[en] Electron-electron two stream instability in many valley semiconductors like n-GaAs embedded with a nanoparticle has been studied in hydrodynamic regime. The ingredients of this study are the consideration of polar optical phonon as the dominant intravalley scattering mechanism and a drifted Maxwellian distribution for the carriers in each valley of the medium. A dispersion relation has been developed by the self consistent solution of the momentum transfer, continuity and Maxwell’s equations. Typical values of the parameters of n-GaAs at room temperature are considered for analyzing the dispersion relation of the electrostatic wave. Detail qualitative analysis of the convective instability of possible four modes of propagation reveals that the dispersion, propagation and gain profiles of all the four modes have been affected profoundly by the presence of a nanoparticle in the medium via electron plasma frequency of electron cloud present in the nanoparticle. (author)