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

Abstract

Subject and purpose. 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 dispersive 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 propagated along the surface of solid-state plasma cylinder has been carried out. Methods and methodology. Using Maxwell's equations and motion equation of plasma electrons based on an integrated approach (analytical and numerical) the nonlinear theory of instability of a tubular electron beam flying over a plasma cylinder has been constructed. The plasma of the cylinder was assumed collisionless. The calculations have been performed in electrostatic approximation due to the nonrelativistic velocity of the beam electrons. Results. It is shown that the nonlinear stabilization of the wave amplitude increase is realized due to the bunching of the beam electrons into bunches and their subsequent capture by the wave field. The law of the instability rise time and the wave maximum amplitude from the plasma cylinder radius has been revealed. It is established that the nonlinear stage of instability begins earlier in an electrodynamic system with a smaller radius of the plasma cylinder. In this system, the maximum value of the slow amplitude has greater value. Conclusions. The research results broaden our understanding about the physical properties of systems with plasma-like media and systematize knowledge about the excitation mechanisms of potential surface waves in electrodynamic systems that form the basis of microwave oscillators.

Keywords

• beam instability
• capture of particles
• electron beam
• instability increment
• nonlinear interaction
• phase portrait
• vavilov-cherenkov effect