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.

Stability of ion–acoustic solitary waves in a multi-species magnetized plasma consisting of non-thermal and isothermal electrons

2009 ◽  
Vol 75 (5) ◽  
pp. 593-607 ◽  
Author(s):  
SK. ANARUL ISLAM ◽  
A. BANDYOPADHYAY ◽  
K. P. DAS
Keyword(s):  
Stability Analysis ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Perturbation Expansion ◽  
Magnetized Plasma ◽  
Wave Number ◽  
First Order ◽  
Zk Equation ◽  
Ion Acoustic Solitary Waves ◽  
Ion Acoustic

AbstractA theoretical study of the first-order stability analysis of an ion–acoustic solitary wave, propagating obliquely to an external uniform static magnetic field, has been made in a plasma consisting of warm adiabatic ions and a superposition of two distinct populations of electrons, one due to Cairns et al. and the other being the well-known Maxwell–Boltzmann distributed electrons. The weakly nonlinear and the weakly dispersive ion–acoustic wave in this plasma system can be described by the Korteweg–de Vries–Zakharov–Kuznetsov (KdV-ZK) equation and different modified KdV-ZK equations depending on the values of different parameters of the system. The nonlinear term of the KdV-ZK equation and the different modified KdV-ZK equations is of the form [φ(1)]ν(∂φ(1)/∂ζ), where ν = 1, 2, 3, 4; φ(1) is the first-order perturbed quantity of the electrostatic potential φ. For ν = 1, we have the usual KdV-ZK equation. Three-dimensional stability analysis of the solitary wave solutions of the KdV-ZK and different modified KdV-ZK equations has been investigated by the small-k perturbation expansion method of Rowlands and Infeld. For ν = 1, 2, 3, the instability conditions and the growth rate of instabilities have been obtained correct to order k, where k is the wave number of a long-wavelength plane-wave perturbation. It is found that ion–acoustic solitary waves are stable at least at the lowest order of the wave number for ν = 4.

Three-dimensional stability of solitary kinetic Alfvé waves and ion-acoustic waves

1994 ◽  
Vol 51 (1) ◽  
pp. 95-111 ◽  
Author(s):  
G. Ghosh ◽  
K. P. Das
Keyword(s):  
Dimensional Stability ◽  
Acoustic Waves ◽  
Three Dimensional ◽  
Perturbation Expansion ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Ion Acoustic Waves ◽  
Linear Dispersion ◽  
Ion Acoustic ◽  
Kinetic Alfvén Waves

Starting from a set of equations that lead to a linear dispersion relation coupling kinetic Alfvén waves and ion-acoustic waves, three-dimensional KdV equations are derived for these waves. These equations are then used to investigate the three-dimensional stability of solitary kinetic Alfvén waves and ion-acoustic waves by the small-k perturbation expansion method of Rowlands and Infeld. For kinetic Alfvén waves it is found that there is instability if the direction of the plane-wave perturbation lies inside a cone, and the growth rate of the instability attains a maximum when the direction of the perturbation lies in the plane containing the external magnetic field and the direction of propagation of the solitary wave.

scholarly journals Nonlinear Ion-Acoustic Waves in Degenerate Plasma with Landau Quantizatized Trapped Electrons

2021 ◽  
Vol 9 ◽  
Author(s):  
R. Jahangir ◽  
S. Ali
Keyword(s):  
Acoustic Waves ◽  
Solitary Wave Solution ◽  
Perturbation Technique ◽  
Stellar System ◽  
Three Dimensional ◽  
Plasma Parameters ◽  
Ion Acoustic Waves ◽  
Trapped Electrons ◽  
Zk Equation ◽  
Ion Acoustic

The formation of nonlinear ion-acoustic waves is studied in a degenerate magnetoplasma accounting for quantized and trapped electrons. Relying on the reductive perturbation technique, a three-dimensional Zakharov–Kuznetsov (ZK) equation is derived, admitting a solitary wave solution with modified amplitude and width parameters. The stability of the ZK equation is also discussed using the k-expansion method. Subsequently, numerical analyses are carried out for plasma parameters of a dense stellar system involving white dwarf stars. It has been observed that the quantized magnetic field parameter η and degeneracy of electrons (determined by small temperature values T) affect the amplitude and width of the electric potential. The critical point at which the nature of the solitary structure changes from compressive to rarefaction is evaluated. Importantly, the growth rate of the instability associated with a three-dimensional ZK equation depends on the plasma parameters, and higher values of η and T tend to stabilize the solitons in quantized degenerate plasmas. The results of the present study may hold significance to comprehend the properties of wave propagation and instability growth in stellar and laboratory dense 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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