Modulation of ion-acoustic waves in a nonextensive plasma with two-temperature electrons

Abstract: We study the amplitude modulation of ion-acoustic wave (IAW) packets in an unmagnetized electron-ion plasma with two-temperature (cool and hot) electrons in the context of the Tsallis' nonextensive statistics. Using the multiple-scale technique, a nonlinear Schr{\"o}dinger (NLS) equation is derived which governs the dynamics of modulated wave packets. It is shown that in nonextensive plasmas, the IAW envelope is always stable for long-wavelength modes $(k\rightarrow0)$ and unstable for short-wavelengths with $k \gtrsim1$. However, the envelope can be unstable at an intermediate scale of perturbations with $0<k<1$. Thus, the modulated IAW packets can propagate in the form of bright envelope solitons or rogons (at small- and medium scale perturbations) as well as dark envelope solitons (at large scale). The stable and unstable regions are obtained for different values of temperature and density ratios as well as the nonextensive parameters $q_c$ and $q_h$ for cool and hot electrons. It is found that the more (less) the population of superthermal cool (hot) electrons, the smaller is the growth rate of instability with cutoffs at smaller wave numbers of modulation.