Broadband electrostatic noise (BEN) which is the term used to describe electro- static wave emissions ranging from a few Hz to well above the electron plasma frequency, is found to be a common feature in various regions of the Earth’s magnetosphere. There have been several studies conducted in an attempt to un- derstand the excitation mechanisms of BEN. The linear electron-acoustic wave instability driven by drifting electrons (field-aligned) is found to explain the high frequency component of BEN fairly well. In this study, we consider an unmagnetized plasma with four components comprising stationary hot and cold Maxwellian electrons, a warm electron beam and stationary ions to theoret- ically study the generation of BEN in some regions of the Earth’s magneto- sphere by unstable electron-acoustic waves. By excluding the magnetic field in our study, our results are only valid for wave propagation parallel to the field. The relevant electrostatic wave dispersion relation will be solved numerically for some plasma parameters characteristic of the dayside auroral region, plasma sheet boundary layer and the polar cusp region of the Earth’s magnetosphere. The dependence of the real frequency and instability growth rate on various plasma parameters such as beam drift speed, particle temperatures and parti- cle densities will be studied. Our numerical results will be compared with the approximate analytical results of Singh and Lakhina (2001). Our results for a four-component plasma will be compared with the results of earlier studied cases of three-component plasmas having only two electron components (Gary and Tokar,1985; Bharuthram,1991).