  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 dense
mode spectrum and small wave amplitude. In this paper, we extensively studied
the collective processes of a mono-energetic electron beam emitted from a
thermionic cathode propagating through a cold plasma by performing a large
number of high resolution two-dimensional (2D) particle-in-cell (PIC)
simulations and using analytical theories. We confirm that the initial stage of
two-stream instability is saturated due to 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 different regimes are analyzed in detail. For the first
time, we identified a new regime in 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 strong ion density perturbations. Consequently, in this
EMI regime, electron beam-plasma interaction occurs in a periodic
(intermittent) process. The beams are strongly scattered by waves, and the
Langmuir wave spectrum is significantly broadened, which in turn gives rise to
strong heating of bulk electrons. A resulting kappa distribution and a
wave-energy spectrum, E^2 (k)~k^(-5), are observed in the strong turbulent
regime.
