Propagation and domains of the invariant ion-acoustic solitons in the plasmas

Recently, the invariant formalism of the ion-acoustic waves in the astrophysical plasmas has been introduced in terms of the invariant kappa index κ0, the zero dimensionality kappa index. In this paper, the propagation and allowed domains of the invariant ion-acoustic solitary waves (IASWs) are studied by considering the advanced aspects of the kappa distribution formalism. Our formalism is developed in terms of the polytropic (adiabatic) index associated with the kappa distributed electrons, γe, and a well-defined and extended Mach number Mγ e (the fractional wave speed to the generalized ion-sound speed), where they are employed for analysis of the allowed domains of the solitary waves and shocks in the plasma. We have used Sagdeev’s methodology for deriving the energy-integral equation of the IASWs, which describes the formation of the possible potential wells (pseudo-potentials) for trapping the arbitrary amplitude solitons (pseudo-particles). The analysis of the Mach number domains is developed by extracting (ϕ, Mγ e) domains for the possibility of the solitary wave solutions in the plasma. Moreover, the Mach number domain is examined in terms of the variation γe, then the relevant (γe, Mγ e) domains are presented. The formalism of this study is presented in two cases. At first, the general aspects of the problem is presented by considering Ti ≪ Te (the cold ion plasma limit), then the formalism is extended to a warm plasma with finite-temperature ions.