Ion-acoustic Cnoidal Waves Research Articles

Nonplanar ion-acoustic solitary and cnoidal waves in a non-Maxwellian plasma: Study on nonplanar (modified) Kawahara equation

This study aims to examine the properties of the nonplanar (cylindrical and spherical) ion-acoustic solitary waves (SWs) and cnoidal waves (CWs) in a collisionless, unmagnetized electron-ion (EI) plasma having a Cairns–Tsallis distribution for the electrons. This study is structured around two main lines. The first trend involves deriving the nonplanar Korteweg-de Vries (KdV) equation by utilizing the method of reductive perturbation (MRP). This equation describes small-amplitude (non)planar acoustic waves (AWs). Furthermore, the nonplanar Kawahara equation (KE) is formulated to examine the significant magnitude of planar and nonplanar SWs and CWs. The current plasma model supports compressive and rarefactive IA solitary and cnoidal structures, depending upon the associated physical factors such as the nonextensive parameter (nonextensivity) and nonthermal parameter (nonthermality). When the plasma compositions reach some critical values, such as the critical value of nonthermality, the coefficient of the quadratic nonlinear term vanishes. Hence, both nonplanar modified KdV (mKdV) equation and modified KE (mKE) with cubic nonlinearity are derived to accurately depict the dynamics of both small and large amplitudes of nonplanar SWs and CWs and any other structures related to this family of evolution equations. The influences of the nonextensivity and nonthermality on the profile of (non)planar KdV soliton and the (non)planar Kawahara SWs and CWs are numerically examined using some semi-analytical and numerical approximations. Also, the impact of the nonextensivity on the profile of (non)planar mKdV soliton and the (non)planar modified Kawahara SWs and CWs is reported. It is tracked down that the variety of different plasma parameters significantly alters the characteristic properties of the small and large amplitude ion-acoustic waves (IAWs) discussed by the nonplanar KdV-type equations.

Ion-acoustic cnoidal waves in a non-Maxwellian plasma with regularized κ-distributed electrons

This study examines how regularized kappa distributed (RKD) electrons affect the characteristics of the ion-acoustic cnoidal waves (IACWs) in normal plasma. The RKD is a generalized form of the standard kappa distribution that accounts for the impacts of thermal broadening and finite size effects on the plasma particles. By employing the reductive perturbation technique, the Korteweg–de Vries equation is derived, and its nonlinear cnoidal wave (CW) solution is obtained and analyzed both analytically and numerically. It is found that the amplitude of compressive IACWs increases with an enhanced cutoff parameter α and decreases with increasing superthermality κ. Rarefactive IACWs yield opposing results as compared to compressive IACWs under the impact of κ and α. The results provide insight into the behavior of CWs in normal plasmas with non-Maxwellian distributions and contribute to the understanding of wave-particle interactions in laboratory and space plasmas.

Low-frequency nonlinear ion-acoustic cnoidal waves in a superthermal plasma with a monoenergetic electron beam

This study analyzes the behavior of nonlinear electrostatic ion-acoustic cnoidal waves (IACWs) in a magnetoplasma characterized by two distinct temperatures of superthermal electrons and a monoenergetic electron beam. For this purpose and based on fluid theory, the reductive perturbation technique is applied to reduce the basic equations to a third-order Korteweg-de Vries (KdV) equation. Under certain conditions, the KdV equation can be used for modeling symmetric CWs; when these conditions are not met, it is replaced by a Kawahara equation to describe these waves correctly. The symmetric IACWs features are examined in detail to determine the effect of pertinent plasma parameters. This study may help model nonlinear structures in astrophysical and space plasmas and understand the mechanism of CWs in the plasma sheath region.

Physical aspects of cnoidal waves in non-thermal electron-beam plasma systems

The effects of electron beam and non-thermal electrons on ion-acoustic cnoidal waves (IACWs) structure in a two-fluid plasma system are investigated. A Kappa-Cairns type distribution is assumed for the background electrons. The Korteweg–de Vries (K-dV) equation is obtained by employing reductive perturbation technique and the analytical solution of K-dV equation is derived by employing the Sagdeev pseudo-potential approach. It is seen that in the presence of the electron beam, four modes can exist in this plasma model. In this study, it is observed that only two modes are real in all cases. Furthermore, it is found that the characteristics of the ion-acoustic cnoidal wave depend strongly on the electron beam parameters (via and ) as well as the non-thermal indexes for the plasma electrons (via and ).

Ion Acoustic Cnoidal Waves in Ion-Beam Dense Plasma in the Presence of Quantizing Magnetic Field

A study of propagation properties of ion-acoustic (IA) cnoidal waves in a magnetized degenerate quantum plasma comprising of inertial positive ions, weakly relativistic ion beam, and trapped electrons in the presence of quantizing magnetic field has been presented. The reductive perturbation technique is adopted to derive the Korteweg–de Vries (KdV)-type equation. Furthermore, the cnoidal wave solution of the KdV-type equation is obtained by using the Sagdeev pseudopotential method. Only positive potential IA cnoidal waves are evolved. The combined effects of ion-beam concentration, ion-beam velocity, quantizing magnetic field, and the temperature degeneracy of trapped electrons on the different characteristics of the IA cnoidal waves have been analyzed. The results of our present investigation may be useful to study the characteristics of IA cnoidal waves in dense astrophysical regions, such as white dwarfs.

Oblique propagation of nonlinear ion-acoustic cnoidal waves in magnetized electron–positron–ion plasmas with nonextensive electrons

Theoretical investigation of nonlinear electrostatic ion-acoustic cnoidal waves (IACWs) is presented in magnetized electron–positron–ion plasma with nonextensive electrons and Maxwellian positrons. Using reductive perturbation technique, Korteweg–de Vries equation is derived and its cnoidal wave solution is analyzed. For given plasma parameters, our model supports only positive potential (compressive) IACW structures. The effect of relevant plasma parameters (viz., nonextensive parameter q, positron concentration p, temperature ratio σ, obliqueness l 3) on the characteristics of IACWs is discussed in detail.

Periodic and localized structures in a degenerate Thomas-Fermi plasma

The propagation of electrostatic ion-acoustic cnoidal waves (IACWs) and solitons in a degenerated electron-positron-ion plasma with cold inertial ions and Thomas-Fermi distributed electrons and positrons is investigated. Adopting a reductive perturbation technique (RPT), the Korteweg-de Vries (KdV) equation is obtained and its cnoidal waves (CWs) solution is analyzed. The plasma configuration parameters (namely, the positron concentration and the Fermi temperature ratio of electron-to-positron) are shown to affect remarkably the dynamical characteristics of IACWs and solitons. The relevance of the present work to superdense white dwarfs is pointed out.

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.

Ion-scale Cnoidal Waves in a Magnetized Anisotropic Superthermal Plasma

The ion acoustic cnoidal waves (IACWs) are investigated in a magnetized anisotropic electron ion plasma with superthermal electron distribution. The ions are warm and manifest pressure anisotropy. ...

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.

Ion acoustic cnoidal waves in a magnetized plasma in the presence of ion pressure anisotropy

An investigation of the ion acoustic nonlinear periodic (cnoidal) waves in a magnetized plasma with positive ions having anisotropic thermal pressure and Maxwellian electrons is carried out. The Korteweg-de Vries equation for the wave potential is derived via a reductive perturbation technique and its cnoidal wave solution is obtained. The effect of various relevant plasma parameters like ion pressure anisotropy and obliqueness of field on the characteristics of ion acoustic nonlinear periodic wave structures is investigated in detail. The present investigation could be useful in space and astrophysical plasma systems having ion pressure anisotropy, particularly, in the magnetosphere and near Earth magnetosheath.

Effects of nonthermal electrons and positrons on the characteristics of ion-acoustic cnoidal wave in electron-positron-ion plasma

Effects of nonthermal electrons and positrons on the nature of ion acoustic cnoidal wave in the plasma contains ions, positrons, and electrons are investigated. Reductive perturbation method was employed to solve the fluid dynamic equations with appropriate boundary condition and derivation of Korteweg-de Vries (KdV) equation for nonlinear periodic ion acoustic wave. Sagdeev potential was extracted and the condition of plasma nonthermality on the formation of solitary and cnoidal ion acoustic wave has been discussed in detail. Results show that for all magnitudes of electrons (positrons) nonthermal coefficient, αe (αp) ion acoustic wave may generate in plasma medium. With increasing both αe and αp the amplitude of cnoidal ion acoustic wave increases. The wavelength of ion acoustic wave increases with increasing αp and decreases with increasing αe.

Effects of external magnetic field on oblique propagation of ion acoustic cnoidal wave in nonextensive plasma

Effects of the obliqueness and the strength of external magnetic field on the ion acoustic (IA) cnoidal wave in a nonextensive plasma are investigated. The reductive perturbation method is employed to derive the corresponding KdV equation for the IA wave. Sagdeev potential is extracted, and the condition of generation of IA waves in the form of cnoidal waves or solitons is discussed in detail. In this work, the domain of allowable values of nonextensivity parameter q for generation of the IA cnoidal wave in the plasma medium is considered. The results show that only the compressive IA wave may generate and propagate in the plasma medium. Increasing the strength of external magnetic field will increase the frequency of the wave and decrease its amplitude, while increasing the angle of propagation will decrease the frequency of the wave and increase its amplitude.

Coupled drift and ion-acoustic cnoidal waves in an inhomogeneous plasma with field-aligned shear flow

The coupled drift and ion-acoustic cnoidal wave structures in an inhomogeneous plasma with shear flow along the magnetic field lines are investigated. The linear analysis and instability condition of the electrostatic drift and ion acoustic waves with the shear flow is also presented. The Sagdeev potential approach is employed for studying nonlinear periodic wave structures. The analytical solutions of cnoidal wave and soliton structures for coupled drift and ion-acoustic waves in the presence of field-aligned shear flow are obtained. It is found that the shear flow along the magnetic field has a significant effect on the formation of cnoidal waves and solitons in inhomogeneous plasmas. The numerical results in phase plane portraits of cnoidal and soliton structures of coupled drift and ion-acoustic waves are agreed with the satellite observations of F-region ionosphere containing shear field-aligned flows.

Dust ion-acoustic cnoidal waves in a plasma with two temperature superthermal electrons

An investigation of dust ion-acoustic (DIA) cnoidal waves in unmagnetized collisionless plasma consisting of two temperature superthermal electrons, inertial warm ions, and negatively charged dust grains is presented. Reductive perturbation technique has been used to derive the modified Korteweg-de Vries (mKdV) equation for the study of nonlinear periodic waves. Further, applying the Sagdeev potential approach, energy balance equation is derived. Using the expression for Sagdeev potential in expanded form, the cnoidal wave solution is determined. Both positive and negative potential (compressive and rarefactive) nonlinear DIA cnoidal structures are observed. The effects of parameters like the number density of cold electrons, superthermality of hot and cold electrons, ions to hot electrons temperature ratio, and dust to ion density ratio on the characteristics of DIA cnoidal waves are analyzed.

Nonlinear ion-acoustic cnoidal waves in a dense relativistic degenerate magnetoplasma.

The complex pattern and propagation characteristics of nonlinear periodic ion-acoustic waves, namely, ion-acoustic cnoidal waves, in a dense relativistic degenerate magnetoplasma consisting of relativistic degenerate electrons and nondegenerate cold ions are investigated. By means of the reductive perturbation method and appropriate boundary conditions for nonlinear periodic waves, a nonlinear modified Korteweg-de Vries (KdV) equation is derived and its cnoidal wave is analyzed. The various solutions of nonlinear ion-acoustic cnoidal and solitary waves are presented numerically with the Sagdeev potential approach. The analytical solution and numerical simulation of nonlinear ion-acoustic cnoidal waves of the nonlinear modified KdV equation are studied. Clearly, it is found that the features (amplitude and width) of nonlinear ion-acoustic cnoidal waves are proportional to plasma number density, ion cyclotron frequency, and direction cosines. The numerical results are applied to high density astrophysical situations, such as in superdense white dwarfs. This research will be helpful in understanding the properties of compact astrophysical objects containing cold ions with relativistic degenerate electrons.

Oblique ion-acoustic cnoidal waves in two temperature superthermal electrons magnetized plasma

A study is presented for the oblique propagation of ion acoustic cnoidal waves in a magnetized plasma consisting of cold ions and two temperature superthermal electrons modelled by kappa-type distributions. Using the reductive perturbation method, the nonlinear Korteweg de-Vries equation is derived, which further gives the solutions with a special type of cnoidal elliptical functions. Both compressive and rarefactive structures are found for these cnoidal waves. Nonlinear periodic cnoidal waves are explained in terms of plasma parameters depicting the Sagdeev potential and the phase curves. It is found that the density ratio of hot electrons to ions μ significantly modifies compressive/refractive wave structures. Furthermore, the combined effects of superthermality of cold and hot electrons κc,κh, cold to hot electron temperature ratio σ, angle of propagation and ion cyclotron frequency ωci have been studied in detail to analyze the height and width of compressive/refractive cnoidal waves. The findings in the present study could have important implications in understanding the physics of electrostatic wave structures in the Saturn's magnetosphere where two temperature superthermal electrons are present.

Ion-acoustic cnoidal waves in a quantum plasma

Nonlinear ion-acoustic cnoidal wave structures are studied in an unmagnetized quantum plasma. Using the reductive perturbation method, a Korteweg-de Vries equation is derived for appropriate boundary conditions and nonlinear periodic wave solutions are obtained. The corresponding analytical solution and numerical plots of the ion-acoustic cnoidal waves and solitons in the phase plane are presented using the Sagdeev pseudo-potential approach. The variations in the nonlinear potential of the ion-acoustic cnoidal waves are studied at different values of quantum parameter He which is the ratio of electron plasmon energy to electron Fermi energy defined for degenerate electrons. It is found that both compressive and rarefactive ion-acoustic cnoidal wave structures are formed depending on the value of the quantum parameter. The dependence of the wavelength and frequency on nonlinear wave amplitude is also presented.

Ion-acoustic cnoidal waves in plasmas with warm ions and kappa distributed electrons and positrons

Electrostatic ion-acoustic periodic (cnoidal) waves and solitons in unmagnetized electron-positron-ion (EPI) plasmas with warm ions and kappa distributed electrons and positrons are investigated. Using the reductive perturbation method, the Korteweg-de Vries (KdV) equation is derived with appropriate boundary conditions for periodic waves. The corresponding analytical and various numerical solutions are presented with Sagdeev potential approach. Differences between the results caused by the kappa and Maxwell distributions are emphasized. It is revealed that only hump (compressive) structures of the cnoidal waves and solitons are formed. It is shown that amplitudes of the cnoidal waves and solitons are reduced in an EPI plasma case in comparison with the ordinary electron-ion plasmas. The effects caused by the temperature variations of the warm ions are also discussed. It is obtained that the amplitude of the cnoidal waves and solitons decreases for a kappa distributed (nonthermal) electrons and positrons plasma case in comparison with the Maxwellian distributed (thermal) electrons and positrons EPI plasmas. The existence of kappa distributed particles leads to decreasing of ion-acoustic frequency up to thermal ions frequency.

Ion-acoustic cnoidal wave and associated non-linear ion flux in dusty plasma

Using reductive perturbation method with appropriate boundary conditions, coupled evolution equations for first and second order potentials are derived for ion-acoustic waves in a collisionless, un-magnetized plasma consisting of hot isothermal electrons, cold ions, and massive mobile charged dust grains. The boundary conditions give rise to renormalization term, which enable us to eliminate secular contribution in higher order terms. Determining the non secular solution of these coupled equations, expressions for wave phase velocity and averaged non-linear ion flux associated with ion-acoustic cnoidal wave are obtained. Variation of the wave phase velocity and averaged non-linear ion flux as a function of modulus (k2) dependent wave amplitude are numerically examined for different values of dust concentration, charge on dust grains, and mass ratio of dust grains with plasma ions. It is found that for a given amplitude, the presence of positively (negatively) charged dust grains in plasma decreases (increases) the wave phase velocity. This behavior is more pronounced with increase in dust concentrations or increase in charge on dust grains or decrease in mass ratio of dust grains. The averaged non-linear ion flux associated with wave is positive (negative) for negatively (positively) charged dust grains in the plasma and increases (decreases) with modulus (k2) dependent wave amplitude. For given amplitude, it increases (decreases) as dust concentration or charge of negatively (positively) charged dust grains increases in the plasma.