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Register a new userEffect of Landau damping on ion acoustic solitary waves in a multi-species collisionless unmagnetized plasma consisting of nonthermal and isothermal electrons
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Added by
Anup Bandyopadhyay Dr.
Publication date
2018
fields
Physics
and research's language is
English
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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 $r =1,2,3$.
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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.
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.
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.
Bandyopadhyay and Das [Phys. Plasmas, 9, 465-473, 2002] have derived a nonlinear macroscopic evolution equation for ion acoustic wave in a magnetized plasma consisting of warm adiabatic ions and non-thermal electrons including the effect of Landau damping. In that paper they have also derived the corresponding nonlinear evolution equation when coefficient of the nonlinear term of the above mentioned macroscopic evolution equation vanishes, the nonlinear behaviour of the ion acoustic wave is described by a modified macroscopic evolution equation. But they have not considered the case when the coefficient is very near to zero. This is the case we consider in this paper and we derive the corresponding evolution equation including the effect of Landau damping. Finally, a solitary wave solution of this macroscopic evolution is obtained, whose amplitude is found to decay slowly with time.
The head-on collision of ion-acoustic solitary waves in a collisionless plasma with cold ions and Boltzmann electrons is studied. It is shown that solitary waves of sufficiently large amplitudes do not retain their identity after a collision. Their amplitudes decrease and their forms change. Dependences of amplitudes of the potential and densities of ions and electrons after a head-on collision of identical solitary waves on their initial amplitude are presented.
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