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Title: Cylindrical and spherical quantum ion acoustic waves

Abstract

Cylindrical and spherical deformed Korteweg-de Vries (dKdV) equations are derived for quantum ion acoustic waves in an unmagnetized two species quantum plasma system, comprised of electrons and ions, by the reductive perturbation technique in the weakly nonlinear limit. The properties of quantum ion acoustic solitary waves are studied taking into account the quantum mechanical effects in a nonplanar cylindrical or spherical geometry, which differs from one-dimensional planar geometry. Both analytical and numerical solutions of the dKdV equations are discussed in some detail. There exists a critical value of quantum parameters beyond which the quantum ion acoustic soliton collapses. It is also found that for the critical values of H, viz., H=2, some nontrivial analytical solution exists for both cylindrical and spherical dKdV equations.

Authors:
;  [1];  [2]
  1. Department of Mathematics, Dinhata College, Coochbehar-736135 (India)
  2. (India)
Publication Date:
OSTI Identifier:
20960092
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 14; Journal Issue: 1; Other Information: DOI: 10.1063/1.2409527; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ANALYTICAL SOLUTION; CYLINDRICAL CONFIGURATION; ELECTRONS; GEOMETRY; ION ACOUSTIC WAVES; IONS; KORTEWEG-DE VRIES EQUATION; NONLINEAR PROBLEMS; NUMERICAL ANALYSIS; NUMERICAL SOLUTION; PERTURBATION THEORY; QUANTUM MECHANICS; QUANTUM PLASMA; SOLITONS

Citation Formats

Sahu, Biswajit, Roychoudhury, Rajkumar, and Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata-700108. Cylindrical and spherical quantum ion acoustic waves. United States: N. p., 2007. Web. doi:10.1063/1.2409527.
Sahu, Biswajit, Roychoudhury, Rajkumar, & Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata-700108. Cylindrical and spherical quantum ion acoustic waves. United States. doi:10.1063/1.2409527.
Sahu, Biswajit, Roychoudhury, Rajkumar, and Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata-700108. Mon . "Cylindrical and spherical quantum ion acoustic waves". United States. doi:10.1063/1.2409527.
@article{osti_20960092,
title = {Cylindrical and spherical quantum ion acoustic waves},
author = {Sahu, Biswajit and Roychoudhury, Rajkumar and Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata-700108},
abstractNote = {Cylindrical and spherical deformed Korteweg-de Vries (dKdV) equations are derived for quantum ion acoustic waves in an unmagnetized two species quantum plasma system, comprised of electrons and ions, by the reductive perturbation technique in the weakly nonlinear limit. The properties of quantum ion acoustic solitary waves are studied taking into account the quantum mechanical effects in a nonplanar cylindrical or spherical geometry, which differs from one-dimensional planar geometry. Both analytical and numerical solutions of the dKdV equations are discussed in some detail. There exists a critical value of quantum parameters beyond which the quantum ion acoustic soliton collapses. It is also found that for the critical values of H, viz., H=2, some nontrivial analytical solution exists for both cylindrical and spherical dKdV equations.},
doi = {10.1063/1.2409527},
journal = {Physics of Plasmas},
number = 1,
volume = 14,
place = {United States},
year = {Mon Jan 15 00:00:00 EST 2007},
month = {Mon Jan 15 00:00:00 EST 2007}
}
  • Cylindrical and spherical amplitude modulation of quantum ion-acoustic (QIA) envelope solitary waves in a dense quantum plasma comprised of electrons and ions is investigated. For this purpose, a one-dimensional quantum hydrodynamic model and the Poisson equation are considered. By using the standard reductive perturbation technique, a modified nonlinear Schroedinger equation with the geometrical and the quantum effects is derived. The effect of quantum corrections and the effect due to the cylindrical and spherical geometries on the propagation of the QIA envelope solitary waves are examined. It is shown that there exists a modulation instability period depending on the quantum parameter,more » which does not exist for the one-dimensional classical case.« less
  • Using the reductive perturbation technique, nonlinear cylindrical and spherical Korteweg-de Vries (KdV) and modified KdV equations are derived for ion acoustic waves in an unmagnetized plasma consisting of warm adiabatic ions and nonthermal electrons. The effects of nonthermally distributed electrons on cylindrical and spherical ion acoustic waves are investigated. It is found that the nonthermality has a very significant effect on the nature of ion acoustic waves.
  • Dusty plasmas have been found almost everywhere in the Universe. Sahu and Roychoudhury [Phys. Plasmas 10, 4162 (2003)] have done their interesting analytic work on the cylindrical dust ion-acoustic waves, without enough guidance to the readers on other existing analytic results. Such lack of guidance turns out to be critical. We hereby try to make the story more complete in the sense that the model does have plenty of exact analytic solutions published already, and to present a brief review on some of them. For the dust-ion-acoustic and dust-acoustic modes supported by the space/laboratory dusty plasmas, we hereby picture outmore » some possibly observable effects for the future experiments, featured by a solitonic pulse aboard the varying ambient field propagating with its varying velocity and amplitude.« less
  • It is shown that the similarity solution of cylindrical Korteweg-de Vries equation given by Tian and Gao in their Comment on our paper can be obtained by the group analysis method using the same generators given in the paper by Sahu and Roychoudhury.