Geodesic
Turbulence in microwave electronics: Teoretical approaches and experimental results
Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 24 (2016) no. 5, pp. 4-36.

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A review of the current state of different theoretical approaches to the description of turbulence in electron beams and electronic devices at microwave frequencies is shown. A three types of turbulent (nonlaminar) electron beams were considered. The first type of turbulent electron beam is caused by the intersection of electronic trajectories (e.g., due to thermal velocity) and it is common to the flow of electrons at all. The turbulence of the second type is due to the instability of the electron beams, because of which a small perturbations grow for an exponentially (such instabilities include diocotron and slipping-instability). The third type – vortex turbulence, the cause of which is filamentarization of electron flow. Formed charged filaments interact among themselves, that leads to the formation of vortex structures; the presence of this structures increases the number of collective degrees of freedom and may lead to turbulence. The results of an experimental study of turbulent flows and electronic generators with their use in standalone mode and when an external signal were shown. Various types of broadband broadband microwave oscillators oscillations were investigated. We discuss the phenomenological model of turbulent the electron beam, which is a chain of superradiant clots containing electron-oscillators, chain of «vortices» ( «vortices» are describes by the modified equations of van der Pol).
Keywords: electron flow, turbulence, instability, vortex, generator, broadband microwave generation. 
@article{IVP_2016_24_5_a1,
     author = {D. I. Trubetskov and Yu. A. Kalinin and A. V. Starodubov and A. S. Fokin},
     title = {Turbulence in microwave electronics: {Teoretical} approaches and experimental results},
     journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
     pages = {4--36},
     publisher = {mathdoc},
     volume = {24},
     number = {5},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVP_2016_24_5_a1/}
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D. I. Trubetskov; Yu. A. Kalinin; A. V. Starodubov; A. S. Fokin. Turbulence in microwave electronics: Teoretical approaches and experimental results. Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 24 (2016) no. 5, pp. 4-36. http://geodesic.mathdoc.fr/item/IVP_2016_24_5_a1/