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Dust acoustic solitary waves in non-thermal plasmas consisting of negatively charged dust grains and isothermal electrons

Published online by Cambridge University Press:  01 August 2009

ANIMESH DAS  and
ANUP BANDYOPADHYAY
ANIMESH DAS
Affiliation:
Department of Mathematics, Jadavpur University, Kolkata 700 032, India ([email protected])
ANUP BANDYOPADHYAY
Affiliation:
Department of Mathematics, Jadavpur University, Kolkata 700 032, India ([email protected])
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Abstract

A Korteweg–de Vries (KdV) equation is derived here, that describes the nonlinear behaviour of long-wavelength weakly nonlinear dust acoustic waves propagating in an arbitrary direction in a plasma consisting of static negatively charged dust grains, non-thermal ions and isothermal electrons. It is found that the rarefactive or compressive nature of the dust acoustic solitary wave solution of the KdV equation does not depend on the dust temperature if σdc < 0 or σdc > σd*, where σdc is a function of β1, α and μ only, and σd*(<1) is the upper limit (upper bound) of σd. This β1 is the non-thermal parameter associated with the non-thermal velocity distribution of ions, α is the ratio of the average temperature of the non-thermal ions to that of the isothermal electrons, μ is the ratio of the unperturbed number density of isothermal electrons to that of the non-thermal ions, Zdσd is the ratio of the average temperature of the dust particles to that of the ions and Zd is the number of electrons residing on the dust grain surface. The KdV equation describes the rarefactive or the compressive dust acoustic solitary waves according to whether σdc < 0 or σdc > σd*. When 0 ≤ σdc ≤ σd*, the KdV equation describes the rarefactive or the compressive dust acoustic solitary waves according to whether σd > σdc or σd < σdc. If σd takes the value σdc with 0 ≤ σdc ≤ σd*, the coefficient of the nonlinear term of the KdV equation vanishes and, for this case, the nonlinear evolution equation of the dust acoustic waves is derived, which is a modified KdV (MKdV) equation. A theoretical investigation of the nature (rarefactive or compressive) of the dust acoustic solitary wave solutions of the evolution equations (KdV and MKdV) is presented with respect to the non-thermal parameter β1. For any given values of α and μ, it is found that the value of σdc completely defines the nature of the dust acoustic solitary waves except for a small portion of the entire range of the non-thermal parameter β1.

Type
Papers
Information
Journal of Plasma Physics , Volume 75 , Issue 4 , August 2009 , pp. 455 - 474
Copyright
Copyright © Cambridge University Press 2009

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