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

For citation:

Novozhilova Y. V. Parametric instability of autooscillator coupled with remote load. I. Theory. Izvestiya VUZ. Applied Nonlinear Dynamics, 2011, vol. 19, iss. 2, pp. 112-127. DOI: 10.18500/0869-6632-2011-19-2-112-127

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
(downloads: 120)
Article type: 

Parametric instability of autooscillator coupled with remote load. I. Theory

Novozhilova Yulija Vladimirovna, Institute of Applied Physics of the Russian Academy of Sciences

At the autooscillator with weakly reflected remote load the number of one-frequency states – longitudinal modes – increases with the growth of the reflection coefficient and the length of the delay line. A mode of this kind can be unstable in some parameter regions. There can be two types of perturbations: a) the perturbations resulting in a slow evolution of principal mode amplitude and frequency; b) the perturbations in the form of two satellites which frequencies are symmetric from that of the principal mode. The modes stability relative to each type of perturbations was studied analytically.

  1. Dmitriev AS, Kislov VY. Stochastic Oscillations in Radiophysics and Electronics. Moscow: Nauka; 1989. 277 p. (in Russian).
  2. Kuznetsov SP. Dynamic chaos. Moscow: Fizmatlit; 2001. 356 p. (in Russian).
  3. Trubetskov DI. Introduction to Synergetics. Chaos and structures. Moscow: Editorial URSS; 2004. 240 p. (in Russian).
  4. Grigorieva EV, Kashchenko SA. Order parameters in models of lasers with delayed feedback. In: New in Synergetics. A Look Into The Third Millennium. Moscow: Nauka; 2002. P. 185 (in Russian).
  5. Anishchenko VS, Vadivasova TE, Astakhov VV. Nonlinear Dynamics of Chaotic and Stochastic Systems. Saratov: Saratov University Press; 1999. 367 p. (in Russian).
  6. Ginzburg NS, Petelin MI, Shapiro MA. Automodulation and Stochastic Oscillation Regimes in Resonant Relativistic Electron Masers. 10-th European Conf. On Contr. Fusion and Plasma Physics. Vol. 1. Moscow; 1981. P. M2.
  7. Ginzburg NS, Kuznetsov SP, Fedoseeva TN. Theory of transients in relativistic backward-wave tubes. Radiophys. Quantum Electron. 1978;21(7):728–739. DOI: 10.1007/BF01033055.
  8. Marchewka C, Larsen P, Bhattacharjee S, Booske J, Sengele S, Ryskin NM, Titov VN. Generation of chaotic radiation in a driven traveling wave tube amplifier with time-delayed feedback. Phys. Plasmas. 2006;13(1):013104. DOI: 10.1063/1.2161170.
  9. Ryskin NM, Shigaev AM. Complex dynamics of a double-cavity delayed feedback Klystron oscillator. Tech. Phys. 2006;51(1):68–77. DOI: 10.1134/S1063784206010117.
  10. Bezruchko BP, Karavaev AS, Ponomarenko VI, Prokhorov MD. Reconstruction of time-delay systems from chaotic time series. Phys. Rev. E. 2001;64(5):056216. DOI: 10.1103/PhysRevE.64.056216.
  11. Losson J, Mackey MC. Coupled map lattices as models of deterministic and stochastic differential delay equations. Phys. Rev. E. 1995;52(1):115–128. DOI: 10.1103/PhysRevE.52.115.
  12. Glyavin MY, Zapevalov VE, Kuftin AN, Luchinin AG. Experimental study of the spectral composition of the output radiation in a gyrotron with partial reflection of the output signal. Radiophys. Quantum Electron. 2000;43(5):396–399. DOI: 10.1007/BF02677156.
  13. Ginzburg NS, Zaitsev NI, Ilyakov EV, Kulagin IS, Rozental’ RM. Self-modulated generation observed in a delayed feedback relativistic microwave gyrotron. Tech. Phys. Lett. 2002;28(5):395–398. DOI: 10.1134/1.1482746.
  14. Rozental R, Ginzburg N, Glyavin M, Zaitsev N, Zapevalov V, Ilyakov E, Kulagin I. Self-modulation spectrum variation in gyrotrons with output reflector. Proceedings of Joint 29th International Conference on Infrared and Millimeter Waves and 12th International Conference on Terahertz Electronics. Karlsruhe, Germany, 2004. Vol. 2. IEEE; 2004. P. 306. DOI: 10.1109/ICIMW.2004.1422249.
  15. Airila MI, Dumbrajs O, Kall P, Piosczyk B. Influence of reflections on the operation of the 2 MW, CW 170 GHz coaxial cavity gyrotron for ITER. Nucl. Fusion. 2003;43(11):1454–1457. DOI: 10.1088/0029-5515/43/11/018.
  16. Airila MI, Kall P. Effect of reflections on nonstationary gyrotron oscillations. IEEE Transactions on Microwave Theory and Techniques. 2004;52(2):522–528. DOI: 10.1109/TMTT.2003.821920.
  17. Dumbrajs O, Idehara T, Watanabe S, Kimura A, Sasagawa H, Agusu L, Mit-sudo S, Piosczyk B. Reflections in gyrotrons with axial output. IEEE Transactions on Plasma Science. 2004;32(3):899–902. DOI: 10.1109/TPS.2004.827596.
  18. Grudiev A, Jelonnek J, and Schunemann K. Time-domain analysis of reflections influence on gyrotron operation. Phys. Plasmas. 2001;8(6):2963–2973. DOI: 10.1063/1.1366330.
  19. Grudiev A, Schunemann K. Nonstationary behavior of a gyrotron in the presence of reflections. International Journal of Infrared and Millimeter Waves. 2003;24(4):429–449.
  20. Landa PS. Nonlinear Oscillations and Waves in Dynamical Systems. Springer, Dordrecht; 1996. 544 p. DOI: 10.1007/978-94-015-8763-1.
  21. Antonsen TM, Cai SY, Nusinovich GS. Effect of window reflection on gyrotron operation. Phys. Fluids B. 1992;4(12):4131–4139. DOI: 10.1063/1.860320.
  22. Novozhilova JV, Sergeev AS, Usacheva SA. Parametric instability of autooscillator coupled with remote load. II. Numerical simulation. Izvestiya VUZ. Applied Nonlinear Dynamics. 2011;19(2):128–140 (in Russian). DOI: 10.18500/0869-6632-2011-19-2-128-140.
  23. Rabinovich MI, Trubetskov DI. Oscillations and Waves in Linear and Nonlinear Systems. Springer, Dordrecht; 1989. 578 p. DOI: 10.1007/978-94-009-1033-1.
  24. Fernandez A, Kharchev NK, Novozhilova YV, Batanov GM, Bondar YF, Kolik LV, Sarkisian KA, Tolkachev A. Gyrotron reaction on small reflection from nonstationary load. Applied Physics. 2009;(6):158–165 (in Russian).
  25. Neimark YI. D-decomposition of the space of quasi-polynomials. (On the stability of linearized distributed systems). Applied Mathematics and Mechanics. 1949;3(4):349–380 (in Russian). 
Short text (in English):
(downloads: 85)