Bilateral approximations for dispersion characteristic of waves over open comb

Closure equation, which takes into account both the dispersion properties and fields’ amplitudes 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 dispersion properties of the eigen waves of open comb. Accuracy of calculation of 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 infinitely thin combs, accuracy of calculation has higher magnitude order than in the case of the same structure without bilateral approximations.