TE Waves in Arbitrary Periodic Slow-wave Structures with Rectangular Grooves
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TE Waves in Arbitrary Periodic Slow-wave Structures with Rectangular Grooves Sotiris A. Mallios & George P. Latsas & Ioannis G. Tigelis
Received: 14 March 2009 / Accepted: 29 May 2009 / Published online: 16 June 2009 # Springer Science + Business Media, LLC 2009
Abstract The dispersion characteristics of the transverse electric modes in a waveguide with circular cross-section and periodic rectangular surface corrugations with smoothed edges are examined by the space harmonic method. The whole structure is divided into two regions, one in the propagation area and one inside the grooves. In the first region, the Floquet theorem is applied and the field distribution is expressed as a summation of spatial Bloch components, while an appropriate Fourier expansion of standing waves is used inside the grooves. Applying the appropriate interface conditions, an infinite system of equations is obtained, which is solved numerically by truncation. Numerical results are presented for several cases to check the convergence and the accuracy of the method, as well as its dependence on the corrugation profile. This formalism could be easily expanded to include all kind of waves that can in principle propagate in such slow-wave structures. Keywords Slow-wave structures . Spatial harmonics . Rectangular grooves with smoothing
1 Introduction Metal hollow waveguides with different types of periodic surface corrugations are widely used as slow-wave structures in high-power microwave sources [1–4]. In the design of these devices, it is essential to study the coupling coefficients of the electron beam with the fields of the structure, as well as the mode competition. In the past, a significant part of the research effort has been directed to increase the operating frequency as well as the output power, mostly in the interaction of the lowest order transverse magnetic (TM) mode (axial interaction) with an electron beam. There are also studies of
S. A. Mallios : G. P. Latsas : I. G. Tigelis (*) Department of Electronics, Computers, Telecommunications and Control, National and Kapodistrian University of Athens, Faculty of Physics, Building V, Panepistimiopolis, Zografou, 157 84 Athens, Greece e-mail: [email protected]
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J Infrared Milli Terahz Waves (2009) 30:1113–1122
transverse electric (TE) and hybrid modes, since the cyclotron interaction is employed in gyro-devices [5–8]. Recently, slow-wave structures with complex profiles have been proposed [9] and some of them are already used in different types of microwaves devices, like multi-wave generators [2, 3]. In order to achieve maximum efficiency with minimum mode interference, it is very important to study carefully the dispersive characteristics of all modes, which can propagate in such slow-wave structures. In fast-wave devices smooth (cylindrical or conical) or slightly corrugated waveguides are used, while for slow-wave ones deep rectangular or sinusoidal corrugations are employed. Note that in the gyrotron, which is a fast-wave device, the beam-tunnel is a slow-wave struct
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