Physical regimes of electrostatic wave-wave nonlinear interactions generated by an electron beam propagating in a background plasma.

Electron-beam plasma interaction has long been a topic of great interest. Despite the success of the quasilinear and weak turbulence theories, their validities are limited by the requirements of a sufficiently dense mode spectrum and a small wave amplitude. In this paper, we extensively study the collective processes of a mono-energetic electron beam emitted from a thermionic cathode propagating through a cold plasma by performing high-resolution two-dimensional particle-in-cell simulations and using analytical theories. We confirm that, during the initial stage of two-stream instability between the beam and background cold electrons, it is saturated due to the well-known wave-trapping mechanism. Further evolution occurs due to strong wave-wave nonlinear processes. We show that the beam-plasma interaction can be classified into four different physical regimes in the parameter space for the plasma and beam parameters. The differences between the regimes are analyzed in detail. We identify a new regime in the strong Langmuir turbulence featured by what we call electron modulational instability (EMI) that could create a local Langmuir wave packet growing faster than the ion plasma frequency. Ions do not have time to respond to EMI in the initial growing stage. On a longer timescale, the action of the ponderomotive force produces very strong ion density perturbations, and eventually, the beam-plasma wave interaction stops being resonant due to the strong ion density perturbations. Consequently, in this EMI regime, electron beam-plasma interaction occurs in a repetitive (intermittent) process. The beam electrons are strongly scattered by waves, and the Langmuir wave spectrum is significantly broadened, which in turn gives rise to strong heating of bulk electrons. Associated energy transfer from the beam to the background plasma electrons has been studied. A resulting kappa (κ) distribution and a wave-energy spectrum E^{2}(k)∼k^{-5} are observed in the strong turbulent regime.