Peculiar behavior of the instability in systems with weak electron beam-plasma coupling

A study is developed, which allows investigating weakly coupled electron beam-plasma systems in general form regardless on geometry and specific parameters. In this case the instability acquires completely new aspects. In contrast to the well-known case of strong coupling, the role of the beam natural oscillations becomes decisive. The instability is due to the growth of the beam wave of negative energy. The study shows that the space-time evolution of an initial perturbation in weakly coupled beam-plasma systems is described by partial differential equation of second order. The equation is solved. Obtained expression for the fields’ space-time distribution gives most complete information on the instability: growth rates, velocities of unstable perturbations, influence of the dissipation on the instability, its character, (absolute/convective), etc. Most of the information is unavailable by conventional methods. In particular, the results clearly show that with an increase in the level of dissipation in the plasma, the instability transforms into a new, previously unknown type of dissipative streaming instability (DSI). Its growth rate depends on dissipation more critically than the growth rate of the single known DSI.