such as the wave amplitude, the velocity, and the propagation length. Unlike the earlier reported work where neutrals tend to heavily damp the IA wave in the frequency regime ω<νin (where ω is the ion-acoustic mode frequency and νin is the ion-neutral collision frequency), the experimental study of the IA wave presented in this paper suggests that the collisions support the wave to propagate for longer distances as the neutral pressure increases. A simple analytical model is shown to qualitatively support the experimental findings.

Three-dimensional modified Korteweg-de Vries equation in a magnetised relativistic plasma with positron beam and vortex-like electron distribution

The nonlinear features of Ion Acoustic (IA) waves are studied in a fully relativistic three-dimensional (3-D) plasma system with consideration of effect of both positron beam and trapped electrons. We consider a set of 3-D magnetised hydrodynamic equations with pressure expansion for our plasma model along with kinetic Vlasov equation for electrons. Applying the perturbative expansion technique, a Modified Korteweg-de Vries (m-KdV)-like equation is derived, exhibiting the evolution of small amplitude IA waves in plasma. The modified coefficient of nonlinear term in K-dV equation has arrived due to impact of vortex-like distribution of electrons. An analytical and numerical investigation of the nonlinear evolution equations is exhibited with external magnetic field effects, the time derivative pressure expansion as well as other parameters like relativistic effect, mass variation, beam velocity and temperature effect have been taken into consideration. The presence of vortex like trapped electron distribution and positron beam governs the influence of soliton structure quite significantly. The present result should help us to understand the experiments that involve particle trapping and also the salient features of astrophysical environment like ionospheric plasma together with situations in plasma describing the electrostatic solitary structures usually seen in antimatter-related environment in interplanetary region.

Simulation studies of strongly turbulent stimulated Brillouin backscattering during ionospheric heating

ABSTRACTRecent experimental observations of stimulated electromagnetic emissions (SEE) during ionospheric heating have shown that the SEE spectrum produced as a result of the stimulated Brillouin backscatter (SBS) instability is structurally very different for low and high pump power regimes. Initial results from electromagnetic Particle-In-Cell (PIC) simulation studies conducted to investigate the difference in the SBS SEE spectrum for the two pump power regimes are presented. Simulation results presented here are used to gain insight into ionospheric heating experiments at the High Frequency Active Auroral Research Program (HAARP) facility in which the pump power either linearly increased from a low power to the maximum available power, or was maintained at the maximum available power during the heating cycle. The observations show (1) a distinct, narrow SEE spectral line downshifted from the pump frequency, due to SBS, for the low power case and (2) a broad, aggregate SBS SEE structure downshifted from the pump frequency for the high power heating. In general, the spectra of the backscattered EM field obtained from PIC simulations for the two pump power regimes show correspondence with the HAARP observational data. Simulations predict that the broad spectral structure for the high power case results from strong ion acoustic (IA) turbulence. Further characteristics of the strong turbulence include cavity development in the ion density in which (I) strong long lifespan EM waves are trapped (II) short-lived ES waves are trapped, and (III) high temperature electrons exist.

Ion-Acoustic Cnoidal Waves with the Density Effect of Spin-up and Spin-down Degenerate Electrons in a Dense Astrophysical Plasma

Abstract An investigation of nonlinear ion acoustic (IA) cnoidal waves in a magnetised quantum plasma is presented by using spin evolution quantum hydrodynamics model, in which inertial classical ions and degenerate inertialess electrons with both spin-up and spin-down states taken as separate species are considered. The Korteweg–de Vries equation is derived using the reductive perturbation method. Further, using the Sagdeev pseudopotential approach, the solution for IA cnoidal waves is derived with suitable boundary conditions. There is the formation of only positive potential cnoidal, and in the limiting case, positive solitary waves are observed. The effects of density polarisation and other plasma parameters on the characteristic features of cnoidal and solitary waves have been analysed numerically. It is seen that the spin density polarisation significantly affects the characteristics of cnoidal structures as we move from strongly spin-polarised (μ = 1) to a zero spin-polarisation case (μ = 0). The results obtained in the present investigation may be useful in comprehending various nonlinear excitations in dense astrophysical regions, such as white dwarfs, neutron stars, and so on.

On the Characteristics of Solitary Waves and Shocks in Nonextensive Plasmas: Collisionality and Kinematic Viscosity Effects

In this article, a comprehensive investigation of the linear and nonlinear waves’ structure in an unmagnetized plasma consisting of nonextensive electrons, considering collisionality and kinematic viscosity effects, is studied. Using a reductive perturbation technique, we have derived a hybrid Korteweg–de Vries–Burgers equation for ion-acoustic (IA) waves. Analytical solutions for solitary waves and shock structures are obtained. We have also solved this equation numerically in order to investigate the basic properties of solitary/shock waves in such a plasma system. The presence of nonextensive electrons with $q$ -distribution influences significantly the solitary and shock wave structures. In other words, the compressive and rarefactive-type solitons or shock waves can also be seen in this plasma model depending on the strength of nonextensivity. On the other hand, the effects of ion-neutral collision and ion kinematic viscosity on the characteristics of IA solitary/shock waves are discussed. It is found that these parameters modify the basic features of the solitonic and shock excitations.

Three dimensional ion-acoustic rogons in quantized anisotropic magnetoplasmas with trapped/untrapped electrons.

Three-dimensional (3D) modulational instability (MI) and ion-acoustic (IA) envelopes are studied in a quantized degenerate magnetoplasma, whose constituents are the trapped/untrapped electrons and anisotropic positive ions. By using quantum hydrodynamic equations and the multiscale reductive perturbation technique, a 3D nonlinear Schrödinger equation is derived to account for electron quantization and ion pressure anisotrophy effects. The potential excitations are shown stable (unstable) against the perturbations for Kc<0(Kc>0), where Kc is a critical parameter that accounts for the longitudinal (transverse) dispersion(s) and nonlinearity effects. Numerically, the nonlinear evolution of IA wavepackets into a 3D MI may be revealed in the ranges of low and high frequencies 0<ω≤0.05 and 0.75≤ω≤1.1. The quantizing magnetic field reduces (enhances) the group speed (wave frequency) of IA excitations, concentrating the wave energy to favor the modulational instability. Finite electronic temperature (viz.,Te≤10keV) enhances the untrapped electrons and significantly widens the instability domain Kc>0. The ionic pressure anisotropy increases the wave frequency (ω), piles up the harmonics under Kc>0, and give rise to modulational instability. The quantized magnetic field and anisotropic pressure reduce the amplitude and spatial extension of the IA rogons. This study is important for understanding the 3D MI and unstable excitations in degenerate plasmas, relevant to white dwarfs, neutron stars, and high-energy density experiments, where strong magnetic field quantizes the dynamics of trapped/untrapped electrons.

Bifurcation of ion-acoustic superperiodic waves in auroral zone of Earth’s magnetosphere

Ion-acoustic (IA) superperiodic waves are explored in an unmagnetized plasma composing of mobile ions, Maxwell distributed cold electrons and non-thermal hot electrons. Implementing the phase portrait concept of the Hamiltonian systems, all distinct phase plots containing superperiodic and superhomoclinic trajectories are displayed for distinct data values of the physical parameters, such as, nonthermal parameter ($\beta $), number density ratio ($\mu $) of cold electrons and ions at equilibrium, temperature ratio ($\sigma $) of cold electrons to hot electrons and of traveling wave velocity ($v$). The IA superperiodic wave features are examined for various conditions of physical parameters by symbolic computations. The outcomes of this study may be beneficial in discerning IA superperiodic wave in auroral zone of the Earth’s magnetosphere.

Bifurcation Analysis of Ion-Acoustic Superperiodic Waves in Dense Plasmas

Bifurcation analysis of ion-acoustic (IA) superperiodic waves is studied in dense plasmas composed of electrons, positrons, and positive ions. Employing bifurcation analysis of dynamical systems, all feasible phase plots including superperiodic trajectory and superhomoclinic trajectory are obtained based on positron concentration (α) and velocity (v) of IA traveling wave. Using symbolic computation, superperiodic wave solutions are obtained for ultra-relativistic environment as well as non-relativistic environment. It is discerned that positron concentration (α) affects the bifurcation of IA superperiodic waves. The results of this work may be applied to understand superperiodic wave features in cold neutron star.

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.

Derivation and solution of space fractional modified Korteweg de Vries equation

All applications of fractional calculus to physics propose fractional equations of motion for various complex phenomena. Complex and nonlinear fractional equations are very familiar and often occur in nature. Therefore, the analytical and numerical solutions of this kind of equations are very important and consequential. An important objective in this study is to derive the space fractional modified Korteweg de Vries (SFMKdV) equation and present an efficient modified G′/G -expansion method to solve it. The exact analytical solution of SFMKdV equation is obtained to describe the space fractional parameter effect on the propagation of the ion acoustic (IA) waves. It has been observed that space fractional parameter can modify the height of the IA waves.