Examining by the Rayleigh-Fourier method the cylindrical waveguide with axially rippled wall

Axially corrugated cylindrical waveguides with wall radius described by R₀(1+εcos2πz/L), where R₀ is the average radius of the periodically rippled wall with period L and amplitude ε, have been largely used as slow-wave structures in high-power microwave generators operating in axisymmetric transverse magnetic (TM) modes. On the basis of a wave formulation whereby the TM eigenmodes are represented by a Fourier-Bessel expansion of space harmonics, this paper investigates the electrodynamic properties of such structures by deriving a dispersion equation through which the relationship between eigenfrequencies and corrugation geometry is explored. Accordingly, it is found that for L/R₀≥1 a stopband always exists at any value of ε; the condition L/R₀=1 gives the widest first stopband with the band narrowing as the ratio L/R₀ increases. For L/R₀=0.5 the stopband sharply reduces and becomes vanishingly small when ε<0.10. Illustrative example of such properties is given on considering a corrugated structure with L/R₀=1,R₀=2.2 cm, and ε=0.1, which yields a stopband of 1.5-GHz width with the central frequency at 8.4 GHz; it is shown that in a ten-period corrugated guide, the attenuation coefficient reaches 165 dB/m, which makes such structures useful as an RF filter or a Bragg reflector. It is also discussed that by varying L/R₀ and ε we can find a variety of mode patterns that arise from the combination of surface and volume modes; this fact can be used for obtaining a particular electromagnetic field configuration to favor energy extraction from a resonant cavity.