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.

scholarly journals Two-Dimensional Nonlinear Propagation of Ion Acoustic Waves through KPB and KP Equations in Weakly Relativistic Plasmas

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
M. G. Hafez ◽  
M. R. Talukder ◽  
M. Hossain Ali
Keyword(s):  
Acoustic Waves ◽  
Finite Amplitude ◽  
Reductive Perturbation Method ◽  
Nonlinear Propagation ◽  
Two Dimensional ◽  
Ion Acoustic Waves ◽  
Ion Acoustic ◽  
Component Plasma ◽  
Basic Characteristics ◽  
Superthermal Electrons And Positrons

Two-dimensional three-component plasma system consisting of nonextensive electrons, positrons, and relativistic thermal ions is considered. The well-known Kadomtsev-Petviashvili-Burgers and Kadomtsev-Petviashvili equations are derived to study the basic characteristics of small but finite amplitude ion acoustic waves of the plasmas by using the reductive perturbation method. The influences of positron concentration, electron-positron and ion-electron temperature ratios, strength of electron and positrons nonextensivity, and relativistic streaming factor on the propagation of ion acoustic waves in the plasmas are investigated. It is revealed that the electrostatic compressive and rarefactive ion acoustic waves are obtained for superthermal electrons and positrons, but only compressive ion acoustic waves are found and the potential profiles become steeper in case of subthermal positrons and electrons.

scholarly journals Modulational Instability of Ion-Acoustic Waves in Pair-Ion Plasma

Plasma ◽  
2021 ◽  
Vol 5 (1) ◽  
pp. 1-11
Author(s):  
Sharmin Jahan ◽  
Rubaiya Khondoker Shikha ◽  
Abdul Mannan ◽  
A A Mamun
Keyword(s):  
Acoustic Waves ◽  
Modulational Instability ◽  
Thermal Parameter ◽  
Reductive Perturbation Method ◽  
Unstable State ◽  
Plasma Parameters ◽  
Ion Acoustic Waves ◽  
Stable Domain ◽  
Ion Acoustic ◽  
Component Plasma

The modulational instability (MI) of ion-acoustic waves (IAWs) is examined theoretically in a four-component plasma system containing inertialess electrons featuring a non-thermal, non-extensive distribution, iso-thermal positrons, and positively as well as negatively charged inertial ions. In this connection, a non-linear Schrödinger equation (NLSE), which dominates the conditions for MI associated with IAWs, is obtained by using the reductive perturbation method. The numerical analysis of the NLSE reveals that the increment in non-thermality leads to a more unstable state, whereas the enhancement in non-extensivity introduces a less unstable state. It also signifies the bright (dark) ion-acoustic (IA) envelope solitons mode in the unstable (stable) domain. The conditions for MI and its growth rate in the unstable regime of the IAWs are vigorously modified by the different plasma parameters (viz., non-thermal, non-extensive q-distributed electron, iso-thermal positron, the ion charge state, the mass of the ion and positron, non-thermal parameter α, the temperature of electron and positron, etc.). Our findings may supplement and add to prior research in non-thermal, non-extensive electrons and iso-thermal positrons that can co-exist with positive as well as negative inertial ions.

scholarly journals Effects of Boundary and Electron Inertia on the Ion Acoustic Wave in a Plasma: A Pseudopotential Approach

1998 ◽  
Vol 51 (1) ◽  
pp. 113 ◽  
Author(s):  
K. K. Mondal ◽  
S. N. Paul ◽  
A. Roy Chowdhury
Keyword(s):  
Acoustic Waves ◽  
Finite Geometry ◽  
Cylindrical Domain ◽  
Plasma Parameters ◽  
Ion Acoustic Waves ◽  
Ion Acoustic Wave ◽  
Electron Inertia ◽  
Ion Acoustic ◽  
Pseudopotential Approach ◽  
Range Of Values

A pseudopotential approach is used to analyse the propagation of ion-acoustic waves in a plasma bounded by a cylindrical domain. The effect of the finite geometry is displayed both analytically and numerically. The phase velocity of the wave is determined and its variation is studied with respect to the plasma parameters. It is observed that the pseudopotential shows a wide variation of shape due to the imposition of a finite boundary condition. It is shown that if the other parameters are kept within a certain range of values, then the trapping of particles is favoured when the presence of the boundary is taken into account.

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

scholarly journals Effect of Space Fractional Parameter on Nonlinear Ion Acoustic Shock Wave Excitation in an Unmagnetized Relativistic Plasma

2022 ◽  
Vol 9 ◽  
Author(s):  
M.F. Uddin ◽  
M.G. Hafez ◽  
Inho Hwang ◽  
Choonkil Park
Keyword(s):  
Shock Wave ◽  
Fluid Model ◽  
Reductive Perturbation Method ◽  
Relativistic Plasma ◽  
Polar Regions ◽  
Viscous Effects ◽  
Plasma Parameters ◽  
Ion Acoustic ◽  
Acoustic Shock Wave ◽  
Space Environments

In this work, the model equation with space fractional-order (FO) is used to investigate the nonlinear ion acoustic shock wave excitations (NIASWEs) in an unmagnetized collisionless weakly relativistic plasma having inertial relativistic ions fluid with viscous effects, inertial-less non-thermal electrons and inertial-less Boltzmann positrons. To do it, the Korteweg-de Vries Burgers equation (KdVBE) is derived from the considered fluid model equations by implementing the standard reductive perturbation method. Accordingly, such equation is converted to space fractional KdVBE via Agrawal’s variational principle with the help of the beta fractional derivative and its properties. The exact analytical solutions of KdVBE with space FO are determined via the modified Kudryashov method. The influence of space fractional and other related plasma parameters on NIASWEs are investigated. The outcomes would be useful to understand the nature of shocks with the presence of non-local or local space in many astrophysical and space environments (especially in the relativistic wind of pulsar magnetosphere, polar regions of neutron stars, etc.) and further laboratory verification.

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.

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