Nonlinear theory of interaction between a tubular beam of charged particles and potential surface waves of plasma cylinder*

Investigation of the generation mechanisms of electromagnetic waves by the motion of charged particles in various electrodynamic systems is an actual problem of modern radiophysics and electronics. Recently, much attention has been paid to the interaction between the streams of charged particles and solid-state structures that have dispersion properties. As a rule, such structures contain plasma-like media. The basis for the generation of electromagnetic waves is the system instabilities caused by perturbations in the streams of charged particles. The stationary mode of wave generation is provided by nonlinear interactions of a charged particle beam with eigenmodes of solid-state structure. In this paper, a theoretical study of the nonlinear stabilization effect of instability of an infinitesimally thin tubular electron beam propagating along the surface of a solid-state plasma cylinder has been carried out. Using Maxwell's equations and motion equation of plasma electrons based on an integrated approach (analytical and numerical), the nonlinear theory of instability of the tubular electron beam flying above the plasma cylinder has been constructed. The plasma of the cylinder was assumed collisionless. The calculations have been performed to an electrostatic approximation due to the nonrelativistic nature of motion of the beam. It is shown that the nonlinear stabilization of increase in the wave amplitude is realized due to the bunching of the beam electrons into clots and their subsequent capture by the wave field. The dependence of the instability rise time and the wave maximum amplitude on the plasma cylinder radius has been found out. It is established that the nonlinear stage of instability begins earlier in an electro-dynamic system with a smaller radius of the plasma cylinder. At that in such a system, the maximum magnitude of the slow amplitude has a greater value. The research results broaden our understanding about the physical properties of systems with plasma-like media and systematize our knowledge about the excitation mechanisms of potential surface waves in the electrodynamic systems that form the basis of microwave oscillators. ©2019 by Begell House, Inc.