A different viewpoint of the Sagdeev's methodology for the allowed domains of ion-acoustic solitons and double layers in typical plasmas

Abstract

In the commonly used analysis of the allowed domains of ion-acoustic (IA) solitons and double layers (DLs) in the celebrated Sagdeev’s methodology, we consider the infinite compression limit, labeled with a critical potential , as the maximum width of the possible potential wells (pseudopotential) for trapping the solitons (pseudo-particle). By imposing the criterion for the formation of a potential well with such a maximum potential, we derive an upper limit of the allowed Mach number domains, besides the threshold Mach number limit for possible excitation of the IA solitons. In this paper, we present a different viewpoint of Sagdeev's methodology based on full analyzing the Mach number domains with respect to the involved potential, where by considering the overlap of all the constraints for formation of the pseudo-potential, we may show an allowed domain for the arbitrary amplitude IA solitons and DLs. Analyzing the allowed domains of plane has some advantages, such as providing a simple context for predicting the possible DLs and also providing a straightforward way for examination of the maximum amplitude of the solitons. We have examined the allowed domains of IA solitons and DLs for two cases of Maxwellian and Cairns-Tsallis distributed electrons.