Dust acoustic solitary waves in non-thermal plasmas consisting of negatively charged dust grains and isothermal electrons

2009 ◽  
Vol 75 (4) ◽  
pp. 455-474 ◽  
Author(s):  
ANIMESH DAS ◽  
ANUP BANDYOPADHYAY
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Acoustic Waves ◽  
Kdv Equation ◽  
Thermal Parameter ◽  
Charged Dust ◽  
Average Temperature ◽  
The Kdv Equation ◽  
Dust Acoustic Solitary Waves ◽  
Dust Acoustic

AbstractA Korteweg–de Vries (KdV) equation is derived here, that describes the nonlinear behaviour of long-wavelength weakly nonlinear dust acoustic waves propagating in an arbitrary direction in a plasma consisting of static negatively charged dust grains, non-thermal ions and isothermal electrons. It is found that the rarefactive or compressive nature of the dust acoustic solitary wave solution of the KdV equation does not depend on the dust temperature if σdc < 0 or σdc > σd*, where σdc is a function of β1, α and μ only, and σd*(<1) is the upper limit (upper bound) of σd. This β1 is the non-thermal parameter associated with the non-thermal velocity distribution of ions, α is the ratio of the average temperature of the non-thermal ions to that of the isothermal electrons, μ is the ratio of the unperturbed number density of isothermal electrons to that of the non-thermal ions, Zdσd is the ratio of the average temperature of the dust particles to that of the ions and Zd is the number of electrons residing on the dust grain surface. The KdV equation describes the rarefactive or the compressive dust acoustic solitary waves according to whether σdc < 0 or σdc > σd*. When 0 ≤ σdc ≤ σd*, the KdV equation describes the rarefactive or the compressive dust acoustic solitary waves according to whether σd > σdc or σd < σdc. If σd takes the value σdc with 0 ≤ σdc ≤ σd*, the coefficient of the nonlinear term of the KdV equation vanishes and, for this case, the nonlinear evolution equation of the dust acoustic waves is derived, which is a modified KdV (MKdV) equation. A theoretical investigation of the nature (rarefactive or compressive) of the dust acoustic solitary wave solutions of the evolution equations (KdV and MKdV) is presented with respect to the non-thermal parameter β1. For any given values of α and μ, it is found that the value of σdc completely defines the nature of the dust acoustic solitary waves except for a small portion of the entire range of the non-thermal parameter β1.

Non-planar dust-acoustic solitary waves and double layers in a four-component dusty plasma with super thermal electrons

2013 ◽  
Vol 79 (5) ◽  
pp. 691-698 ◽  
Author(s):  
PRASANTA CHATTERJEE ◽  
DEB KUMAR GHOSH ◽  
UDAY NARAYAN GHOSH ◽  
BISWAJIT SAHU
Keyword(s):  
Dusty Plasma ◽  
Solitary Waves ◽  
Nonlinear Coefficient ◽  
Thermal Parameter ◽  
Reductive Perturbation Method ◽  
Double Layers ◽  
Planar Geometry ◽  
Charged Dust ◽  
Dust Acoustic Solitary Waves ◽  
Dust Acoustic

AbstractThe properties of non-planar (cylindrical and spherical) dust-acoustic solitary waves (DA SWs) and double layers (DLs) in an unmagnetised collisionless four-component dusty plasma, whose constituents are positively and negatively charged dust grains, super thermal electrons and Boltzmannian ions are investigated by deriving the modified Gardner (MG) equation. The well known reductive perturbation method is employed to derive the MG equation and solve it numerically to study the nonlinear features of the finite amplitude non-planar DA Gardner solitons (GSs) and DLs, which are shown to exist for κ around its critical value κc (where, κ is the super thermal parameter and κc is the value of κ corresponding to the vanishing of the nonlinear coefficient of the Korteweg-de Vries (K-dV) equation). It is seen that the properties of non-planar DA SWs and DLs are significantly differs in non-planar geometry from planar geometry. It is also found that the magnitude of the amplitude of positive and negative GSs decreases with κ and the width of positive and negative GSs increases with the increase of κ.

Localized coherent nonlinear wave structures in dusty plasma with non-thermal ions

2007 ◽  
Vol 73 (6) ◽  
pp. 921-932 ◽  
Author(s):  
TARSEM SINGH GILL ◽  
CHANCHAL BEDI ◽  
NARESHPAL SINGH SAINI ◽  
HARVINDER KAUR
Keyword(s):  
Perturbation Method ◽  
Solitary Waves ◽  
Vries Equation ◽  
Thermal Parameter ◽  
Reductive Perturbation Method ◽  
Double Layers ◽  
Dust Charge ◽  
Dust Acoustic Solitary Waves ◽  
Reductive Perturbation ◽  
Dust Acoustic

AbstractIn the present research paper, the characteristics of dust-acoustic solitary waves (DASWs) and double layers (DLs) are studied. Ions are treated as non-thermal and variable dust charge is considered. The Korteweg–de Vries equation is derived using a reductive perturbation method. It is noticed that compressive solitons are obtained up to a certain range of relative density δ (=ni0/ne0) beyond which rarefactive solitons are observed. The study is further extended to investigate the possibility of DLs. Only compressive DLs are permissible. Both DASWs and DLs are sensitive to variation of the non-thermal parameter.

Effect of Higher-Order Corrections on the Propagation of Nonlinear Dust-Acoustic Solitary Waves in Mesospheric Dusty Plasmas

2006 ◽  
Vol 61 (7-8) ◽  
pp. 316-322 ◽  
Author(s):  
Sayed A. Elwakil ◽  
Mohamed T. Attia ◽  
Mohsen A. Zahran ◽  
Emad K. El-Shewy ◽  
Hesham G. Abdelwahed
Keyword(s):  
Acoustic Waves ◽  
Kdv Equation ◽  
Type Equation ◽  
Dusty Plasmas ◽  
Higher Order ◽  
Reductive Perturbation Method ◽  
Dust Acoustic Solitary Waves ◽  
Dust Acoustic ◽  
Renormalization Method ◽  
Higher Order Corrections

The contribution of the higher-order correction to nonlinear dust-acoustic waves are studied using the reductive perturbation method in an unmagnetized collisionless mesospheric dusty plasma. A Korteweg - de Vries (KdV) equation that contains the lowest-order nonlinearity and dispersion is derived from the lowest order of perturbation, and a linear inhomogeneous (KdV-type) equation that accounts for the higher-order nonlinearity and dispersion is obtained. A stationary solution is achived via renormalization method

scholarly journals Plasma Parameters Effects on Dust Acoustic Solitary Waves in Dusty Plasmas of Four Components

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Abeer A. Mahmoud ◽  
Essam M. Abulwafa ◽  
Abd-alrahman F. Al-Araby ◽  
Atalla M. Elhanbaly
Keyword(s):  
Solitary Waves ◽  
Kdv Equation ◽  
Nonlinear Coefficient ◽  
Dusty Plasmas ◽  
Reductive Perturbation Method ◽  
Plasma Parameters ◽  
First Order ◽  
Dust Acoustic Solitary Waves ◽  
Reductive Perturbation ◽  
Dust Acoustic

The presence and propagation of dust-acoustic solitary waves in dusty plasma contains four components such as negative and positive dust species beside ions and electrons are studied. Both the ions and electrons distributions are represented applying nonextensive formula. Employing the reductive perturbation method, an evolution equation is derived to describe the small-amplitude dust-acoustic solitons in the considered plasma system. The used reductive perturbation stretches lead to the nonlinear KdV and modified KdV equations with nonlinear and dispersion coefficients that depend on the parameters of the plasma. This study represents that the presence of compressive or/and rarefactive solitary waves depends mainly on the value of the first-order nonlinear coefficient. The structure of envelope wave is undefined for first-order nonlinear coefficient tends to vanish. The coexistence of the two types of solitary waves appears by increasing the strength of nonlinearity to the second order using the modified KdV equation.

Dust-acoustic solitary waves in a dusty plasma with dust of opposite polarity and vortex-like ion distribution

2013 ◽  
Vol 79 (5) ◽  
pp. 859-865 ◽  
Author(s):  
M. A. ZAHRAN ◽  
E. K. EL-SHEWY ◽  
H. G. ABDELWAHED
Keyword(s):  
Dusty Plasma ◽  
Constant Temperature ◽  
Solitary Waves ◽  
Opposite Polarity ◽  
Charge Ratio ◽  
Charged Dust ◽  
Dust Acoustic Solitary Waves ◽  
Dust Acoustic ◽  
Dust Fluid ◽  
Positively Charged

AbstractThe nonlinear propagation of small but finite-amplitude dust-acoustic solitary waves in an unmagnetized, collisionless dusty plasma has been investigated. The fluid model is a generalization to the model of Mamun and Shukla to a more realistic space dusty plasma in different regions of space, viz., cometary tails, mesosphere, and Jupiter's magnetosphere, by considering a four-component dusty plasma consisting of the charged dusty plasma of opposite polarity, isothermal electrons and vortex-like ion distributions in the ambient plasma. A reductive perturbation method was employed to obtain a modified Korteweg–de Vries equation for the first-order potential. The effect of the presence of a positively charged dust fluid, the specific charge ratio μ, the temperature of the positively charged dust fluid, the ratio of constant temperature of free hot ions and the constant temperature of trapped ions, and ion temperature on the soliton properties and dusty grains energy are discussed.

scholarly journals Effect of Size Distribution on the Dust Acoustic Solitary Waves in Dusty Plasma with Two Kinds of Nonthermal Ions

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Samira Sharif Moghadam ◽  
Davoud Dorranian
Keyword(s):  
Dusty Plasma ◽  
Solitary Waves ◽  
Perturbation Methods ◽  
Relative Size ◽  
Dust Particles ◽  
Charged Dust ◽  
Kp Equation ◽  
Dust Acoustic Solitary Waves ◽  
Dust Acoustic ◽  
Frequency Changes

Effect of dust size, mass, and charge distributions on the nonlinear dust acoustic solitary waves (DASWs) in a dusty plasma including negatively charged dust particles, electrons, and nonthermal ions has been studied analytically. Dust particles masses and electrical charges are assumed to be proportional with dust size. Using reductive perturbation methods the Kadomtsev-Petviashvili (KP) equation is derived and its solitary answers are extracted. The coefficients of nonlinear term of KP equation are affected strongly by the size of dust particles when the relative size (the ratio of the largest dust radius to smallest dust radius) is smaller than 2. These coefficients are very sensitive toα, the nonthermal coefficient. According to the results, only rarefactive DASWs will generate in such dusty plasma. Width of DASW increases with increasing the relative size and nonthermal coefficient, while their amplitude decreases. The dust cyclotron frequency changes with relative size of dust particles.

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