Modulational instability and envelope excitation of ion-acoustic waves in quantum electron-positron-ion plasmas

Abstract

The theoretical study of modulational instability (MI) and localized envelope excitations of finite amplitude ion-acoustic waves (IAWs) is revisited in an unmagnetized quantum electron-positron-ion plasma. For this purpose, a one-dimensional nonlinear Schrödinger equation, which governs the slow modulation of IAW packets, is derived by using the standard reductive perturbations technique. Two parameters, defining the ratio of the electron to ion number density (μ) and the quantum coupling parameter (H) describing the ratio of the “plasmonic energy density” to the Fermi energy density, are shown to play crucial roles in determining the modulational stability/MI domains, as well as for the existence of both bright and dark envelope solitons. It is found that the stability region increases (decreases) with increasing μ(H), whereas the MI region for the IAW mode shifts to larger (smaller) wave number k as the value of μ(H) increases. Moreover, the parameter H is shown to suppress the MI growth rate of the IAWs. The present results may be relevant to dense astrophysical plasmas (e.g., white dwarfs, where the electron-positron annihilation can be important, and where the particle density is of the order of 1034–1035 m−3) as well as to the next generation intense laser solid density plasma experiments.