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

Abstract

Axially corrugated cylindrical waveguides with wall radius described by 0 (1 + cos 2 ), where 0 is the average radius of the periodically rippled wall with period and amplitude , have been largely used as slow-wave structures in highpower 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 0 1 a stopband always exists at any value of ; the condition 0 = 1 gives the widest first stopband with the band narrowing as the ratio 0 increases. For 0 = 0 5 the stopband sharply reduces and becomes vanishingly small when 0.10. Illustrative example of such properties is given on considering a corrugated structure with 0 = 1 0 = 2 2 cm, and = 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 0 and 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.

Dispersion Characteristics of Arbitrary Periodic Structures with Rectangular Grooves

“…Figure 2 shows the convergence of the dispersion curve of the first TM mode with the number of spatial harmonics used to describe the field in Region I for a waveguide with L=15 mm, R 0 =10 mm and ɛ=0.025 (2πR 0 ɛ/L ≈ 0.105, i.e., this case is enough below the Rayleigh criterion [13]). Obviously, even with seven spatial harmonics (N max =3) the convergence is very satisfactory and the numerical results are identical to those of previous works [14]. The last conclusion is still valid for the case presented in Fig.…”

“…The electromagnetic properties as well as their dependence on the geometrical characteristics of the metallic wall for a sinusoidally corrugated cylindrical waveguide have been also examined by a Fourier-Bessel expansion [14]. The same technique has been applied to calculate the dispersion characteristics of TM modes for a piecewise continuous, but not sinusoidally corrugated cylindrical waveguide, for which the Rayleigh criterion is satisfied [15].…”

“…In this work, the mathematical formulations employed to study cylindrical waveguides with sinusoidal [14] and rectangular [17] surface corrugations are combined to study the dispersion relation of TM modes for a periodic corrugation profile, which may contain a deep or a shallow rectangular groove with smoothing. The mathematical formulation of the corresponding electromagnetic problem is presented for the case of axisymmetric TM modes.…”

The sinusoid as the longitudinal profile in backward-wave oscillators of large cross sectional area

“…Adressing this basic question, here we present design tools for the synthesis of sinusoidal profiles from the technical goals for the BWO, namely, the operating frequency and the beam energy. The analysis develops on the basis of the Rayleigh-Fourier method, whereby the field solution is represented by a single expansion of TM space harmonics [10]. This method has been verified by some authors [11][12][13][14] as the one (among the least-squares and the integral methods) giving by far the best overall description of wave scattering from sinusoidal surfaces.…”

Transmission Characteristics of Corrugated Elliptic Guide Considering Higher Order Modes in the Slot Region

“…Corrugated circular guide [1][2][3] had been studied by rayleigh-fourier method and mode matching method. Corrugated rectangular guide [4,5] had been studied in detail.…”