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.

Modified Korteweg—de Vries ion-acoustic solitons in a plasma

1985 ◽  
Vol 34 (3) ◽  
pp. 401-415 ◽  
Author(s):  
Y. Nakamura ◽  
I. Tsukabayashi
Keyword(s):  
Acoustic Waves ◽  
Vries Equation ◽  
Critical Concentration ◽  
Soliton Solutions ◽  
Negative Ions ◽  
Ion Acoustic Waves ◽  
Ion Acoustic ◽  
De Vries ◽  
Component Plasma ◽  
Ion Acoustic Solitons

Propagation of nonlinear ion-acoustic waves in a multi-component plasma with negative ions is investigated experimentally. At a critical concentration of negative ions, both compressive and rarefactive solitons are observed. The velocities and widths of the solitons are measured and compared with the soliton solutions of the modified Korteweg–de Vries equation and of the pseudopotential method. The modified Korteweg–de Vries equation is solved numerically to investigate overtaking collisions of a positive and a negative soliton. Fluid equations together with Poisson's equation are numerically integrated to simulate their head-on collisions.

Weakly relativistic effect on the modulation of nonlinear ion-acoustic waves in a warm plasma

1995 ◽  
Vol 54 (3) ◽  
pp. 295-308 ◽  
Author(s):  
S. K. El-Labany
Keyword(s):  
Perturbation Theory ◽  
Acoustic Waves ◽  
Relativistic Effect ◽  
Type Equation ◽  
Oscillatory Solution ◽  
Ion Temperature ◽  
Ion Acoustic Waves ◽  
Ion Density ◽  
Ion Acoustic ◽  
Warm Plasma

The derivative expansion perturbation method is applied to investigate the modulation of nonlinear ion-acoustic waves in a weakly relativistic warm plasma. At the second order of perturbation theory, a nonlinear Schrödingertype equation for the complex amplitude of the perturbed ion density is obtained. The coefficients in this equation show that the condition of modulational stability is modified by the relativistic effect as well as by the finite ion temperature. The association between the small-wavenumber limit of the nonlinear Schrödinger-type equation and the oscillatory solution of the Korteweg-de Vries equation obtained by reductive perturbation theory is considered. Different limits are considered in order to compare with previous work.

Contribution of higher-order nonlinearity to nonlinear ion-acoustic waves in a weakly relativistic warm plasma. Part 1. Isothermal case

1993 ◽  
Vol 50 (3) ◽  
pp. 495-504 ◽  
Author(s):  
S. K. El-Labany
Keyword(s):  
Perturbation Theory ◽  
Acoustic Waves ◽  
Type Equation ◽  
Higher Order ◽  
Ion Acoustic Waves ◽  
Ion Acoustic ◽  
Warm Plasma ◽  
Relativistic Parameter ◽  
Renormalization Method ◽  
Parameter Dependent

The contribution of higher-order nonlinearity to nonlinear ion-acoustic waves in a weakly relativistic plasma consisting of warm ion-fluid and hot isothermal electrons is investigated using reductive perturbation theory. A Korteweg-de Vries-type equation, with temperature- and relativistic-parameter-dependent coefficients is obtained. The renormalization method is applied to the equations obtained from the different orders of perturbation theory to obtain a stationary solution. Relativistic cold and non-relativistic warm plasma limits are considered in order to make comparisons with previous results.

Contribution of higher-order nonlinearity to nonlinear ion-acoustic waves in a weakly relativistic warm plasma. Part 2. Non-isothermal case

1995 ◽  
Vol 53 (2) ◽  
pp. 245-252 ◽  
Author(s):  
S. K. El-Labany ◽  
S. M. Shaaban
Keyword(s):  
Perturbation Theory ◽  
Acoustic Waves ◽  
Higher Order ◽  
Inhomogeneous Equation ◽  
Ion Acoustic Waves ◽  
Coupled Equations ◽  
Reductive Perturbation ◽  
Ion Acoustic ◽  
Renormalization Method ◽  
Linear Inhomogeneous Equation

The contribution of higher-order nonlinearity to nonlinear ion-acoustic waves in a weakly relativistic plasma consisting of a warm ion fluid and hot non- isothermal electrons is studied using reductive perturbation theory. At the lowest order of the perturbation theory a modified Korteweg–de Vries equation is obtained. At the next order a linear inhomogeneous equation is obtained. The stationary solution of the coupled equations is obtained using the renormalization method introduced by Kodama and Taniuti for reductive perturbation theory.

scholarly journals Soliton Characteristics at the Critical Density of Negative Ions in Ion-beam Plasmas

1990 ◽  
Vol 43 (3) ◽  
pp. 319 ◽  
Author(s):  
GC Das ◽  
Kh lbohanbi Singh
Keyword(s):  
Solitary Waves ◽  
Acoustic Waves ◽  
Ion Beam ◽  
Perturbation Technique ◽  
Critical Density ◽  
Negative Ions ◽  
Ion Acoustic Waves ◽  
Multicomponent Plasma ◽  
Laboratory Plasmas ◽  
Ion Acoustic

By using the reductive perturbation technique, ion-acoustic waves are studied in a generalised multicomponent plasma. The multiple ions modify drastically the characteristics of the solitary waves. In particular, the negative ions have a critical density at which the nonlinearity of the Korteweg-deVries (K-dV) equation vanishes and the ion-acoustic solitary wave is seen to be described by a modified K-dV (mK-dV) equation. Using higher order nonlinearities, the non-uniform transition of the K-dV equation to the mK-dV equation along with the conservation of the Sagdeev potential is described. Theoretical observations on the existence of the solitary waves, as expected, could be of interest in laboratory plasmas

scholarly journals Cylindrical and Spherical Solitons at the Critical Density of Negative Ions in a Generalised Multicomponent Plasma

1991 ◽  
Vol 44 (5) ◽  
pp. 523 ◽  
Author(s):  
GC Das ◽  
Kh Ibohanbi Singh
Keyword(s):  
Solitary Wave ◽  
Acoustic Waves ◽  
Critical Density ◽  
Negative Ions ◽  
Ion Acoustic Waves ◽  
Multicomponent Plasma ◽  
Laboratory Plasmas ◽  
Ion Acoustic ◽  
Geometrical Effects

Propagation of nonlinear ion-acoustic waves in generalised multicomponent plasmas bounded by cylindrical and spherical geometries is investigated. At the critical density of negative ions where the nonlinearity of the Korteweg-deVries (K-dV) equation vanishes, the ion-acoustic solitary wave is described by a modified K-dV (mK-dV) equation. It is also emphasised that near the critical density neither the K-dV nor mK-dV equation is sufficient to describe fully the ion-acoustic waves and thus there is a need to derive a further mK-dV (fmK-dV) equation in the vicinity of this critical density. Furthermore, the amplitude variations of the K-dV and mK-dV solitons depending on the limitations of geometrical effects are also discussed, emphasising that the results could be of interest for diagnosing the soliton properties of laboratory plasmas.

Stability and instability of some nonlinear dispersive solitary waves in higher dimension

1996 ◽  
Vol 126 (1) ◽  
pp. 89-112 ◽  
Author(s):  
Anne de Bouard
Keyword(s):  
Solitary Waves ◽  
Acoustic Waves ◽  
Vries Equation ◽  
Three Dimensional ◽  
Higher Dimension ◽  
Ion Acoustic Waves ◽  
Stability And Instability ◽  
Ion Acoustic ◽  
De Vries ◽  
The Stability

We study the stability of positive radially symmetric solitary waves for a three dimensional generalisation of the Korteweg de Vries equation, which describes nonlinear ion-acoustic waves in a magnetised plasma, and for a generalisation in dimension two of the Benjamin–Bona–Mahony equation.

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