Bifurcation Analysis for Small-Amplitude Nonlinear and Supernonlinear Ion-Acoustic Waves in a Superthermal Plasma

2020 ◽  
Vol 75 (3) ◽  
pp. 183-191 ◽  
Author(s):  
Durga Prasad Chapagai ◽  
Jharna Tamang ◽  
Asit Saha
Keyword(s):  
Dynamical Systems ◽  
Bifurcation Analysis ◽  
Acoustic Waves ◽  
Small Amplitude ◽  
Perturbation Technique ◽  
Travelling Wave ◽  
Mkdv Equation ◽  
Ion Acoustic Waves ◽  
Ion Acoustic ◽  
Superthermal Plasma

AbstractBifurcation analysis of small-amplitude nonlinear and supernonlinear periodic ion-acoustic waves (SNPIAWs) is reported in a three-constituent superthermal plasma composing of cold fluid ions and kappa-distributed electrons of two temperatures (cold and hot). Using the reductive perturbation technique, the plasma system is studied under the Korteweg-de Vries (KdV) and the modified KdV (mKdV) equations. Furthermore, the KdV and mKdV equations are transformed into planar dynamical systems applying travelling wave transfiguration. Possible qualitative phase profiles for the corresponding dynamical systems controlled by system parameters ($\kappa,{\alpha_{c}},{\alpha_{h}}$ and f) are shown. Small-amplitude SNPIAW solution for the mKdV equation is presented for the first time. Small-amplitude nonlinear periodic ion-acoustic wave (NPIAW) and ion-acoustic solitary wave solutions (IASWS) for both the KdV and mKdV equations are obtained. Effects of parameters κ and αh on IASW, NPIAW and SNPIAW solutions are investigated.

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 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.

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.

The theory of nonlinear ion-acoustic waves revisited

1996 ◽  
Vol 56 (3) ◽  
pp. 441-450 ◽  
Author(s):  
W. Malfliet ◽  
E. Wieërs
Keyword(s):  
Acoustic Waves ◽  
Collisionless Plasma ◽  
Travelling Wave ◽  
Perturbation Approach ◽  
Third Order ◽  
Ion Acoustic Waves ◽  
First Order ◽  
Basic Set ◽  
Ion Acoustic ◽  
Higher Order Corrections

The basic set of equations describing nonlinear ion-acoustic waves in a cold collisionless plasma, in the limit of long wavelengths, is reconsidered. First, a travelling-wave solution is found up to third order by means of a straightforward perturbation approach based on the smallness of the wavenumber. As a result, a positive dressed solitary wave shows up, which is larger, taller and faster than the KdV soliton, the first-order result. Furthermore, the accuracy of this approach is tested and compared with previous result. Secondly, the reductive perturbation techique to study higher-order corrections is revised and adapted to the present problem.

Multistability and chaotic scenario in a quantum pair-ion plasma

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Barsha Pradhan ◽  
Sayan Mukherjee ◽  
Asit Saha ◽  
Hayder Natiq ◽  
Santo Banerjee
Keyword(s):  
Lyapunov Exponents ◽  
Acoustic Waves ◽  
Negative Ions ◽  
Travelling Wave ◽  
Basins Of Attraction ◽  
Quantum Plasma ◽  
Ion Acoustic Waves ◽  
Ion Acoustic ◽  
Arbitrary Amplitude ◽  
Basic Equations

AbstractMultistability and chaotic scenario of arbitrary amplitude ion-acoustic waves in a quantum plasma consisting of negative ions, positive ions and electrons are investigated. The normalized basic equations are transformed to a four dimensional conservative dynamical system by introducing a travelling wave variable. Stability of the fixed points for the corresponding linearized system is briefly examined. Chaotic and quasi-periodic features of the arbitrary amplitude ion-acoustic waves are discussed using effective tools, viz. phase orientations, time series graph and graphs of Lyapunov exponents. Multistability phenomena is established with the help of phase spaces, largest Lyapunov exponents and cross-section of basins of attraction. The chaotic phenomena is further verified by 0−1 test. Results of this study can be applied in understanding dynamical phenomena of arbitrary amplitude ion-acoustic waves in quantum pair-ion plasmas.

Three-dimensional stability of ion-acoustic solitary waves in a magnetized plasma consisting of non-isothermal electrons

1998 ◽  
Vol 59 (2) ◽  
pp. 333-342 ◽  
Author(s):  
G. GHOSH ◽  
K. P. DAS
Keyword(s):  
Stability Analysis ◽  
Solitary Wave ◽  
Acoustic Waves ◽  
Solitary Wave Solution ◽  
Three Dimensional ◽  
Perturbation Expansion ◽  
Mkdv Equation ◽  
Magnetized Plasma ◽  
Ion Acoustic Waves ◽  
Ion Acoustic

A stability analysis is performed for solitary ion-acoustic waves in a magnetized plasma in which the electrons are non-isothermal. Including the effect of ion drift velocity and magnetic perturbation, a three-dimensional mKdV equation is derived for ion-acoustic waves. The solitary-wave solution of this equation is found to have a sech4 profile. A stability analysis of this solitary wave is performed using the small-k perturbation expansion method of Rowlands and Infeld. A condition for the onset of instability is obtained. The growth rate of the instability is found to attain a maximum for perturbations in the plane perpendicular to the direction of propagation of the solitary wave.

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