Reductive perturbation method in magnetized plasma and role of negative ions

Abstract

An analysis of reductive perturbation method (RPM) is presented to show why the solitary structures of non-linear ion acoustic waves (IAWs) cannot be obtained in magnetized electron ion plasma by employing this technique. In RPM, the non-linear Korteweg–de Vries equation is derived using stretched co-ordinates in the reference frame of the wave phase speed, considering the dispersion to be a higher-order effect that balances the non-linearity to produce a solitary structure. The maximum amplitude |Φm| of the non-linear solitary wave turns out to be larger than one that contradicts the small amplitude approximation. In the presence of negative ions, the maximum amplitude satisfies the condition |Φm|<1. To elaborate these points, the results have been applied to an experimental plasma consisting of positive ions of xenon (Xe+) and negative ions of fluorene (F−) along with electrons. The amplitude and width of the solitary structures depend upon the ratio of the electron to positive ion density (ne0ni0). Since the non-linear coefficient turns out to be negative, rarefied (dip) solitons are formed in the magnetized Xe+−F−−e plasma.