Geodesic
Analogy in interactions of electronic beams and hydrodynamic flows with fields of resonators and periodic structures. Part 2. Self-excitation, amplification and dip conditions
Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 24 (2016) no. 2, pp. 5-26.

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The subject of this research concerns the problem of excitation of acoustic oscillations and waves in the flow of fluid interacting with resonators and periodic structures, in relation to which application of methods and theoretical apparatus similar to those developed in the electronics and electrodynamics in the context of the excitation of electromagnetic oscillations and waves is productive. The proposed approach is based on reduction of the hydrodynamic equations of compressible fluid to a form similar to the Maxwell equations with subsequent developing theory of excitation of resonators and waveguides as discussed in the previous part of this article. By analogy with the theory of microwave electronic devices with crossed fields, basing on the self-consistent theory, we study the interaction of vortex currents with a periodic structure in the case of strong own instability. A linear theory of the acoustic amplifier is developed, in which the interaction is weak, and the flow at the input of the interaction space is not perturbed. The possibility of a full suppression of the surface waves in certain modes of functioning of such a system is noted. It has been shown that efficient coupling of the flow with a backward wave is possible in the structure, and conditions for the self-excitation of the counter-directed wave are found. It can be concluded that the analogy between the hydrodynamic problem and the processes in electronic devices with crossed fields is of considerable interest from the point of view of describing the phenomena of excitation of acoustic oscillations and waves by the vortex currents and evaluating the prospects for their practical use. Special attention should be put for self-excitation of oscillations due to the interaction of the flow with the counter-directed waves, similar to the effect occuring in the backward-wave tubes.
Keywords: Electron beam, hydrodynamic flow, vortices, periodic structures, theory of excitation, dip conditions, signal self-excitation. 
@article{IVP_2016_24_2_a1,
     author = {A. P. Kuznetsov and S. P. Kuznetsov},
     title = {Analogy in interactions of electronic beams and hydrodynamic flows with fields of resonators and periodic structures. {Part} 2. {Self-excitation,} amplification and dip conditions},
     journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
     pages = {5--26},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVP_2016_24_2_a1/}
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A. P. Kuznetsov; S. P. Kuznetsov. Analogy in interactions of electronic beams and hydrodynamic flows with fields of resonators and periodic structures. Part 2. Self-excitation, amplification and dip conditions. Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 24 (2016) no. 2, pp. 5-26. http://geodesic.mathdoc.fr/item/IVP_2016_24_2_a1/