Envelope excitations in nonextensive plasmas with warm-ions

•Plasmas with q-entropy electrons are modulationally unstable.•Ion-temperature has an important effect on modulational instability.•Rogue wave can propagate in nonextensive plasmas.•There is two distinct regions of instability q>1q>1 and q<1q<1.

In this work we study the modulational instability of plasmas with q-entropy electrons and warm ions, using the hydrodynamic approach. A nonlinear Schrödinger equation (NLSE), governing the dynamics of envelope excitations in the plasma, is obtained by using the conventional multiscales method. Investigation of the modulational instability of the nonextensive plasmas reveals that the criteria for propagation of bright/dark envelope excitations in such plasmas are significantly affected by value of the nonextensivity parameter, q, and the fractional ion-temperature, σ  . In particular, by setting σ≠0σ≠0, a new region of modulational instability appears, indicating that the study of modulation instability in the cold-ion limit (σ=0σ=0) is completely different from that of warm ions. The study of the growth-rate and rogue-wave amplitudes in terms of different plasma parameters, reveals that their magnitude is of different scales for two ranges of the nonextensivity parameters, q>1q>1 and q<1q<1.