Existence and stability of alternative dust ion acoustic solitary waves in a dusty plasma consisting of nonthermal electrons having vortex-like velocity distribution

Abstract

The recent work of Sardar et al. [Phys. Plasmas 23, 073703 (2016)] on the existence and stability of the small amplitude dust ion acoustic solitary waves in a collisionless unmagnetized plasma consisting of warm adiabatic ions, static negatively charged dust grains, isothermal positrons, and nonthermal electrons due to Cairns et al. [Geophys. Res. Lett. 22, 2709 (1995)] has been extended by considering nonthermal electrons having a vortex-like velocity distribution due to Schamel [Plasma Phys. 13, 491 (1971); 14, 905 (1972)] instead of taking nonthermal electrons. This distribution takes care of both free and trapped electrons. A Schamel's modified Kadomtsev Petviashvili (SKP) equation describes the nonlinear behaviour of dust ion acoustic waves in this plasma system. The nonlinear behaviour of the dust ion acoustic wave is described by the same Kadomtsev Petviashvili (KP) equation of Sardar et al. [Phys. Plasmas 23, 073703 (2016)] when B = 0, where B is the coefficient of nonlinear term of the SKP equation. A combined SKP-KP equation more efficiently describes the nonlinear behaviour of dust ion acoustic waves when B → 0. The solitary wave solution of the SKP equation and the alternative solitary wave solution of the combined SKP-KP equation having profile different from both sech4 and sech2 are stable at the lowest order of the wave number. It is found that this alternative solitary wave solution of the combined SKP-KP equation and its lowest order stability analysis are exactly the same as those of the solitary wave solution of the KP equation when B → 0.

Modulational instability of dust-ion-acoustic waves and associated envelope solitons in a non-thermal plasma

“…A dusty plasma (DP), which is defined as fully or partially ionized electrically conducting low-temperature gas, is referred as "complex plasma" due to the existence of the micron or submicron sized dust grains [1,2,3,4,5]. The presence of massive dust grains significantly modifies the dynamics of the DP medium (DPM) [6,7,8,9,10]. The size and shape of the dust grains (million times heavier than the protons and their sizes range from nanometres to millimetres) are considerable with those of the ions/protons [1,2,3].…”

“…The size and shape of the dust grains (million times heavier than the protons and their sizes range from nanometres to millimetres) are considerable with those of the ions/protons [1,2,3]. Over the last few decades, there has been a great interest in investigating the linear and nonlinear wave propagation in DPM which can be found in both space environments (viz., cometary tails [3], the magnetosphere of the Jupiter and the Saturn [4], interstellar medium [5,6], in the galactic centre [6], and the Earth's ionosphere [9], etc.) and also laboratory plasmas (viz., electronics industry [11,12]).…”

“…The moment of inertia (restoring force) is contributed by the mass of the massive dust grains (thermal pressure of the electrons and ions) for the formation of the dust-acoustic waves (DAWs) [7,8,9,10] in three components DPM (viz., electrons, ions, and dust grains, etc). On the other hand, in the propagation of the dust-ion-acoustic waves (DIAWs) [3,4,5,6], the moment of inertia (restoring force) is contributed by the mass of the massive ions (thermal pressure of the electrons) in the presence of immobile massive dust grains. So, the massive dust grains do not play direct role in the formation of DIAWs but their existence in the background rigorously changes the dynamics of the DPM.…”

Higher order stability of dust ion acoustic solitary wave solution described by the KP equation in a collisionless unmagnetized nonthermal plasma in presence of isothermal positrons

“…The small-k perturbation expansion method of Rowlands and Infeld [1][2][3][4][5] is generally used to analyse the lowest order stability of solitary wave solutions of different nonlinear evolution equations in plasmas, where k is the wave number for long-wavelength plane-wave perturbation. Several authors [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] have used this method to investigate the lowest order stability of solitary waves in plasmas with or without magnetic field.…”

“…Sardar et al [20][21][22] have used the small-k perturbation expansion method of Rowlands and Infeld [1][2][3][4][5] to investigate the lowest order stability of DIA solitary wave solutions of different nonlinear evolution equations describing the nonlinear behaviour of DIA waves in a collisionless unmagnetized e-p-i-d plasma consisting of warm adiabatic ions, static negatively charged dust grains, nonthermal electrons and isothermal positrons. In particular, Sardar et al 20 have investigated the stability of the solitary wave solutions of the KdV and different modified KdV equations with the help of KP and different modified KP equations describing the nonlinear behaviour of DIA waves in different region of parameter space when the weak dependence of the spatial coordinates perpendicular to the direction of propagation of the wave is taken into account.…”