The role of Cairns–Gurevich distributed electrons on obliquely propagating ion-acoustic waves

We used a new distribution of electrons in a two-component magnetized plasma to study the non-linear ion-acoustic solitary structures. The distribution called “Cairns–Gurevich distribution” describes simultaneously the evolution of the energetic electrons and those trapped in the plasma potential well. A modified KdV equation describing the non-linear comportment of the ion-acoustic wave (IAW) was found by using the standard reductive perturbation technique and the appropriate independent variables. The behaviour of the soliton by changing the plasma parameters has been investigated, and we demonstrated that by decreasing the non-thermality parameter, the soliton solution amplitude is enhanced. In addition, we have discussed the growth rate of the solitary waves by calculating the instability criterion. Through discussion, we have conferred how different plasma parameters, such as the trapping, non-thermality, Mach number, obliqueness via the angle of propagation, and magnetic field via the ion-cyclotron frequency, can affect the solitary wave structures. This kind of theoretical studies can be relevant to understand the non-linear propagation of IA solitary waves plasmas of electrons and particles in laser-plasma interaction, pulsar magnetosphere, the auroral zone, and the upper ionosphere, where plasma with trapped and energetic electrons are often present.     

Effect of Resonant Electrons on Propagation of Nonlinear Electrostatic Drift Waves

A modified Korteweg-de Vries equation in a two-dimensional space comprising the externla magnetic field and the direction normal to a density gradient is derived for a plasma consisting of warm ion fluid (?i = 3) and nonisothermal electrons (?e > 1). The effect of ionic temperature and resonant electrons (both trapped and free electrons) on the amplitude and the width of the drift solitary wave is examined.     

Propagation of ion-acoustic waves in a dusty plasma with non-isothermal electrons

For an unmagnetised collisionless plasma consisting of warm ions, nonisothermal electrons and cold, massive and charged dust grains, the Sagdeev potential equation, considering both ion dynamics and dust dynamics has been derived. It has been observed that the Sagdeev potential V(ϕ) exists only for ϕ > 0 up to an upper limit (ϕ ≃ 1.2). This implies the possibility of existence of compressive solitary wave in the plasma. Exhaustive numerics done for both the large-amplitude and small-amplitude ion-acoustic waves have revealed that various parameters, namely, ion temperature, non-isothermality of electrons, Mach numbers etc. have considerable impact on the amplitude as well as the width of the solitary waves. Dependence of soliton profiles on the ion temperature and the Mach number has also been graphically displayed. Moreover, incorporating dust-charge fluctuation and non-isothermality of electrons, a non-linear equation relating the grain surface potential to the electrostatic potential has been derived. It has been solved numerically and interdependence of the two potentials for various ion temperatures and orders of non-isothermality has been shown graphically.      

Effect of dust charge variation on dust—acoustic solitary waves in a magnetized two—ion—temperature dusty plasma

The effect of dust charge variation on the dust-acoustic solitary structures is investigated in a warm magnetized two-ion-temperature dusty plasma consisting of a negatively and variably charged extremely massive dust fluid and ions of two different temperatures. It is shown that the dust charge variation as well as the presence of a second component of ions would modify the properties of the dust-acoustic solitary structures and may exite both dust-acoustic solitary holes (soliton waves with a density dip) and positive solitons (soliton waves with a density hump).     

对含有非热力学平衡离子的尘埃等离子体中孤波特性的理论研究

得到了描述由尘埃颗粒电荷变化、非热力学平衡分布的离子和Boltzmann分布的电子组成的未磁化的热尘埃等离子体中的尘埃声波的修正的KdV (mKdV) 方程. 并对诸多的尘埃等离子体参数对尘埃声孤波结构的影响进行了理论研究，结果表明，尘埃等离子体参数决定着尘埃声孤波结构，且只在这些参数特别选定的一些区域，才会出现稳定的孤波. 关键词： 非热力学平衡离子 尘埃颗粒电荷变化 尘埃声孤波     

Current-driven electron drift solitons

The soliton formation by the current-driven drift-like wave is investigated for heavier ion (such as barium) plasma experiments planned to be performed in future. It is pointed out that the sheared flow of electrons can give rise to short scale solitary structures in the presence of stationary heavier ions. The nonlinearity appears due to convective term in the parallel equation of motion and not because of temperature gradient unlike the case of low frequency usual drift wave soliton. This higher frequency drift-like wave requires sheared flow of electrons and not the density gradient to exist.     

New explicit exact solutions to a nonlinear dispersive－dissipative equation

Using the first-integral method, we obtain a series of new explicit exact solutions such as exponential function solutions, triangular function solutions, singular solitary wave solution and kink solitary wave solution of a nonlinear dispersive－dissipative equation, which describes weak nonlinear ion-acoustic waves in plasma consisting of cold ions and warm electrons.     

A numerical study of the transient behaviors of solitary waves inrelativistic plasmas

The authors study the transient behaviors of solitary waves in a relativistic plasma with nonisothermal electrons. In particular, the modified Korteweg-de Vries (K-dV) equation is solved numerically with a Gaussian function as the initial condition. In addition, it is found that the time evolution of solitons from the initial profile is quite similar to that of a K-dV equation with the exception that the soliton speeds are faster. It is also found that the relativistic ions and the nonisothermal electrons tend to have a similar effect on the soliton behavior of the wave, making nonisothermal electrons more noticeable     

The Nonlinear Langmuir Waves in a Multi-ion-Component Plasma

We investigated the nonlinear Langmuir waves in a multi-ion-component low-temperature plasma. Beginning with the fluid theory of plasma, and taking fully nonlinear response of the low-frequency ion motion into account, we derived a set of equations governing the nonlinear coupling of the amplitude of the Langmuir wave and the low-frequency perturbation density. Using the Sagdeev potential method, we analyzed the characteristics of solitary wave. In the limit of small amplitude, the envelope soliton was found. Our investigation demonstrates that the properties of soliton in a multi-ion-component plasma are different from those of soliton in an electron-ion plasma.     

Ion acoustic solitary waves in density and temperature gradients

The propagation of ion-acoustic K-dV solitary waves in weakly inhomogeneous, collisionless plasmas with gradients both in the density and the temperature of the ions has been considered. The electrons are assumed to be hot and isothermal, and the ions to be warm and adiabatic. The reductive perturbation analysis of the fluid equations is then carried out. The zero order quantities existing in the system due to the presence of the inhomogeneities are taken into account consistently and a set of ‘stretched coordinates’ appropriate for the inhomogeneous system is employed. A more general modified K-dV equation has been derived and its soliton solution is obtained explicitly. It is shown that as the soliton propagates along the temperature gradient, its amplitude and the velocity decrease, and the width increases. Further, it is found that when the two gradients are in opposite directions, the amplitude of the soliton remains constant.     

Electron-Acoustic Solitary Waves in a Two-Electron Temperature Plasma

Using fluid model the propagation of the solitary wave has been analytically investigated in a plasma of two-temperature electrons and ions. It is found that under suitable conditions ion-acoustic solitons of compressive nature and electron-acoustic solitons of rare-factive nature can exist.     

Weak dissipation of electrostatic solitary structures in warm collisional pair-ion plasmas with non-Maxwellian electron population

The localized electrostatic structures with dissipation due to ion-neutral collisions in a symmetric warm pair-ion plasma in the presence of non-Maxwellian population of electrons are studied. The analytical model for ion dynamics is based on fluid equations and the evolution equation is derived by using the reductive perturbation scheme in the form of a damped Korteweg-de Vries equation. The parameter regime relevant to space-based observations and laboratory plasmas is considered and time evolution of the propagating ion-acoustic soliton is discussed. The energetic-particles-driven properties of soliton for various spectral indices, dissipation, ion temperature, and density are illustrated with comparison to the thermal mode for Boltzmann distribution of electrons.     

Propagation of Electron Acoustic Soliton,Periodic and Shock Waves in Dissipative Plasma with a q-Nonextensive Electron Velocity Distribution

The nonlinear properties of small amplitude electron-acoustic(EA) solitary and shock waves in a homogeneous system of unmagnetized collisionless plasma with nonextensive distribution for hot electrons have been investigated.A reductive perturbation method used to obtain the Kadomstev-Petviashvili-Burgers equation.Bifurcation analysis has been discussed for non-dissipative system in the absence of Burgers term and reveals different classes of the traveling wave solutions.The obtained solutions are related to periodic and soliton waves and their behavior are shown graphically.In the presence of the Burgers term,the EXP-function method is used to solve the Kadomstev-Petviashvih-Burgers equation and the obtained solution is related to shock wave.The obtained results may be helpful in better conception of waves propagation in various space plasma environments as well as in inertial confinement fusion laboratory plasmas.     

Propagation of Electron Acoustic Soliton,Periodic and Shock Waves in Dissipative Plasma with a q-Nonextensive Electron Velocity Distribution

The nonlinear properties of small amplitude electron-acoustic (EA) solitary and shock waves in a homogeneous system of unmagnetized collisionless plasma with nonextensive distribution for hot electrons have been investigated. A reductive perturbation method used to obtain the Kadomstev-Petviashvili-Burgers equation. Bifurcation analysis has been discussed for non-dissipative system in the absence of Burgers term and reveals different classes of the traveling wave solutions. The obtained solutions are related to periodic and soliton waves and their behavior are shown graphically. In the presence of the Burgers term, the EXP-function method is used to solve the Kadomstev-Petviashvili-Burgers equation and the obtained solution is related to shock wave. The obtained results may be helpful in better conception of waves propagation in various space plasma environments as well as in inertial confinement fusion laboratory plasmas.     

Electrostatic cnoidal waves and soliton structures in multi‐ions plasmas

Using a reductive perturbation technique (RPT), the Korteweg‐de Vries (KdV) equation for nonlinear electrostatic waves in multi‐ion plasmas is derived with appropriate boundary conditions. Furthermore, compressive and rarefactive cnoidal wave and soliton solutions are discussed. In our model, the multi‐ion plasma consists of light dynamic warm ions, heavy cold ions, and inertialess electrons, which follows the Maxwell‐Boltzmann distribution. It is observed that in such an unmagnetized multi‐ion plasma, two characteristic electrostatic waves i.e., slow ion‐acoustic (SIA) waves and fast ion‐acoustic (FIA) waves, can propagate. The results are discussed by considering two types of multi‐ion plasmas i.e., H⁺–O⁺–e plasma and H^?–O⁺–e plasma that exist in space plasmas. It is found that for H⁺–O⁺–e plasma, the SIA cnoidal wave and soliton form both positive (compressive) and negative (rarefactive) potential pulses, which depend on the temperature and density of the light and warm ions. However, only electrostatic positive potential structures are obtained for FIA cnoidal wave and soliton in H⁺–O⁺–e plasma. In the case of H^?–O⁺–e plasma, the SIA cnoidal wave and soliton form only compressive structures, while the FIA cnoidal wave and soliton compose rarefactive structures. The effects of light ions' density and temperature on nonlinear potential structures are investigated in detail. The parametric results are also demonstrated, which are applicable to space and laboratory multi‐ion plasma situations.     

On the modulation of ion-acoustic solitary waves in a cylindrical warm plasma near critical density

Summary We have derived a modified cylindrical K-dV (MCK-dV) equation for an ion-acoustic wave in a warm plasma with two-temperature electrons, in a cylindrical geometry, near the critical density where the nonlinearity of the usual CK-dV vanishes. The solitary-wave solution of MCK-dV is then discussed analytically using the concept of adiabatic invariants and the basic theorem due to Lax, instead of any numerical evaluation. This modulated form of the solitary wave is then discussed graphically as regards its variation with respect to the change in concentration of law- and high-temperature electrons.     

Stability of two-dimensional ion acoustic solitons

A modified KdV equation for two-dimensional ion acoustic soliton has been derived for warm (adiabatic) ions and hot isothermal electrons in a collision free plasma. Its solution is found to be stable against transverse perturbations.     

Ion-acoustic waves in plasma of warm ions and isothermal electrons using time-fractional KdV equation

The ion-acoustic solitary wave in collisionless unmagnetized plasma consisting of warm ions-fluid and isothermal electrons is studied using the time fractional KdV equation. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation for small but finite amplitude ion-acoustic wave in warm plasma. The Lagrangian of the time fractional KdV equation is used in a similar form to the Lagrangian of the regular KdV equation with fractional derivative for the time differentiation. The variation of the functional of this Lagrangian leads to the Euler-Lagrange equation that gives the time fractional KdV equation. The variational-iteration method is used to solve the derived time fractional KdV equation. The calculations of the solution are carried out for different values of the time fractional order. These calculations show that the time fractional can be used to modulate the electrostatic potential wave instead of adding a higher order dissipation term to the KdV equation. The results of the present investigation may be applicable to some plasma environments,such as the ionosphere plasma.     

Obliquely propagating quantum solitary waves in quantum‐magnetized plasma with ultra‐relativistic degenerate electrons and positrons

The oblique propagation of the quantum electrostatic solitary waves in magnetized relativistic quantum plasma is investigated using the quantum hydrodynamic equations. The plasma consists of dynamic relativistic degenerate electrons and positrons and a weakly relativistic ion beam. The Zakharov‐Kuznetsov equation is derived using the standard reductive perturbation technique that admits an obliquely propagating soliton solution. It is found that two types of quantum acoustic modes, that is, a slow acoustic mode and fast acoustic mode, could be propagated in our plasma model. The parameter that determines the nature of soliton, that is, compressive or rarefactive soliton, for slow mode is investigated. Our numerical results show that for the slow mode, the determining parameter is ion beam velocity in the case of relativistic degenerate electrons. We also have examined the effects of plasma parameters (like the beam velocity, the density ratio of positron to electron, the relativistic factor, and the propagation angle) on the characteristics of solitary waves.     

Nonlinear ion-acoustic waves in magnetized plasmas in presence of energetic electrons and positively charged dust

A theoretical investigation has been carried out for exploring different features of ion-acoustic solitary and shock waves in a three-component magnetized plasma containing a mixture of thermal and nonthermal (energetic) inertialess electrons, warm inertial ions, and positively charged stationary dust particles. The standard Korteweg-de Vries (Burgers) equation has been derived by employing the reductive perturbation method, and its solitary (shock) wave solution has been derived and examined analytically as well as numerically. The latter exhibits characteristic properties (amplitude, width, speed, and polarity) of the ion-acoustic solitary and shock waves. It has been shown that the ion-acoustic solitary and shock waves are significantly modified by different plasma parameters (viz. parameter measuring the ratio of dust charge density to ion charge density, parameter measuring the fraction of energetic electrons, parameter measuring ion or electron temperature, and the external magnetic field). The present investigation may help in understanding the physics of various nonlinear phenomena formed in many space plasma systems, (viz. earth's mesosphere, solar wind, and cometary tails) and laboratory devices (laboratory experiments of Samarian et al., Phys. rev. E. 64 , 056407 [2001] and of Fortov et al., New J. Physics 5 , 102 [2003]).