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Bilateral approximations for dispersion characteristic of waves over open comb

Viktor I. Naidenko, A. S. Postulga


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.


open comb; bilateral approximations; closure equation

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