Electrostatic plasma waves above and below the local electron plasma frequency represent a characteristic feature of the foreshock region. These waves are known to be generated by electron beams originating from the bow shock and their spectrum varies from narrowband intense waves close to foreshock edge to weaker broadband emissions further downstream. We present a statistical analysis of electron beams observed in the terrestrial foreshock by the Cluster spacecraft. We compared the energy of foreshock electron beams with the spectrum of electrostatic waves and established a clear correspondence between beam energy and spectrum of the waves. The broadband emissions are correlated with low-energy beams, while high-energy electron beams are associated with narrowband Langmuir waves. Next we solved the linear dispersion relation for a subset of observed electron plasma distributions. We discovered that while the observed electron distributions often exhibit a "bump on tail" feature necessary for an instability, the observed combination of beam energy, density, and temperature typically corresponds to a stable situation. This indicates that strongly unstable electron beams are quickly dissipated by the quasi-linear processes and only stable or marginally stable beams persist long enough to be observed by the instrument.
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