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

The interaction of energetic electron beams with a cold plasma is important for a wide range of applications, such as in the hollow cathode and in electron beam-generated plasmas. A crucial outstanding problem is to determine how quickly the beam heats cold electrons for different experimental conditions as well as the physical processes in the systems relevant for industrial applications, such as plasma processing reactors that use electron beams, or hollow cathodes for electrical propulsions and plasma switches. By performing a large number of high resolution two-dimensional (2D) particle-in-cell (PIC) simulations with analytical theory, we extensively studied the collective processes of a mono-energetic electron beam emitted from a thermionic cathode propagating through a cold plasma. We confirm that an initial two-stream instability between the beam and background cold electrons is saturated by wave trapping. Further evolution then 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 beam energy to plasma temperature versus beam density to plasma density . We found a new regime, in which a local Langmuir wave packet grows, faster than the ion frequency, is found. In this new regime, electron beam-plasma interaction occurs as a periodic burst (intermittent) process. The beams are strongly scattered, and the Langmuir wave spectrum is significantly broadened, which gives rise to the strong heating of bulk electrons. We propose scaling laws for the boundary of the unstable regimes and methods to suppress the instabilities, which could be used to guide future operations of low-pressure large-scale plasma devices.