Nonlinear ion-acoustic waves in multicomponent plasmas

1988 ◽  
Vol 66 (1) ◽  
pp. 79-81 ◽  
Author(s):  
G. C. Das ◽  
B. Karmakar
Keyword(s):  
Acoustic Waves ◽  
Kdv Equation ◽  
Perturbation Technique ◽  
Ionic Species ◽  
System Of Equations ◽  
Ion Acoustic Waves ◽  
Plasma Dynamics ◽  
Small Magnitude ◽  
Reductive Perturbation ◽  
Ion Acoustic

By applying the reductive perturbation technique to the basic system of equations governing plasma dynamics, a modified Korteweg–de Vries (KdV) equation is derived. The inclusion of nonisothermality, together with its reduction to a small magnitude, yields various interesting characteristics relating to the existence of solitons in multicomponent plasmas that include several ionic species and multiple nonisothermal electrons. The mathematical development shows that a closed relation among the solitons existing in the various plasmas arises due to the different magnitude of nonisothermalities.

Cylindrical ion-acoustic waves in a warm multicomponent plasma

2000 ◽  
Vol 63 (4) ◽  
pp. 343-353 ◽  
Author(s):  
S. K. EL-LABANY ◽  
S. A. EL-WARRAKI ◽  
W. M. MOSLEM
Keyword(s):  
Perturbation Theory ◽  
Acoustic Waves ◽  
Vries Equation ◽  
Negative Ions ◽  
Ion Acoustic Waves ◽  
Multicomponent Plasma ◽  
Reductive Perturbation ◽  
Ion Acoustic ◽  
Ion Acoustic Solitons ◽  
Warm Plasma

Cylindrical ion-acoustic solitons are investigated in a warm plasma with negative ions and multiple-temperature electrons through the derivation of a cylindrical Korteweg–de Vries equation using a reductive perturbation theory. The results are compared with those for the corresponding planar solitons.

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

2011 ◽  
Vol 20 (4) ◽  
pp. 040508 ◽  
Author(s):  
Sayed A El-Wakil ◽  
Essam M Abulwafa ◽  
Emad K El-Shewy ◽  
Abeer A Mahmoud
Keyword(s):  
Acoustic Waves ◽  
Kdv Equation ◽  
Ion Acoustic Waves ◽  
Ion Acoustic

Higher-order corrections to the ion-acoustic waves in a relativistic plasma (isothermal case)

1988 ◽  
Vol 40 (2) ◽  
pp. 359-367 ◽  
Author(s):  
Gobinda Pada Pakira ◽  
A. Roy Chowdhury ◽  
S. N. Paul
Keyword(s):  
Acoustic Waves ◽  
Kdv Equation ◽  
Perturbation Technique ◽  
Type Equation ◽  
Higher Order ◽  
Relativistic Plasma ◽  
Singular Perturbation Technique ◽  
Ion Acoustic ◽  
Physical Profile ◽  
Higher Order Corrections

As a continuation of our earlier work, we have analysed the higher-order perturbative corrections to the formation of (ion-acoustic) solitary waves in a relativistic plasma. It is found that the relativistic considerations affect the amplitude and width variation - as conjectured in our previous paper. Our analysis employs a higher-order singular perturbation technique, with the elimination of secular terms in stages. In this way we arrive at an inhomogeneous KdV-type equation, which is then solved exactly. At this point a new phenomena arises at a critical value of the phase velocity at which the coefficient of the nonlinear term in the KdV equation vanishes. A new set of stretched co-ordinate is then used to derive a modified KdV equation. In both cases we have numerically computed the specific physical profile of the new solitary wave and its width.

Nonlinear ion–acoustic waves in an inhomogeneous plasma with non-thermal distribution of electrons

2015 ◽  
Vol 81 (3) ◽  
Author(s):  
S. V. Singh
Keyword(s):  
Boundary Layer ◽  
Acoustic Waves ◽  
Kdv Equation ◽  
Thermal Parameter ◽  
Ion Acoustic Waves ◽  
Earth’S Magnetosphere ◽  
Thermal Distribution ◽  
Ion Plasma ◽  
Ion Acoustic ◽  
Earth's Magnetosphere

In the Earth's magnetosphere, the boundary layer regions are the sources for inhomogeneous plasmas and are natural laboratories to study wave phenomena. In these regions, particles distributions also differ from Maxwellian and are found to be non-thermal. Therefore, amplitude of the waves propagating through these regions can vary differently compared to the homogeneous plasmas. In this study, propagation of ion–acoustic waves (IAWs) in an inhomogeneous, warm electron-ion plasma is examined. The electrons are considered to be having non-thermal Cairn's type distribution and ions follow the fluid dynamical equations. Further, inhomogeneity is assumed in equilibrium density of the electrons and ions. The evolution of the nonlinear IAWs is governed by the Korteweg–de Vries (KdV) equation with variable coefficients. Analytical solution of the KdV equation shows that for a cold ion plasma and non-thermal electrons, the amplitude and the width of the nonlinear IAWs decreases and increases, respectively with the inclusion of the non-thermal distribution of electrons. It is interesting to note that nonlinear IAWs in this model can not propagate for whole range of non-thermal parameter, α. The novel result of this study is that for nonlinear IAWs to propagate in the inhomogeneous two component plasma with ions and non-thermal electrons, the non-thermal parameter, α ⩽ 0.155. Results from our study may have impact on the propagation of the IAWs in the boundary layer regions of the Earth's magnetosphere where density inhomogeneities are appreciable.

Modulational instability of ion-acoustic waves in fully relativistic two-component plasma

2015 ◽  
Vol 81 (3) ◽  
Author(s):  
B. Ghosh ◽  
S. Banerjee
Keyword(s):  
Growth Rate ◽  
Acoustic Waves ◽  
Relativistic Effect ◽  
Modulational Instability ◽  
Perturbation Technique ◽  
Multiple Scale ◽  
Nls Equation ◽  
Ion Acoustic Waves ◽  
Ion Acoustic ◽  
Component Plasma

Nonlinear amplitude modulation of ion-acoustic waves (IAWs) in a fully relativistic unmagnetized two-fluid plasma has been theoretically studied by using complete set of fully relativistic dynamic equations. To describe the nonlinear evolution of the wave envelope a nonlinear Schrödinger (NLS) equation is derived by using standard multiple scale perturbation technique. Using this equation it is shown that the wave becomes modulationally unstable as the wavenumber exceeds certain critical value. This critical wavenumber is found to decrease with increase in relativistic effect. The instability growth rate has also been calculated numerically for different values of plasma drift velocity. The growth rate is shown to decrease with increase in the relativistic effect.

Nonlinear modulation of ion-acoustic waves in two-electron-temperature plasmas

2010 ◽  
Vol 76 (2) ◽  
pp. 169-181 ◽  
Author(s):  
A. ESFANDYARI-KALEJAHI ◽  
I. KOURAKIS ◽  
M. AKBARI-MOGHANJOUGHI
Keyword(s):  
Electron Temperature ◽  
Acoustic Waves ◽  
Modulational Instability ◽  
Perturbation Technique ◽  
Density Ratio ◽  
Cold Electron ◽  
Ion Temperature ◽  
Ion Acoustic Waves ◽  
Ion Acoustic ◽  
Nonlinear Modulation

AbstractThe amplitude modulation of ion-acoustic waves is investigated in a plasma consisting of adiabatic warm ions, and two different populations of thermal electrons at different temperatures. The fluid equations are reduced to nonlinear Schrödinger equation by employing a multi-scale perturbation technique. A linear stability analysis for the wave packet amplitude reveals that long wavelengths are always stable, while modulational instability sets in for shorter wavelengths. It is shown that increasing the value of the hot-to-cold electron temperature ratio (μ), for a given value of the hot-to-cold electron density ratio (ν), favors instability. The role of the ion temperature is also discussed. In the limiting case ν = 0 (or ν → ∞), which correspond(s) to an ordinary (single) electron-ion plasma, the results of previous works are recovered.

Nonlinear oblique modulation of ion-acoustic waves in a two warm ion plasma

1986 ◽  
Vol 35 (3) ◽  
pp. 505-517 ◽  
Author(s):  
R. S. Chhabra ◽  
S. R. Sharma
Keyword(s):  
Acoustic Waves ◽  
Modulational Instability ◽  
Perturbation Technique ◽  
Nonlinear Frequency ◽  
Ion Acoustic Waves ◽  
Ion Acoustic ◽  
The Stability ◽  
Ion Species ◽  
Nonlinear Frequency Shift ◽  
Good Agreement

Using the KBM perturbation technique, the stability of oblique modulation on ion-acoustic waves in a plasma with two species of warm ions is studied. The effect of the temperatures of two ion species on the modulational instability is discussed in detail. The nonlinear frequency shift and the change in zeroth-order density are also calculated for different values of ion temperatures. Predictions of the theory are in fairly good agreement with the experimental observation of modulational instability.

Nonlinear excitations and dynamic features of dust ion-acoustic waves in a magnetized electron–positron–ion plasma

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Rabindranath Maity ◽  
Biswajit Sahu
Keyword(s):  
Numerical Simulation ◽  
Acoustic Waves ◽  
Kdv Equation ◽  
Phase Portraits ◽  
Dust Particles ◽  
Superthermal Electrons ◽  
Ion Acoustic Waves ◽  
Nonlinear Excitations ◽  
Ion Acoustic ◽  
Extended Kdv Equation

Abstract A wide class of nonlinear excitations and the dynamics of wave groups of finite amplitude ion-acoustic waves are investigated in multicomponent magnetized plasma system comprising warm ions, and superthermal electrons as well as positrons in presence of negatively charged impurities or dust particles. Employing the reductive perturbation technique (RPT), the Korteweg–de-Vries (KdV) equation, and extended KdV equation are derived. The presence of excess superthermal electrons as well as positrons and other plasma parameters are shown to influence the characteristics of both compressive and rarefactive solitons as well as double layers (DLs). Also, we extend our investigation by deriving the nonlinear Schrödinger equation from the extended KdV equation employing a suitable transformation to study the wave group dynamics for long waves. The analytical and numerical simulation results demonstrate that nonlinear wave predicts solitons, “table-top” solitons, DLs, bipolar structure, rogue waves, and breather structures. Moreover, implementing the concept of dynamical systems, phase portraits of nonlinear periodic, homoclinic trajectories, and supernonlinear periodic trajectories are presented through numerical simulation.

scholarly journals Nonlinear Waveforms for Ion-Acoustic Waves in Weakly Relativistic Plasma of Warm Ion-Fluid and Isothermal Electrons

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
S. A. El-Wakil ◽  
Essam M. Abulwafa ◽  
E. K. El-Shewy ◽  
H. G. Abdelwahed ◽  
Hamdi M. Abd-El-Hamid
Keyword(s):  
Acoustic Waves ◽  
Kdv Equation ◽  
Algebraic Method ◽  
Finite Amplitude ◽  
Reductive Perturbation Method ◽  
Relativistic Plasma ◽  
Plasma Parameters ◽  
Ion Acoustic Waves ◽  
Ion Acoustic ◽  
Weakly Relativistic Plasma

The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small- but finite-amplitude electrostatic ion-acoustic waves in weakly relativistic plasma consisting of warm ions and isothermal electrons. An algebraic method with computerized symbolic computation is applied in obtaining a series of exact solutions of the KdV equation. Numerical studies have been made using plasma parameters which reveal different solutions, that is, bell-shaped solitary pulses, rational pulses, and solutions with singularity at finite points, which called “blowup” solutions in addition to the propagation of an explosive pulses. The weakly relativistic effect is found to significantly change the basic properties (namely, the amplitude and the width) of the ion-acoustic waves. The result of the present investigation may be applicable to some plasma environments, such as ionosphere region.

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