Slow cyclotron instability due to surface modulation of an annular beam

Abstract

The Cherenkov instability used in slow-wave devices has been well studied in the literature. However, in previous analyses, the beam motion is restricted to the longitudinal direction assuming an infinitely strong magnetic field. For the finite strength magnetic field, the transverse beam perturbation cannot be ignored and leads to the slow cyclotron instability. Recently, a new version of self-consistent field theory considering three-dimensional perturbation has been developed based on a solid beam, in which the effect of the transverse perturbation appears as a surface charge at a fixed boundary. In the case of a thin annular beam, the boundary is modulated and is essentially different from the solid beam case. We propose a self-consistent field theory considering the moving modified boundary surface. The slow cyclotron instability due to the modulation of an infinitesimally thin annular electron beam is presented.

Operation Characteristics of Microwave Sources Based on Slow-Wave Interactions in Rectangular Corrugations

“…Beam space-charge effects are included in the interactions using a field theory based on an infinitesimally thin annular beam in Ref. [9]. The slow cyclotron mode depends on the axial magnetic field B 0 .…”

Numerical Analysis of Slow-Wave Instabilities in an X-Band Sinusoidally Corrugated Waveguide with Coaxial Slow-Wave Structure

“…With this assumption, the dispersion relation can be derived self-consistently considering three-dimensional beam perturbations in accordance with the method in Refs. [1,8]. For the beam, relativistic effects are considered.…”

“…[1,7], the perturbation of the sheet beam is treated following the method of Ref. [8]. Boundary conditions at the corrugations are formulated using the methods in Ref.…”

Surface Waves in Oversized G-Band Slow-Wave Structures with Rectangular Corrugations

“…For example, a magnetic field less than 1.0 T is used to guide an annular electron beam in the weakly relativistic oversized BWOs [6] and a magnetic field around 0.4 T was necessary for a ribbon-like beam focusing of Ledatron and SP-FEL [7,9]. The three-dimensional (3D) beam perturbations lead to the slow cyclotron interaction as well as the Cherenkov interaction [10][11][12][13][14]. The slow cyclotron interaction is caused by the anomalous Doppler effect and essentially different from the fast cyclotron interaction, which is due to the normal Doppler effect.…”