Abstract
The evolution of initial perturbation in the case of electron beam instability development in various systems is investigated generally. The approach is based on the equation for slowly varying amplitude of an induced wave packet. It is shown that the space-time dynamics of fields in the case of beam instability development is described by a partial differential equation of third order independently on system geometry, presence of external fields, specific parameters, etc. This equation is solved and the analytical expression for the fields’ space-time structure is obtained and analyzed. The shape of the induced wave packet is presented. The velocities of unstable perturbations vary between the group velocity of the resonant wave (without beam) and the beam velocity. The dependence of the growth rates of the perturbations from their velocities is obtained. The well-known maximal growth rate of resonant beam instability is nothing else than the growth rate in the peak of the wave packet. Previous investigations on beam instability dynamics actually are particular cases of the present result. The dynamics of beam instability in other cases also may be obtained from this one by specifying the system parameters. For a given system, only two parameters must be specified (in a system with dissipation—three). Some often encountered examples are presented: boundless beam-plasma system, magnetized beam-plasma waveguide, dissipative beam instability, rippled-wall waveguide. Obtained results are valid both for plasma-filled and vacuum systems for a large class of monoenergetic electron beam instabilities: Cherenkov-type, cyclotron-type, beam instability in periodical structures, etc.
Published Version
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