ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Titov V. N., Volkov D. V., Jakovlev A. V., Ryskin N. M. Reflex klystron as an example of a self­-oscillating delayed feedback system. Izvestiya VUZ. Applied Nonlinear Dynamics, 2010, vol. 18, iss. 6, pp. 138-158. DOI: 10.18500/0869-6632-2010-18-6-138-158

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Language: 
Russian
Heading: 
Methodical Papers on Nonlinear Dynamics
Article type: 
Article
UDC: 
621.385.623.5:517.929
DOI: 
10.18500/0869-6632-2010-18-6-138-158

Reflex klystron as an example of a self­-oscillating delayed feedback system

Autors: 
Titov Vladimir Nikolayevich, Saratov State University
Volkov Dmitrij Viktorovich, Saratov State University
Jakovlev Anton Valerevich, Saratov State University
Ryskin Nikita Mikhailovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Abstract: 

Nonstationary theory of the reflex klystron oscillator based on differential equation with delay is developed. Analysis of self-excitation conditions, steady-state oscillation regimes and their stability is presented. Application of the developed theory for calculating of output characteristics of micromachined submillimetre-band reflex klystron is presented as well. Theoretical results are compared with the results of numerical simulation based on the particle-in-cell method. 

Key words: 
self-oscillation
delayed feedback
reflex klystron
particle-in-cell method
Reference: 
  1. Kuznetsov SP. Complex dynamics of oscillators with delayed feedback. Radiophys. Quant. El. 1982;25(12):996–1009.
  2. Dmitriev AS, Kislov VYa. Stochastic oscillations in radiophysics and electronics. Moscow: Nauka; 1989. 280 p. (in Russian).
  3. Ikeda K, Daido H, Akimoto O. Optical turbulence: Chaotic behavior of transmitted light from a ring cavity. Phys. Rev. Lett. 1980;45(9):709–712. DOI: 10.1103/PhysRevLett.45.709.
  4. Rozanov NN. Optical Bistability and Hysteresis in Distributed Nonlinear Systems. Moscow: Nauka; 1997. (in Russian).
  5. Ghil M, Zaliapin I, Thompson S. A delay differential model of ENSO variability: parametric instability and the distribution of extremes. Nonlin. Processes Geophys. 2008;15:417–433. DOI: 10.5194/npg-15-417-2008.
  6. Glass L, Mackey M. From Clocks to Chaos The Rhythms of Life. Princeton: Princeton University; 1988.
  7. Marchuk GI. Mathematical models in immunology. Moscow: Nauka; 1980. 240 p. (in Russian).
  8. Trubetskov DI, Mchedlova ES, Krasichkov LV. Introduction to the Theory of Self-Organization of Open Systems: Textbook for Students on Physical Specialties. Moscow: Fizmatlit; 2005. 212 p. (in Russian).
  9. Kislov VY, Zalogin NN, Myasin EA. Investigation of stochastic self- oscillation oscillatory processes in oscillators with delayed feedback. Sov. J. Comm. Technol. Electr. 1979;24(6):1118–1130 (in Russian).
  10. Kislov VYa. Theoretical analysis of noise-like oscillations in electron-wave systems and autogenerators with delay and strong nonlinearity. Radio engineering and electronics. 1980;25(8):1683–1690 (in Russian).
  11. Blioh JP, Borodkin AV, Ljubarskij MG, Onishenko IN, Fajnberg JB. The application of the functional reflection method to the twt-generator with delayed feedback. Izvestiya VUZ. Applied Nonlinear Dynamics. 1993;1(1):34–49 (in Russian).
  12. Dmitriev BS, Zharkov YD, Ryskin NM, Shigaev AM. Chaotic Operation of a Delayed-Feedback Klystron Oscillator: Theory and Experiment. Journal of Communications Technology and Electronics. 2001;46(5):561–566.
  13. Dmitriev BS, Zharkov YuD, Kizhaeva KK, Klokotov DV, Ryskin NM, Shigaev AM. Complex dynamics of multiresonator klystron autogenerators with delayed feedback. Izvestiya VUZ. Applied Nonlinear Dynamics. 2002;10(5):37–46 (in Russian).
  14. Shigaev AM, Dmitriev BS, Zharkov YD, Ryskin NM. Chaotic dynamics of delayed feedback klystron oscillator and its control by external signal. IEEE Trans. Electron Devices. 2005;52(5):790–797. DOI: 10.1109/TED.2005.845839.
  15. Ryskin NM, Shigaev AM. Complex dynamics of a double-cavity delayed feedback Klystron oscillator. Technical Physics. 2006;51(1)68–77. DOI: 10.1134/S1063784206010117.
  16. Dmitriev BS, Zharkov YuD, Klokotov DV, Ryskin NM. Experimental study of complex dynamics in a delayed-feedback multiple-cavity klystron self-oscillator. Technical Physics. 2003;48(7):901–905. DOI: 10.1134/1.1593198.
  17. Vainshtein LA, Solntsev VA. Lectures on Microwave Electronics. Moscow: Sov. Radio; 1973. 400 p. (in Russian).
  18. Shevchik VN. Fundamentals of microwave electronics. Moscow: Sov. Radio; 1963. 307 p. (in Russian).
  19. Gaiduk VI, Palatov KI, Petrov DM. Physical foundations of microwave electronics. Moscow: Sov. Radio; 1971. 600 p. (in Russian).
  20. Ultrahigh frequency electronic devices. Study guide. Ed. by Shevchik VN, Grigoriev MA. Saratov: Sarat. State Univ. Publ.; 1980. 460 p. (in Russian).
  21. Trubetskov DI, Khramov AE. Lectures on microwave electronics for physicists. Vol. 1. Moscow: Fizmatlit; 2003. (in Russian).
  22. Kontorovich MI. Nonlinear oscillations in radio engineering. Moscow: Sov. Radio; 1973. 320 p. (in Russian).
  23. Kuznetsov SP. Application of the mathematical apparatus of the theory of differential equations with a deviating argument to some problems of microwave electronics. Lectures on microwave electronics. 3rd winter school-seminar of engineers. Book 1. Saratov: Sarat. State Univ. Publ. 1974:112 (in Russian).
  24. Ives RL. Microfabrication of high-frequency vacuum electron devices. IEEE Trans. Plasma Sci. 2004;32(3):1277–1291. DOI: 10.1109/TPS.2004.827595.
  25. Garcia-Garcia J, Martin F, Miles RE, Steenson DP, Chamberlain JM, Fletcher JR, Thorpe JR. Parametric analysis of micromachined reflex klystrons for operation at millimeter and submillimeter wavelengths. J. Appl. Phys. 2002;92(11):6900. DOI: 10.1063/1.1519955.
  26. Fletcher JR, Thorpe JR, Huq E, Mann C, Steenson DP, Chamberlain JM. Design considerations for submillimeter-wave reflex klystrons. IEEE Trans. Microwave Theory and Techniques. 2004;52(10):2344–2351. DOI: 10.1109/TMTT.2004.835977.
  27. Garcia-Garcia J, Martin F, Miles RE. Optimization of micromachined reflex klystrons for operation at terahertz frequencies. IEEE Transactions on Microwave Theory and Techniques. 2004;52(10):2366–2370. DOI: 10.1109/TMTT.2004.835975.
  28. Jang KH, Jeon SG, Kim JI, Won JH, So JK, Bak SH, Srivastava A, Jung SS, Park GS. High order mode oscillation in a terahertz photonic-band-gap multibeam reflex klystron. Appl. Phys. Lett. 2008;93:211104. DOI: 10.1063/1.3037026.
  29. Jeon SG, Jin YS, Kim JI, Kim GJ, Shon CH. Three-dimensional particle-in-cell simulations of 300 GHz reflex klystrons. J. Appl. Phys. 2007;101(5):054519. DOI: https://doi.org/10.1063/1.2710353.
  30. Dmitrieva TV, Ryskin NM, Titov VN, Shigaev AM. Complex dynamics of simple models of extended electron-wave systems. Izvestiya VUZ. Applied Nonlinear Dynamics. 1999;7(6):66–82 (in Russian).
  31. Atabekov GI. Fundamentals of the theory of circuits. M.: Energiya, 1969. 427 p. (in Russian).
  32. Kuznetsov SP. Nonlinear dynamics of backward-wave tube: self-modulation, multi-stability, control. Izvestiya VUZ. Applied Nonlinear Dynamics. 2006;14(4):3–35. DOI: 10.18500/0869-6632-2006-14-4-3-35 (in Russian).
  33. Badsel Ch, Langdon A. Plasma physics and numerical modeling. Translated from English. Moscow: Atomizdat; 1989.
  34. Hockney R, Eastwood J. Numerical modeling by the particle method. Trans. from English. Moscow: Mir; 1987.
  35. Rowe J. Theory of nonlinear phenomena in ultrahigh frequency devices. Moscow: Sov. Radio; 1969. (in Russian).
  36. Chodorow M, Westburg VB. Space-charge effects in reflex klystrons. Proc. IRE. 1951;39(12):1548–1555. DOI: 10.1109/JRPROC.1951.273645.
Received: 
04.06.2010
Accepted: 
02.08.2010
Published: 
31.01.2011
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