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Register a new userIon acoustic solitary structures in a collisionless unmagnetized plasma consisting of nonthermal electrons and isothermal positrons
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Added by
Anup Bandyopadhyay Dr.
Publication date
2016
fields
Physics
and research's language is
English
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Employing the Sagdeev pseudo-potential technique the ion acoustic solitary structures have been investigated in an unmagnetized collisionless plasma consisting of adiabatic warm ions, nonthermal electrons and isothermal positrons. The qualitatively different compositional parameter spaces clearly indicate the existence domains of solitons and double layers with respect to any parameter of the present plasma system. The present system supports the negative potential double layer which always restricts the occurrence of negative potential solitons. The system also supports positive potential double layers when the ratio of the average thermal velocity of positrons to that of electrons is less than a critical value. However, there exists a parameter regime for which the positive potential double layer is unable to restrict the occurrence of positive potential solitary waves and in this region of the parameter space, there exist positive potential solitary waves after the formation of a positive potential double layer. Consequently, positive potential supersolitons have been observed. The nonthermality of electrons plays an important role in the formation of positive potential double layers as well as positive potential supersolitons. The formation of positive potential supersoliton is analysed with the help of phase portraits of the dynamical system corresponding to the ion acoustic solitary structures of the present plasma system.
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We have used the Sagdeev pseudo-potential technique to investigate the arbitrary amplitude ion acoustic solitons, double layers and supersolitons in a collisionless magnetized plasma consisting of adiabatic warm ions, isothermal cold electrons and nonthermal hot electrons immersed in an external uniform static magnetic field. We have used the phase portraits of the dynamical system describing the nonlinear behaviour of ion acoustic waves to confirm the existence of different solitary structures. We have also investigated the transition of different solitary structures: soliton (before the formation of double layer) $rightarrow$ double layer $rightarrow$ supersoliton $rightarrow$ soliton (soliton after the formation of double layer) by considering the variation of $theta$ only, where $theta$ is the angle between the direction of the external uniform static magnetic field and the direction of propagation of the wave.
A Korteweg-de Vries (KdV) equation including the effect of Landau damping is derived to study the propagation of weakly nonlinear and weakly dispersive ion acoustic waves in a collisionless unmagnetized plasma consisting of warm adiabatic ions and two different species of electrons at different temperatures. The hotter energetic electron species follows the nonthermal velocity distribution of Cairns et al. [Geophys. Res. Lett. 22, 2709 (1995)] whereas the cooler electron species obeys the Boltzmann distribution. It is found that the coefficient of the nonlinear term of this KdV like evolution equation vanishes along different family of curves in different parameter planes. In this context, a modified KdV (MKdV) equation including the effect of Landau damping effectively describes the nonlinear behaviour of ion acoustic waves. It has also been observed that the coefficients of the nonlinear terms of the KdV and MKdV like evolution equations including the effect of Landau damping, are simultaneously equal to zero along a family of curves in the parameter plane. In this situation, we have derived a further modified KdV (FMKdV) equation including the effect of Landau damping to describe the nonlinear behaviour of ion acoustic waves. In fact, different modified KdV like evolution equations including the effect of Landau damping have been derived to describe the nonlinear behaviour of ion acoustic waves in different region of parameter space. The method of Ott & Sudan [Phys. Fluids 12, 2388 (1969)] has been applied to obtain the solitary wave solution of the evolution equation having the nonlinear term $(phi^{(1)})^{r}frac{partial phi^{(1)}}{partial xi}$, where $phi^{(1)}$ is the first order perturbed electrostatic potential and $r =1,2,3$. We have found that the amplitude of the solitary wave solution decreases with time for all $r =1,2,3$.
The Sagdeev pseudo-potential technique and the analytic theory developed by Das et al. [J. Plasma Phys. 78, 565 (2012)] have been used to investigate the dust ion acoustic solitary structures at the acoustic speed in a collisionless unmagnetized dusty plasma consisting of negatively charged static dust grains, adiabatic warm ions, nonthermal electrons and isothermal positrons. The present system supports both positive and negative potential solitary waves at the acoustic speed, but the system does not support the coexistence of solitary structures of opposite polarity at the acoustic speed. The system also supports negative potential double layer at the acoustic speed, but does not support positive potential double layer. Although the system supports positive potential supersoliton at the supersonic speed, but there does not exist supersoliton of any polarity at the acoustic speed. Solitary structures have been investigated with the help of compositional parameter spaces and the phase portraits of the dynamical system describing the nonlinear behaviour of the dust ion acoustic waves at the acoustic speed. For the case, when there is no positron in the system, there exist negative potential double layer and negative potential supersoliton at the acoustic speed and for such case, the mechanism of transition of supersoliton to soliton after the formation of double layer at the acoustic speed has been discussed with the help of phase portraits. The differences between the solitary structures at the acoustic speed and the solitary structures at the supersonic speed have been analysed with the help of phase portraits.
We have studied the modulation instability of obliquely propagating ion acoustic waves in a collisionless magnetized warm plasma consisting of warm adiabatic ions and two different species of electrons at different temperatures. We have derived a nonlinear Schr{o}dinger equation using the standard reductive perturbation method to describe the nonlinear amplitude modulation of ion acoustic wave satisfying the dispersion relation of ion acoustic wave propagating at an arbitrary angle to the direction of the external uniform static magnetic field. We have investigated the correspondence between two nonlinear Schr{o}dinger equations $-$ one describes the amplitude modulation of ion acoustic waves propagating along any arbitrary direction to the direction of the magnetic field and other describes the amplitude modulation of ion acoustic waves propagating along the direction of the magnetic field. We have derived the instability condition and the maximum growth rate of instability of the modulated ion acoustic wave. We have seen that the region of existence of maximum growth rate of instability decreases with increasing values of the magnetic field intensity whereas the region of existence of the maximum growth rate of instability increases with increasing $cos theta$, where $theta$ is the angle of propagation of the ion acoustic wave with the external uniform static magnetic field. Again, the maximum growth rate of instability increases with increasing $cos theta$ and also this maximum growth rate of instability increases with increasing $beta_{e}$ upto a critical value of the wave number, where $beta_{e}$ is the parameter associated with the nonthermal distribution of hotter electron species.
Sardar et al. [Phys. Plasmas 23, 073703 (2016)] have studied the stability of small amplitude dust ion acoustic solitary waves in a collisionless unmagnetized electron - positron - ion - dust plasma. They have derived a Kadomtsev Petviashvili (KP) equation to investigate the lowest - order stability of the solitary wave solution of the Korteweg-de Vries (KdV) equation for long-wavelength plane-wave transverse perturbation when the weak dependence of the spatial coordinates perpendicular to the direction of propagation of the wave is taken into account. In the present paper, we have extended the lowest - order stability analysis of KdV solitons given in the paper of Sardar et al. [Phys. Plasmas 23, 073703 (2016)] to higher order with the help of multiple-scale perturbation expansion method of Allen and Rowlands [J. Plasma Phys. 50, 413 (1993); 53, 63 (1995)]. It is found that solitary wave solution of the KdV equation is stable at the order k^2, where k is the wave number for long-wavelength plane-wave perturbation.
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