This project is similar to Project 1 (The electron-acoustic instability driven by a field-aligned electron beam) in that here we also study the generation of the high frequency component of broadband electrostatic noise (BEN) in the plasma sheet boundary layer by unstable electron-acoustic waves propagating along the magnetic field. The four-component plasma model adopted in this study, viz, stationary hot and cold electrons, stationary ions and drifting ions differs from that considered in Project 1 in that here, the effects of streaming (field-aligned) ions is investigated. The simulation results of Ashour-Abdalla (1986) reveals that it is the increase in the temperature of the cold electrons that stabilizes the electron-acoustic mode since Landau damping increases. The relevant electrostatic wave dispersion relation will be solved numerically which complements the analytical and simulation results of Ashour-Abdalla (1986).