Stability of ion acoustic solitary waves in a magnetized plasma consisting of warm adiabatic ions and non-thermal electrons having vortex-like velocity distribution

2013 ◽  
Vol 80 (1) ◽  
pp. 89-112
Author(s):  
Jayasree Das ◽  
Anup Bandyopadhyay ◽  
K. P. Das
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Solitary Wave ◽  
Velocity Distribution ◽  
Plasma Phys ◽  
Solitary Wave Solutions ◽  
Long Wavelength ◽  
Zk Equation ◽  
Wave Solutions ◽  
Ion Acoustic

AbstractSchamel's modified Korteweg-de Vries–Zakharov–Kuznetsov (S-ZK) equation, governing the behavior of long wavelength, weak nonlinear ion acoustic waves propagating obliquely to an external uniform static magnetic field in a plasma consisting of warm adiabatic ions and non-thermal electrons (due to the presence of fast energetic electrons) having vortex-like velocity distribution function (due to the presence of trapped electrons), immersed in a uniform (space-independent) and static (time-independent) magnetic field, admits solitary wave solutions having a sech4 profile. The higher order stability of this solitary wave solution of the S-ZK equation has been analyzed with the help of multiple-scale perturbation expansion method of Allen and Rowlands (Allen, M. A. and Rowlands, G. 1993 J. Plasma Phys. 50, 413; 1995 J. Plasma Phys. 53, 63). The growth rate of instability is obtained correct to the order k2, where k is the wave number of a long wavelength plane wave perturbation. It is found that the lowest order (at the order k) instability condition is strongly sensitive to the angle of propagation (δ) of the solitary wave with the external uniform static magnetic field, whereas at the next order (at the order k2) the solitary wave solutions of the S-ZK equation are unstable irrespective of δ. It is also found that the growth rate of instability up to the order k2 for the electrons having Boltzmann distribution is higher than that of the non-thermal electrons having vortex-like distribution for any fixed δ.

Ion-acoustic double layers in magnetized plasma consisting of warm adiabatic ions and non-thermal electrons having vortex-like velocity distribution: existence and stability

2008 ◽  
Vol 74 (2) ◽  
pp. 163-186 ◽  
Author(s):  
JAYASREE DAS ◽  
ANUP BANDYOPADHYAY ◽  
K. P. DAS
Keyword(s):  
Magnetic Field ◽  
Distribution Function ◽  
Velocity Distribution ◽  
Double Layer ◽  
Static Magnetic Field ◽  
Velocity Distribution Function ◽  
Plasma Phys ◽  
Zk Equation ◽  
Ion Acoustic ◽  
Layer Solution

AbstractA combined Schamel's modified Korteweg–de Vries–Zakharov– Kuznetsov (S–KdV–ZK) equation efficiently describes the nonlinear behaviour of ion-acoustic waves in a plasma consisting of warm adiabatic ions and non-thermal electrons (due to the presence of fast energetic electrons) having vortex-like velocity distribution function (due to the presence of trapped electrons), immersed in a uniform (space-independent) and static (time-independent) magnetic field, when the vortex-like velocity distribution function of electrons approaches the non-thermal velocity distribution function of electrons as prescribed by Cairns et al. (1995 Electrostatic solitary structures in non-thermal plasmas. Geophys. Res. Lett. 22, 2709–2712), i.e. when the contribution of trapped electrons tends to zero. This combined S–KdV–ZK equation admits a double-layer solution propagating obliquely to the external uniform and static magnetic field. The condition for the existence of this double-layer solution has been derived. The three-dimensional stabilities of the double-layer solutions propagating obliquely to the external uniform and static magnetic field have been investigated by the multiple-scale perturbation expansion method of Allen and Rowlands (1993 Determination of growth rate for linearized Zakharov–Kuznetsov equation. J. Plasma Phys. 50, 413–424; 1995 Stability obliquely propagating plane solitons of the Zakharov–Kuznetsov equation. J. Plasma Phys. 53, 63–73). It is found that the double-layer solutions of the combined S–KdV–ZK equation are stable at the lowest order, i.e. up to the order k, where k is the wave number of perturbation.

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.

Construction of bright–dark solitons and ion-acoustic solitary wave solutions of dynamical system of nonlinear wave propagation

2019 ◽  
Vol 34 (37) ◽  
pp. 1950309 ◽  
Author(s):  
Mujahid Iqbal ◽  
Aly R. Seadawy ◽  
Dianchen Lu ◽  
Xianwei Xia
Keyword(s):  
Solitary Wave ◽  
Perturbation Technique ◽  
Nonlinear Behavior ◽  
Physical Structure ◽  
Magnetized Plasma ◽  
Solitary Wave Solutions ◽  
Nonlinear Wave Propagation ◽  
Zk Equation ◽  
Dark Solitons ◽  
Wave Solutions

The nonlinear (2 + 1)-dimensional Zakharov–Kuznetsov (ZK) equations deal with the nonlinear behavior of waves in collision-less plasma, which contains non-isothermal cold ions and electrons. Two-dimensional dust acoustic solitary waves (DASWs) in magnetized plasma, which consist of trapped electrons and ions are leading to (2 + 1)-dim (ZK) equation by using the perturbation technique. We found the solitary wave solutions of (2 + 1)-dimensional (ZK)-equation, generalized (ZK)-equation and generalized form of modified (ZK)-equation by implementing the modified mathematical method. As a result, we obtained the bright–dark solitons, traveling wave and solitary wave solutions. The physical structure of obtained solutions is represented in 2D and 3D, graphically with the help of Mathematica.

Alternative ion-acoustic solitary waves in magnetized plasma consisting of warm adiabatic ions and non-thermal electrons having vortex-like velocity distribution: existence and stability

2007 ◽  
Vol 73 (6) ◽  
pp. 869-899 ◽  
Author(s):  
JAYASREE DAS ◽  
ANUP BANDYOPADHYAY ◽  
K.P. DAS
Keyword(s):  
Distribution Function ◽  
Solitary Wave ◽  
Velocity Distribution ◽  
Solitary Waves ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Velocity Distribution Function ◽  
Trapped Electrons ◽  
Zk Equation ◽  
Ion Acoustic

AbstractThe solitary structures of the ion-acoustic waves have been considered in a plasma consisting of warm adiabatic ions and non-thermal electrons (due to the presence of fast energetic electrons) having a vortex-like velocity distribution function (due to the presence of trapped electrons), immersed in a uniform (space-independent) and static (time-independent) magnetic field. The nonlinear dynamics of ion-acoustic waves in such a plasma is governed by the Schamel's modified Korteweg–de Vries–Zakharov–Kuznetsov (S-ZK) equation. This equation admits solitary wave solutions having a profile sech4. When the coefficient of the nonlinear term of this equation vanishes, the vortex-like velocity distribution function of electrons simply becomes the non-thermal velocity distribution function of electrons and the nonlinear behaviour of the same ion-acoustic wave is described by a Korteweg–de Vries–Zakharov–Kuznetsov (KdV-ZK) equation. This equation admits solitary wave solutions having a profile sech2. A combined S–KdV–ZK equation more efficiently describes the nonlinear behaviour of an ion-acoustic wave when the vortex-like velocity distribution function of electrons approaches the non-thermal velocity distribution function of electrons, i.e. when the contribution of trapped electrons tends to zero. This combined S-KdV-ZK equation admits an alternative solitary wave solution having a profile different from either sech4 or sech2. The condition for the existence of this alternative solitary wave solution has been derived. It is found that this alternative solitary wave solution approaches the solitary wave solution (the sech2 profile) of the KdV-ZK equation when the contribution of trapped electrons tends to zero. The three-dimensional stability of these solitary waves propagating obliquely to the external uniform and static magnetic field has been investigated by the multiple-scale perturbation expansion method of Allen and Rowlands. The instability condition and the growth rate of the instability have been derived at the lowest order. It is also found that the instability condition and growth rate of instability of the alternative solitary waves are exactly the same as those of the solitary waves as determined from the KdV-ZK equation (the sech2 profile) when the contribution of trapped electrons tends to zero.

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