Coupled-mode theory of Langmuir space-charge waves for general electron-beam and waveguide cross sections

An alternative approach for the analysis of the electromagnetic field and plasma-wave propagation in a waveguide filled with an electron (e) beam is presented. The analysis is based on a formal exact expansion of the total electromagnetic field in terms of waveguide modes. We subsequently use linear fluid plasma equations and electromagnetic coupled-mode theory to find the dispersion relation for the eigenmodes of the beam (plasma) loaded waveguide. The proposed method enables one to solve for the Langmuir space-charge waves in an e beam with an arbitrary transverse geometry and density distribution, moving along any uniform-cross-section waveguide at constant average velocity. The use of the method is demonstrated by presenting a calculation of the dispersion curve and the plasma frequency reduction factor of plasma modes in a practical case of a circular beam drifting along a rectangular waveguide.