Excitation of electron acoustic waves near the electron plasma frequency and at twice the plasma frequency

In this paper we investigate the nonlinear development of the electron acoustic instability that can lead to the transfer of wave energy to frequencies just above the electron plasma frequency (ω pe ) and to waves with approximately twice the electron plasma frequency (2ω pe ). Using plasma conditions in the upstream electron foreshock region based on data from the AMPTE‐UKS spacecraft, an electron beam is considered in plasma containing a background of hot and cold electrons. This leads to the linear excitation of large‐amplitude electron acoustic waves at frequencies between about 0.8 and 1.0 ω pe . A modified decay instability then excites waves in the spectrum just above ω pe . This is followed by a second nonlinear coalescence process that causes the excitation of waves at frequencies just below 2ω pe . The linear and nonlinear properties of the electron acoustic instability are examined for observed conditions using analytical theory, particle‐in‐cell simulations, and Vlasov simulations. These results have application to observations made inside the electron foreshock region, as well as the polar cap and auroral zone, where plasma oscillations and waves at 2ω pe are observed.