The Langmuir oscillations, Landau damping, and growing unstable modes in an electron-positron (EP) plasma are studied by using the Vlasov and Poisson's equations in the context of the Tsallis's nonextensive statistics. Logically, the properties of the Langmuir oscillations in a nonextensive EP plasma are remarkably modified in comparison with that of discussed in the Boltzmann-Gibbs statistics, i.e., the Maxwellian plasmas, because of the system under consideration is essentially a plasma system in a nonequilibrium stationary state with inhomogeneous temperature. It is found that by decreasing the nonextensivity index q which corresponds to a plasma with excess superthermal particles, the phase velocity of the Langmuir waves increases. In particular, depend on the degree of nonextensivity, both of damped and growing oscillations are predicted in a collisionless EP plasma, arise from a resonance phenomena between the wave and the nonthermal particles of the system. Here, the mechanism leads to the unstable modes is established in the context of the nonextensive formalism yet the damping mechanism is the same developed by Landau. Furthermore, our results have the flexibility to reduce to the solutions of an equilibrium Maxwellian EP plasma (extensive limit q→1), in which the Langmuir waves are only the Landau damped modes.

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A generalized ion-sound speed for space and astrophysical plasmas in the regions of near- and far-from-thermal equilibrium is derived in the context of the new formulated invariant Kappa distribution. Inspired by the recent studies on the origin of polytropic behavior in space plasmas, it has been shown that the sound speed is connected to the extended polytropic index of Kappa distributed particles, which itself depends on the invariant Kappa index and the potential degrees of freedom. Generally, the ion-sound speed is a function of the polytropic index of Kappa distributed particles, which varies between two asymptotic regions of equilibrium and anti-equilibrium states. It is found that the ion-sound speed takes its maximum value in an equilibrium plasma and it reduces by approaching to the anti-equilibrium states. Furthermore, dispersion relation of the ion-acoustic waves in our formulism confirms, correspondingly, the recent study on the generalized formulation of Debye shielding in space plasmas. Finally, the classical and generalized relations between the ion-sound speed, the Debye length and the ion oscillation frequency have been discussed.

The propagation of ion-acoustic (IA) solitons is studied in a plasma system, comprised of warm ions and superthermal (Kappa distributed) electrons in the presence of an electron-beam by using a hydrodynamic model. In the linear analysis, it is seen that increasing the superthermality lowers the phase speed of the IA waves. On the other hand, in a fully nonlinear investigation, the Mach number range and characteristics of IA solitons are analyzed, parametrically and numerically. It is found that the accessible region for the existence of IA solitons reduces with increasing the superthermality. However, IA solitons with both negative and positive polarities can coexist in the system. Additionally, solitary waves with both subsonic and supersonic speeds are predicted in the plasma, depending on the value of ion-temperature and the superthermality of electrons in the system. It is examined that there are upper critical values for beam parameters (i.e., density and velocity) after which, IA solitary waves could not propagate in the plasma. Furthermore, a typical interaction between IA waves and the electron-beam in the plasma is confirmed.