Indian Journal of Pure & Applied Physics Vol. 46, September 2008, pp. 621-628 Small amplitude solitary waves propagating in a plasma with negative ions Runmoni Gogoi, Nirupama Devi & G C Das* Department of Mathematics, Cotton College, Guwahati 781001, Assam *Mathematical Sciences Division, Institute of Advanced Study in Science and Technology, Paschim Boragaon, Guwahati 781 035, Assam E-mail: runmoni_gogoi@rediffmail.com; nirupama_cotton@rediffmail.com Received 21 May 2007; accepted 15 May 2008 One-dimensional motion of positive ions, negative ions and electrons leading to the propagation of K-dV soliton has been considered. Different aspects of soliton amplitude and width have been studied in relation to density ratio (r), mass ratio (Q′) of the plasma medium. The role played by the temperature of the negative ions is critically considered to find possible regions of soliton radiation. It is also observed that there are two mutually opposite directions of wave propagation due to the presence of negative ions. Keywords: K-dV soliton, Soliton radiation, Sagdeev potential, Plasma, Small amplitude solitary waves 1 Introduction The heuristic features of nonlinear dispersive plasma waves leading to propagation of solitary wavse have been studied in extensive ways following the major mathematical treatments extended by Washimi and Tanuity 1 and Sagdeev 2 . Solitary waves are localized symmetric potential structures which do not produce net potential drop. Numerous wave modes were observed during last several decades, through mathematical analyses 3 that are very interesting and have weightage in relation to experimental findings. It was the S3-3 and Viking satellites which have detected such localized structures from the auroral acceleration region i.e. at altitude between 6000 and 12000 km. These observations have initiated various numerical and analytical studies of solitary waves 4-6 . For many long years, the simple aspects of plasma models with positive ions and electrons were given importance in the study of solitary waves. Such situations have resemblance with plasma regions at different altitudes above the upper atmosphere with multispecies of positive ions. Specifically, the role played by nonlinear whistler waves in ionospheric plasmas is of vast interest. In 1965, the crucial role played by the negative ions in the propagation of whistlers in the ionosphere was shown 7 . Following which such types of ions were studied by many researchers with nonlinear plasma waves of different kinds 8-11 . In relation to ionospheric plasma the presence of negative ions in the lower ionosphere has been considered by Uberoi and Das 12 . In such a case, combination of Ar + , SF 6 - or K + , Cl - with Maxwellian electrons is generally taken 11,13 . Although many researchers have established soliton theory using cold ion approximation, in reality cold ion theory cannot support the experimental observations 14-17 . In cases of comparable ion and electron temperature, wave break may occur which can be controlled by taking T e >>T i . In the second case, solitons are likely to be formed when the plasma is warm. It has been established theoretically that finite ion temperature effect leads to propagation of two ion acoustic modes with different phase velocities. Moreover, inclusion of different ion species implies increase in the number of modes of propagation with different phase velocities 18 . In most of the theoretical studies on nonlinear plasma waves considering the presence of negative ions, temperatures of both positive and negative ion have been considered as equal. In such consideration with equal ion masses the waves propagate with same phase velocity. Kalita and Devi 19 have shown different phase velocities with different ion masses, but with equal ion temperatures. Experimental observation on soliton propagation in negative ion- positive ion plasma can be found in many studies. Ludwig et al. 20 , Nakamura et al. 21 , Nakamura 22 , have found that adiabatic motion of negative ions increases the phase velocity of ion acoustic waves. But it is