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Electron-beam plasma interaction has long been a topic of great interest.Despite the success of Quasi-Linear (QL) theory and Weak Turbulence (WT)theory, their validities are limited by the requirement of sufficiently densemode spectrum and small wave amplitude. In this paper, we extensively studiedthe collective processes of a mono-energetic electron beam emitted from athermionic cathode propagating through a cold plasma by performing a largenumber of high resolution two-dimensional (2D) particle-in-cell (PIC)simulations and using analytical theories. We confirm that the initial stage oftwo-stream instability is saturated due to well-known wave-trapping mechanism.Further evolution occurs due to strong wave-wave nonlinear processes. We showthat the beam-plasma interaction can be classified into four different physicalregimes in the parameter space for the plasma and beam parameters. Thedifferences between the different regimes are analyzed in detail. For the firsttime, we identified a new regime in strong Langmuir turbulence featured by whatwe call Electron Modulational Instability (EMI) that could create a localLangmuir wave packet growing faster than the ion plasma frequency. Ions do nothave time to respond to EMI in the initial growing stage. On a longertimescale, the action of the ponderomotive force produces very strong iondensity perturbations, and eventually the beam-plasma wave interaction stopsbeing resonant due to strong ion density perturbations. Consequently, in thisEMI regime, electron beam-plasma interaction occurs in a periodic(intermittent) process. The beams are strongly scattered by waves, and theLangmuir wave spectrum is significantly broadened, which in turn gives rise tostrong heating of bulk electrons. A resulting kappa distribution and awave-energy spectrum, E^2 (k)~k^(-5), are observed in the strong turbulentregime.

Physical Regimes of Electrostatic Wave-Wave nonlinear interactions generated by an Electron Beam Propagating in a Background Plasma