Cut-on modes versus plasma radius a.

This study introduces a method for analyzing the propagation of electromagnetic waves in cylindrical structures with central chambers facilitating beam-plasma interactions, particularly relevant for slow-wave structures in backward wave oscillators. The boundary value problem, governed by the Helmholtz equation, is resolved using the mode-matching technique, yielding an exact solution. The analysis elucidates key phenomena, including reflection, transmission, orthogonality relations, and power flux variations with frequency and material properties. By examining the effects of plasma frequency and beam radius on phase velocity, group velocity, and interaction efficiency, the study provides insights into optimizing wave propagation and energy transfer. The results demonstrate that higher plasma frequencies and reduced beam radii enhance scattering characteristics, offering practical guidance for designing efficient electromagnetic devices.