Higher-order growth rate of instability of obliquely propagating kinetic Alfvén and ion-acoustic solitons in a magnetized non-thermal plasma

2002 ◽  
Vol 68 (4) ◽  
pp. 285-303 ◽  
Author(s):  
ANUP BANDYOPADHYAY ◽  
K. P. DAS
Keyword(s):  
Growth Rate ◽  
Solitary Waves ◽  
Thermal Plasma ◽  
Perturbation Expansion ◽  
Expansion Method ◽  
Higher Order ◽  
Wave Number ◽  
Ion Acoustic ◽  
Ion Acoustic Solitons ◽  
Non Thermal Plasma

The higher-order growth rate of instability for obliquely propagating kinetic Alfvén and ion-acoustic solitons in a magnetized non-thermal plasma have been obtained by the multiple-scale perturbation expansion method developed by Allen and Rowlands (1993). The growth rate of instability is obtained correct to order k2, where k is the wave number of a long-wavelength plane-wave perturbation. The corresponding lowest-order stability analysis has been considered recently by Bandyopadhyay and Das (2000b). It has been found that the kinetic Alfvén solitary waves are stable at the order of k but are unstable at the order of k2. It has also been found that the growth rate of instability at the order of k for ion-acoustic solitary waves is free from the parameters of the non-thermal plasma but at the order of k2 depends on the parameters of the non-thermal plasma.

Stability of solitary waves in a magnetized non-thermal plasma

1996 ◽  
Vol 56 (1) ◽  
pp. 175-185 ◽  
Author(s):  
A. A. Mamun ◽  
R. A. Cairns
Keyword(s):  
Solitary Waves ◽  
Thermal Plasma ◽  
Three Dimensional ◽  
Perturbation Expansion ◽  
Expansion Method ◽  
Instability Criterion ◽  
Electrostatic Waves ◽  
Non Thermal Plasma ◽  
Stability Of Solitary Waves ◽  
The Stability

A theoretical investigations is made of the stability of electrostatic waves in a magnetized non-thermal plasma. The Zakharov-Kuznetsov equation (or Korteweg-de Vries equation in three dimensionas) for these solitary waves in this plasma system is derived, and their three-dimensional stability is studied by the small-k (long wavelength plane-wave) perturbation expansion method. The instability criterion and its growth rate depending on the magnetic field and the propagation directions of the solitary wave and its perturbation mode are discussed.

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.

Stability of ion-acoustic solitons in a multispecies plasma consisting of non-isothermal electrons

1998 ◽  
Vol 60 (1) ◽  
pp. 151-158 ◽  
Author(s):  
DEBALINA CHAKRABORTY ◽  
K. P. DAS
Keyword(s):  
Acoustic Waves ◽  
Perturbation Expansion ◽  
Expansion Method ◽  
Ion Acoustic Waves ◽  
Long Wavelength ◽  
Petviashvili Equation ◽  
Ion Acoustic ◽  
Ion Acoustic Solitons ◽  
The Stability ◽  
Perturbation Expansion Method

A modified Kadomtsev–Petviashvili equation is derived for ion-acoustic waves in a multispecies plasma consisting of non-isothermal electrons. This equation is used to investigate the stability of modified KdV solitons against long-wavelength plane-wave perturbation using the small-k perturbation expansion method of Rowlands and Infeld. It is found that modified KdV solitons are stable.

Growth rate of instability of obliquely propagating ion-acoustic solitons in a magnetized non-thermal plasma

2001 ◽  
Vol 65 (2) ◽  
pp. 131-150 ◽  
Author(s):  
ANUP BANDYOPADHYAY ◽  
K. P. DAS
Keyword(s):  
Growth Rate ◽  
Thermal Plasma ◽  
Acoustic Waves ◽  
Soliton Solutions ◽  
Plasma Phys ◽  
Weakly Nonlinear ◽  
Long Wavelength ◽  
Zk Equation ◽  
Ion Acoustic ◽  
Non Thermal Plasma

The Korteweg–de Vries–Zakharov–Kuznetsov (KdV–ZK) equation, governing the behaviour of long-wavelength weakly nonlinear ion-acoustic waves propagating obliquely to an external uniform magnetic field in a non-thermal plasma, admits soliton solutions having a sech2 profile. The higher-order growth rates of instability are obtained using the method developed by Allen and Rowlands [J. Plasma Phys.50, 413 (1993); 53, 63 (1995)]. The growth rate of instability is obtained correct to order k2, where k is the wavenumber of a long-wavelength plane-wave perturbation. The case where the coefficient of the nonlinear term in the KdV–ZK equation vanishes is also considered.

Effect of Concentration of Negative Ion and Temperature of both Ions on Amplitude and Width for Non-Thermal Plasma

2015 ◽  
Vol 54 ◽  
pp. 166-183
Author(s):  
Sankar Chattopadhyay
Keyword(s):  
Solitary Waves ◽  
Thermal Plasma ◽  
Negative Ions ◽  
Second Order ◽  
Negative Ion ◽  
Ion Acoustic Solitary Waves ◽  
Ion Acoustic ◽  
Non Thermal Plasma ◽  
Unmagnetized Plasma

In an unbounded, collisionless and unmagnetized plasma consisting of positive and negative ions together with non-thermal electrons, first and second order amplitudes and widths of the ion-acoustic solitary waves are discussed here properly along with the effect of the concentration of negative ion and temperature of both positive and negative ions.

Wave-number dependence of the static screening function of an interacting electron gas. II. Higher-order exchange and correlation effects

1970 ◽  
Vol 48 (2) ◽  
pp. 167-181 ◽  
Author(s):  
D. J. W. Geldart ◽  
Roger Taylor
Keyword(s):  
Density Dependence ◽  
Ground State ◽  
Electron Gas ◽  
Perturbation Expansion ◽  
Interpolation Formula ◽  
Higher Order ◽  
Wave Number ◽  
Correlation Effects ◽  
Many Body ◽  
Static Screening

An interpolation formula is suggested for the wave-number and density dependence of the static screening function for an interacting electron gas in its ground state. The approximate screening function simulates a number of properties of the exact screening function which have been established by analysis of its many-body perturbation expansion. The accuracy of the interpolation formula is discussed and is considered to be adequate for practical calculations in the range of intermediate metallic densities.

Ion-acoustic waves in a degenerate multicomponent magnetoplasma

2012 ◽  
Vol 79 (2) ◽  
pp. 163-168 ◽  
Author(s):  
U. M. ABDELSALAM ◽  
M. M. SELIM
Keyword(s):  
Solitary Waves ◽  
Acoustic Waves ◽  
Three Dimensional ◽  
Negative Ions ◽  
Expansion Method ◽  
Reductive Perturbation Method ◽  
Negative Ion ◽  
Zk Equation ◽  
Ion Acoustic ◽  
Astrophysical Objects

AbstractThe hydrodynamic equations of positive and negative ions, degenerate electrons, and the Poisson equation are used along with the reductive perturbation method to derive the three-dimensional Zakharov–Kuznetsov (ZK) equation. The G′/G-expansion method is used to obtain a new class of solutions for the ZK equation. At certain condition, these solutions can describe the solitary waves that propagate in our plasma. The effects of negative ion concentrations, the positive/negative ion cyclotron frequency, as well as positive-to-negative ion mass ratio on solitary pulses are examined. Finally, the present study might be helpful to understand the propagation of nonlinear ion-acoustic solitary waves in a dense plasma, such as in astrophysical objects.

Higher order solutions to ion-acoustic solitons in a weakly relativistic two-fluid plasma

2008 ◽  
Vol 15 (12) ◽  
pp. 122309 ◽  
Author(s):  
Tarsem Singh Gill ◽  
Parveen Bala ◽  
Harvinder Kaur
Keyword(s):  
Higher Order ◽  
Ion Acoustic ◽  
Ion Acoustic Solitons ◽  
Two Fluid ◽  
Two Fluid Plasma
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