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Aphanasyeva V. V., Lazerson A. G. Chaotic dynamics of two-cavity clystron oscillators with delayed feedback. Izvestiya VUZ. Applied Nonlinear Dynamics, 1995, vol. 3, iss. 5, pp. 88-99.

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Russian
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Article
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621.385.396

Chaotic dynamics of two-cavity clystron oscillators with delayed feedback

Autors: 
Aphanasyeva Vera Vladimirovna, Saratov State University
Lazerson Aleksandr Grigorevich, Saratov State University
Abstract: 

Chaotic behaviour of two-cavity clystron oscillators with delayed feedback is studied. The equations of several types of the devices are derived which are studied by computer simulations. Various chaotic oscillations have been found in wide parameter range on (a, m) - plane where o is the cavity loss parameter, m is the generalised excitation parameter. Transitions to chaos are typical for the dynamical systems with the kind of symmetry discovered earlier in these systems: two asymmetric limit circles instead of period doubling merge with a metastable chaotic set which appears in the phase space after symmetry breaking. This bifurcation gives birth to a symmetric strange attractor which differs from Feigenbaum’s one in spectrum and statistical characteristics. Asymmetric Feigenbaum’s strange attractor does not appear in these systems. At large values of m several symmetric strange «metaattractors» are bounded, and high-dimensional wide- spread hyperchaotic set is formed. The spectrum of this «hyperchaotic» attractor is of 1/f-type. The efficiency of the two-cavity clystron oscillator reaches its maximum value near the bifurcation points, and in the chaotic mode it may exceed that of the singlefrequency mode. The electron beam in chaotic oscillation mode presents a sufficient active load which greatly enhances the bandwidth of the resonant cavity providing superbroadband perfomance of the oscillator. This active load depends not on the direct current density of the beam, but оп its dynamics only.

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Acknowledgments: 
The authors express deep gratitude to D.I. Trubetskov for posing the problem and a number of valuable comments on the content of the manuscript, as well as L.V. Krasichkov and A.A. Kapchatov for kindly providing the program for reconstructing and calculating the dimensions of attractors and advice on its practical application.
Reference: 
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Received: 
26.08.1994
Accepted: 
23.03.1995
Published: 
21.10.1996