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Title: Stability of dust ion acoustic solitary waves in a collisionless unmagnetized nonthermal plasma in presence of isothermal positrons

Abstract

A three-dimensional KP (Kadomtsev Petviashvili) equation is derived here describing the propagation of weakly nonlinear and weakly dispersive dust ion acoustic wave in a collisionless unmagnetized plasma consisting of warm adiabatic ions, static negatively charged dust grains, nonthermal electrons, and isothermal positrons. When the coefficient of the nonlinear term of the KP-equation vanishes an appropriate modified KP (MKP) equation describing the propagation of dust ion acoustic wave is derived. Again when the coefficient of the nonlinear term of this MKP equation vanishes, a further modified KP equation is derived. Finally, the stability of the solitary wave solutions of the KP and the different modified KP equations are investigated by the small-k perturbation expansion method of Rowlands and Infeld [J. Plasma Phys. 3, 567 (1969); 8, 105 (1972); 10, 293 (1973); 33, 171 (1985); 41, 139 (1989); Sov. Phys. - JETP 38, 494 (1974)] at the lowest order of k, where k is the wave number of a long-wavelength plane-wave perturbation. The solitary wave solutions of the different evolution equations are found to be stable at this order.

Authors:
;  [1];  [2]
  1. Department of Mathematics, Jadavpur University, Kolkata 700032 (India)
  2. Department of Applied Mathematics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700009 (India)
Publication Date:
OSTI Identifier:
22600065
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 23; Journal Issue: 7; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; COLLISIONLESS PLASMA; DISTURBANCES; DUSTS; ELECTRONS; EQUATIONS; ION ACOUSTIC WAVES; IONS; NONLINEAR PROBLEMS; PERTURBATION THEORY; POSITRONS; SOLUTIONS; STABILITY; THREE-DIMENSIONAL CALCULATIONS; WAVE PROPAGATION; WAVELENGTHS

Citation Formats

Sardar, Sankirtan, Bandyopadhyay, Anup, E-mail: abandyopadhyay1965@gmail.com, and Das, K. P.. Stability of dust ion acoustic solitary waves in a collisionless unmagnetized nonthermal plasma in presence of isothermal positrons. United States: N. p., 2016. Web. doi:10.1063/1.4956462.
Sardar, Sankirtan, Bandyopadhyay, Anup, E-mail: abandyopadhyay1965@gmail.com, & Das, K. P.. Stability of dust ion acoustic solitary waves in a collisionless unmagnetized nonthermal plasma in presence of isothermal positrons. United States. doi:10.1063/1.4956462.
Sardar, Sankirtan, Bandyopadhyay, Anup, E-mail: abandyopadhyay1965@gmail.com, and Das, K. P.. 2016. "Stability of dust ion acoustic solitary waves in a collisionless unmagnetized nonthermal plasma in presence of isothermal positrons". United States. doi:10.1063/1.4956462.
@article{osti_22600065,
title = {Stability of dust ion acoustic solitary waves in a collisionless unmagnetized nonthermal plasma in presence of isothermal positrons},
author = {Sardar, Sankirtan and Bandyopadhyay, Anup, E-mail: abandyopadhyay1965@gmail.com and Das, K. P.},
abstractNote = {A three-dimensional KP (Kadomtsev Petviashvili) equation is derived here describing the propagation of weakly nonlinear and weakly dispersive dust ion acoustic wave in a collisionless unmagnetized plasma consisting of warm adiabatic ions, static negatively charged dust grains, nonthermal electrons, and isothermal positrons. When the coefficient of the nonlinear term of the KP-equation vanishes an appropriate modified KP (MKP) equation describing the propagation of dust ion acoustic wave is derived. Again when the coefficient of the nonlinear term of this MKP equation vanishes, a further modified KP equation is derived. Finally, the stability of the solitary wave solutions of the KP and the different modified KP equations are investigated by the small-k perturbation expansion method of Rowlands and Infeld [J. Plasma Phys. 3, 567 (1969); 8, 105 (1972); 10, 293 (1973); 33, 171 (1985); 41, 139 (1989); Sov. Phys. - JETP 38, 494 (1974)] at the lowest order of k, where k is the wave number of a long-wavelength plane-wave perturbation. The solitary wave solutions of the different evolution equations are found to be stable at this order.},
doi = {10.1063/1.4956462},
journal = {Physics of Plasmas},
number = 7,
volume = 23,
place = {United States},
year = 2016,
month = 7
}
  • The Sagdeev potential technique has been employed to study the dust ion acoustic solitary waves and double layers in an unmagnetized collisionless dusty plasma consisting of negatively charged static dust grains, adiabatic warm ions, isothermally distributed electrons, and positrons. A computational scheme has been developed to draw the qualitatively different compositional parameter spaces or existence domains showing the nature of existence of different solitary structures with respect to any parameter of the present plasma system. The present system supports both positive and negative potential double layers. The negative potential double layer always restricts the occurrence of negative potential solitary waves,more » i.e., any sequence of negative potential solitary waves having monotonically increasing amplitude converges to a negative potential double layer. However, there exists a parameter regime for which the positive potential double layer is unable to restrict the occurrence of positive potential solitary waves. As a result, in this region of the parameter space, there exist solitary waves after the formation of positive potential double layer, i.e., positive potential supersolitons have been observed.« less
  • The nonlinear propagation of dust-acoustic (DA) waves in an unmagnetized dusty plasma consisting of nonthermal electrons, vortex-like (trapped) distributed ions and mobile negative dust have been investigated by employing the reductive perturbation technique. The effects of nonthermal electrons and trapped ions are found to modify the properties of the DA solitary waves.
  • Dust acoustic solitary waves and periodic waves in an unmagnetized dusty plasma with kappa distributed electrons and ions are investigated through non-perturbative approach. Basic equations are reduced to a system of ordinary differential equations involving electrostatic potential. After that by applying the bifurcation theory of planar dynamical systems to this system, we have studied the existence of solitary wave solutions and periodic wave solutions. New analytical solutions for the above waves are derived depending on the parametric space. Regarding the solitary and periodic wave solutions, the combined effects of temperature ratio (σ) of ions and electrons, spectral index (κ) andmore » density ratio (p) are studied on characteristics of dust acoustic (DA) solitary waves and periodic waves. The spectral index (κ), density ratio (p) of ions and electrons and temperature ratio (σ) significantly influence the characteristics of dust acoustic solitary and periodic structures.« less
  • The effect of nonthermal ions and variable dust charge on small-amplitude nonlinear dust-acoustic (DA) waves is investigated. It is found that both compressive and rarefactive solitons exist and depend on the nonthermal parameter a. Using a reductive perturbation theory, a Zakharov-Kuznetsov (ZK) equation is derived. At critical value of a, a{sub c}, a modified ZK equation with third- and fourth-order nonlinearities, is obtained. Depending on a, the solution of the evolution equation reveals whether there is coexistence of both compressive and rarefactive solitary waves or double layers (DLs) with the possibility of their two kinds. In addition, for certain plasmamore » parameters, the solitary wave disappears and a DL is expected. The variation of dust charge number, wave velocity, and soliton amplitude and its width against system parameters is investigated for the DA solitary waves. It is shown that the incorporation of both the adiabatic dust-charge variation and the nonthermal distributed ions modifies significantly the nature of DA solitary waves and DA DLs. The findings of this investigation may be useful in understanding the ion acceleration mechanisms close to the Moon and also enhances our knowledge on pickup ions around unmagnetized bodies, such as comets, Mars, and Venus.« less
  • A computational scheme has been developed to study the arbitrary amplitude dust acoustic solitary waves and double layers in nonthermal plasma consisting of negatively charged dust grains, nonthermal ions, and isothermal electrons including the effect of dust temperature. The Sagdeev potential approach, which is valid to study the arbitrary amplitude solitary waves and double layers, has been employed. The computation has been carried out over the entire interval of {beta}{sub 1}:0{<=}{beta}{sub 1}<{beta}{sub M}. This {beta}{sub 1} is a parameter associated with the nonthermal distribution of ions and {beta}{sub M} is the upper bound of {beta}{sub 1}. Depending on the naturemore » of existence of solitary waves and double layers, the interval for {beta}{sub 1} can be broken up into four disjoint subintervals holding the other parameters fixed. By nature of existence of solitary waves and double layers, it is meant that in some subinterval only negative potential solitary waves can exist, whereas in another both negative and positive potential solitary waves can coexist along with a double layer, etc. Corresponding to every {beta}{sub 1} lying within a subinterval of {beta}{sub 1}, there is a definite interval for the Mach number (definite value of the Mach number) for which there exists solitary waves (double layer) specific for that subinterval of {beta}{sub 1}. The role of dust temperature on the subintervals of {beta}{sub 1} and on amplitude of solitary waves and double layers has been explored.« less