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Stability of ion–acoustic solitary waves in a multi-species magnetized plasma consisting of non-thermal and isothermal electrons

Published online by Cambridge University Press:  01 October 2009

SK. ANARUL ISLAM ,
A. BANDYOPADHYAY  and
K. P. DAS
SK. ANARUL ISLAM
Affiliation:
Department of Mathematics, Sri Ramakrishna Sarada Vidya Mahapitha, Kamarpukur, Hooghly 712 612, West Bengal, India
A. BANDYOPADHYAY
Affiliation:
Department of Mathematics, Jadavpur University, Kolkata 700 032, India
K. P. DAS
Affiliation:
Department of Applied Mathematics, University of Calcutta, 92 Acharya Prfulla Chandra Road, Kolkata 700 009, India (daskalipada@ymail.com)
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Abstract

A theoretical study of the first-order stability analysis of an ion–acoustic solitary wave, propagating obliquely to an external uniform static magnetic field, has been made in a plasma consisting of warm adiabatic ions and a superposition of two distinct populations of electrons, one due to Cairns et al. and the other being the well-known Maxwell–Boltzmann distributed electrons. The weakly nonlinear and the weakly dispersive ion–acoustic wave in this plasma system can be described by the Korteweg–de Vries–Zakharov–Kuznetsov (KdV-ZK) equation and different modified KdV-ZK equations depending on the values of different parameters of the system. The nonlinear term of the KdV-ZK equation and the different modified KdV-ZK equations is of the form [φ(1)]ν(∂φ(1)/∂ζ), where ν = 1, 2, 3, 4; φ(1) is the first-order perturbed quantity of the electrostatic potential φ. For ν = 1, we have the usual KdV-ZK equation. Three-dimensional stability analysis of the solitary wave solutions of the KdV-ZK and different modified KdV-ZK equations has been investigated by the small-k perturbation expansion method of Rowlands and Infeld. For ν = 1, 2, 3, the instability conditions and the growth rate of instabilities have been obtained correct to order k, where k is the wave number of a long-wavelength plane-wave perturbation. It is found that ion–acoustic solitary waves are stable at least at the lowest order of the wave number for ν = 4.

Type
Papers
Information
Journal of Plasma Physics , Volume 75 , Issue 5 , October 2009 , pp. 593 - 607
Copyright
Copyright © Cambridge University Press 2009

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