The study of nonlinear dust acoustic wave propagation in a Lorentzian dusty Vlasov plasma in the presence of negative io
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ORIGINAL PAPER
The study of nonlinear dust acoustic wave propagation in a Lorentzian dusty Vlasov plasma in the presence of negative ions S Paul*
, R Denra and S Sarkar
Department of Applied Mathematics, University of Calcutta, 92, Acharya Prafulla Chandra Road, Kolkata 700009, India Received: 17 March 2019 / Accepted: 30 July 2019
Abstract: Applying a reductive perturbation analysis in the Vlasov–Poisson model, a Korteweg–de Vries (KdV) equation has been derived for small amplitude dust acoustic waves in a Lorentzian dusty plasma composed of electrons, positive ions, negative ions and charged dust particles. In this paper, two models have been considered, one containing negative and the other containing positive grain charges. Nonlinear propagation of dust acoustic waves in both cases of negative and positive grain charges is governed by KdV equation which gives dust acoustic soliton solution. This dust acoustic soliton solution is rarefied for negative equilibrium dust charge and compressive for positive equilibrium dust charge. Our investigation also shows that the amplitude of dust acoustic soliton in both cases is less than their amplitudes if they are obtained by fluid theory. Thus, our kinetic model captures the nonlinear damping effect of dust acoustic soliton which is absent in fluid theory. The effect of kappa index and dust temperature on the soliton amplitude and width are also studied. Keywords: Lorentzian dusty plasma; KdV equation; Negative ion PACS Nos.: 52.27.Lw; 52.35.-g; 52.35.Mw
1. Introduction The dusty plasma is a complex medium composed of electrons, different species of positive ions, negative ions and massive dust particles which not only perturb the plasma properties but also introduce new phenomena. Interest in the study of dust acoustic wave and dust ion acoustic wave characteristics has been developed due to their importance in space, laboratory and astrophysical plasmas where dust particles are found to exist [1, 2]. So the study of dusty plasma draws an immense interest among plasma physicists. Coexistence of negative and positive ions with dust particles is found in the Earth’s ionosphere [3]. Negative ions are frequently observed in afterglow when the source of ionization is absent. The lower part of the ionosphere is a rich source of negative ions where solar radiation does not reach at night and ion– ion plasma is produced [4, 5]. In normal condition, in which plasma contains a lesser number of negative ions compared to electrons and positive ions, the equilibrium
*Corresponding author, E-mail: [email protected]
dust charge is negative. If the density of negative ions increases, positively charged dust can exist in dusty plasma because in such plasma relative concentration of free electrons is sufficiently small; consequently, total positive flux to the dust grains will dominate over the negative flux, and the dust charge will be positive. Thus, dust grains may be negatively or positively charged depending on the concentration of negative ions. This mechanism of positive
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