Nonlinear Coupling of Ion-Acoustic Waves in a Collisionless Plasma

1972 ◽  
Vol 15 (11) ◽  
pp. 2020 ◽  
Author(s):  
L. P. Mix
Keyword(s):  
Acoustic Waves ◽  
Collisionless Plasma ◽  
Nonlinear Coupling ◽  
Ion Acoustic Waves ◽  
Ion Acoustic

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.

scholarly journals Modulation Instability of Ion-Acoustic Waves in Plasma with Nonthermal Electrons

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Basudev Ghosh ◽  
Sreyasi Banerjee
Keyword(s):  
Acoustic Waves ◽  
Modulational Instability ◽  
Perturbation Technique ◽  
Collisionless Plasma ◽  
Multiple Scale ◽  
Ion Temperature ◽  
Nls Equation ◽  
Ion Acoustic Waves ◽  
Nonthermal Electrons ◽  
Ion Acoustic

Modulational instability of ion-acoustic waves has been theoretically investigated in an unmagnetized collisionless plasma with nonthermal electrons, Boltzmann positrons, and warm positive ions. To describe the nonlinear evolution of the wave amplitude a nonlinear Schrödinger (NLS) equation has been derived by using multiple scale perturbation technique. The nonthermal parameter, positron concentration, and ion temperature are shown to play significant role in the modulational instability of ion-acoustic waves and the formation of envelope solitons.

Modulational instability of ion acoustic waves in the presence of density gradients

1979 ◽  
Vol 57 (5) ◽  
pp. 642-644 ◽  
Author(s):  
I. R. Durrani ◽  
G. Murtaza ◽  
H. U. Rahman
Keyword(s):  
Density Gradient ◽  
Acoustic Waves ◽  
Schrodinger Equation ◽  
Modulational Instability ◽  
Collisionless Plasma ◽  
Higher Order ◽  
Density Gradients ◽  
Ion Acoustic Waves ◽  
Ion Acoustic ◽  
Non Linear

Using the Krylov–Bogoliubov–Mitropolsky method of perturbation for weak non-linearities, we study the modulational instability of ion-acoustic waves in a collisionless plasma in the presence of a density gradient. We find that the density gradient of second or higher order of perturbation does not effect the dispersion and the non-linearity coefficients in the non-linear Schrödinger equation.

scholarly journals The Excitation of Ion-acoustic Waves by a Magnetic Pump in Cylindrical Geometry

1983 ◽  
Vol 36 (5) ◽  
pp. 675
Author(s):  
NF Cramer ◽  
IJ Donnelly
Keyword(s):  
Growth Rate ◽  
Growth Rates ◽  
Acoustic Waves ◽  
Pump Wave ◽  
Modulational Instability ◽  
Collisionless Plasma ◽  
Cylindrical Geometry ◽  
Alfvén Waves ◽  
Ion Acoustic Waves ◽  
Ion Acoustic

The modulational, parametric and purely 8rowing mode instabilities of a magnetic pump with a finite radial wavenumber in cylindrical geometry are investigated. The modulational instability is compared with the instability of a parallel propagating pump wave, and the growth rates are found to be similar. The growth rate of a pair of ion-acoustic waves is shown to be zero for a collisionless plasma, in agreement with less general results found previously. The growth rate in the collisional case is found to be nonzero. The purely growing mode growth rate is calculated for excitation of ionacoustic plus torsional Alfven waves.

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