Bilateral approximations for dispersion characteristic of waves over open comb
DOI:
https://doi.org/10.3103/S0735272711010018Keywords:
open comb, bilateral approximations, closure equationAbstract
Closure equation, which takes into account both the dispersion and amplitude properties in both areas of open comb: area of interaction of electrons and waves and resonators, was obtained. On the basis of the closure equation the bilateral approximations were theoretically justified for the eigen waves of open comb. The dispersion characteristic, found with use of the bilateral approximations for the open comb with combs of infinite thickness, has higher order of accuracy, than one of solutions of dispersion equation without bilateral approximations, using the system with the same order. Regularities for the numbers of accountable space harmonics, using the system of certain order for oscillations in resonators, were found for bilateral approximations to obtain the lowest average error. Bilateral approximations are correct for the comb with the combs of finite thickness. As for the comb with combs of finite thickness, accuracy of calculation has an order of magnitude higher, than the one with the same order has without bilateral approximations.
References
G. V. Kisunko, “Variation principles for boundary (diffraction) electrodynamic problems,” DAN 66, No. 5, 863 (1948).
R. Courant, Methods of Mathematical Physics, Vol. 1 (Wiley, New York, 1949; GITTL, Moscow–Leningrad, 1951).
Sh. Ye. Tsimring, “Variation method of calculating waveguides with periodic resonators,” Radiotekh. Elektron. 2, No. 1, 3, No. 8, 969 (1957).
I. Sh. Beluga, “On methods of partial regions based on stationary nature of some functionals,” Radiotekh. Elektron. 9, No. 3, 459 (1964).
I. Sh. Beluga, “On bilateral approximations when calculating dispersion of slow-wave systems,” Elekronnaya Tekhnika, Ser. 1. Elektronika SVCh, No. 1, 50 (1966).
U. Swinger, “Heterogeneities in waveguides. Lecture course,” Zarubezhnaya Radioelektronika, No. 3, 3 (1970).
Т. Kato, Perturbation Theory for Linear Operators (Springer-Verlag, New York, 1968; Mir, Moscow, 1972).
V. I. Naidenko and Ye. V. Guseva, “Bilateral approximations for resonant frequency of axially-symmetrical electrodynamic systems,” Radiotekh. Elektron. 31, No. 8, 1473 (1986).
V. I. Naidenko and G. N. Shelamov, “Bilateral approximations for eigen frequencies of waveguide microwave resonators of open type,” Radiotekh. Elektron. 33, No. 7, 1541 (1988).
V. I. Naidenko, “Characteristics of Eigen Waves of an Open Comb,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 53(2), 16 (2010) [Radioelectron. Commun. Syst. 53(2), 74 (2010)].
V. I. Naidenko and F. F. Dubrovka, Axially-Symmetrical Periodic Structures and Resonators (Vyssh. Shkola, Kyiv, 1985) [in Russian].
R. А. Silin and V. P. Sazonov, Slow-Wave Systems (Sov. Radio, Moscow, 1966) [in Russian].
V. V. Nikolskii, Variation Methods for Internal Electrodynamic Problems (GIFML, Moscow, 1967) [in Russian].
L. А. Weinestein, Diffraction Theory and Factorization Method (Sov. Radio, Moscow, 1966) [in Russian].
