Geodesic
Nonlinear dynamics of the backward-wave oscillator as the origin of nonstationary microwave electronics
Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 29 (2021) no. 4, pp. 480-514.

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Aim. This article presents a review of the non-stationary nonlinear phenomena in backward-wave oscillators (BWO). Methods. Numerical modeling using the nonstationary (time-domain) 1-D, 2-D, and 2-D nonlinear theory of electron beam interaction with a backward electromagnetic wave in the slowly varying amplitude approximation. Results. Main results of nonstationary nonlinear theory of O-type and M-type BWO are presented. The typical bifurcation scenario is described, which is observed with an increase of electron beam current in numerical simulations as well as in experiments. Different kinds of chaotic behavior are demonstrated. Nonstationary phenomena in BWOs with oversized electromagnetic systems are discussed, namely, the diffractive mode selection as well as the generation of Cherenkov superradiance pulses by short electron bunches. Conclusion. The nonstationary nonlinear theory is a powerful tool for modeling of beam-wave in BWO as well as in other microwave tubes. Using this theory, algorithms and computer codes for time-domain simulation have been developed, which are widely used in fundamental and applied research. These codes not only provide analysis of different modes of interaction in existing electron devices, but also allow to propose and analyze new schemes for which the standard stationary approach is ineffective.
Keywords: nonstationary theory of excitation, backward-wave oscillator, self-modulation, chaos, superradiance, diffractive mode selection. 
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     author = {N. M. Ryskin and A. G. Rozhnev and N. S. Ginzburg and I. V. Zotova},
     title = {Nonlinear dynamics of the backward-wave oscillator as the origin of nonstationary microwave electronics},
     journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
     pages = {480--514},
     publisher = {mathdoc},
     volume = {29},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVP_2021_29_4_a2/}
}
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N. M. Ryskin; A. G. Rozhnev; N. S. Ginzburg; I. V. Zotova. Nonlinear dynamics of the backward-wave oscillator as the origin of nonstationary microwave electronics. Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 29 (2021) no. 4, pp. 480-514. http://geodesic.mathdoc.fr/item/IVP_2021_29_4_a2/