AUTOMODULATION AND CHAOTIC REGIMES OF GENERATION IN A TWO-RESONATOR GYROKLYSTRON WITH DELAYED FEEDBACK
Cite this article as:
Rozental R. M., Isaeva O. B., Ginzburg N. S., Zotova I. V., Rozhnev А. G., Tarakanov V. P., Sergeev A. S. AUTOMODULATION AND CHAOTIC REGIMES OF GENERATION IN A TWO-RESONATOR GYROKLYSTRON WITH DELAYED FEEDBACK . Izvestiya VUZ. Applied Nonlinear Dynamics, 2018, vol. 26, iss. 3, pp. 78-98. DOI: https://doi.org/10.18500/0869-6632-2018-26-3-78-98
Topic and aim. The dynamics of a double-resonator gyroklystron of the 93 GHz band with delayed feedback is studied. A comparative analysis of the dynamical regimes of amplifier generation obtained in the numerical experiment both on the basis of averaged equations and in the framework of direct numerical simulation by the «particle-in-cells» method using the KARAT code is carried out. Method. To identify the dynamical properties of system behavior we apply the spectrum of of statistical methods from the theory of chaos: the calculation of fractal dimensions, Lyapunov exponents, etc. To find the Lyapunov exponents we apply a method of estimating them from dynamical time series. This method is extremely convenient, since it requires only the single scalar time realization in a fixed in space point of spatially distributed system, for example, the amplitude of output radiation. Moreover, this method imitates the processing of the data that can be obtained in natural experiment. Results. The analysis of the time series obtained in numerical simulation showed the existence of hyperchaotic regimes for both approaches to the modeling of gyroklystron. Such regimes correspond to attractors with a high correlation dimension and more than one positive Lyapunov exponents. It was found that mentioned hyperchaotic regimes occur, for example, with an increase in the transmission factor for the feedback loop. The multimode «strong» hyper-chaos arises from chaos resulting from the sequence of period doubling bifurcations of the periodic automodulation mode intensity of output radiation gyroklystron. Discussion. UHF chaotic and noise generators are extremely important for various technical applications. One can note, for example, radars and wideband communication. Thus, the production of multimode, chaotic and hyper-chaotic regimes of gyro-amplifiers generation is a priority branch of microwave electronics. Being proposed in this paper the mathematical modeling methods allow to detect complex regimes for gyroklystron. Being proposed in this paper the approaches to amplifier generations analysis can be applied in a physical experiment.
DOI: 10.18500/0869-6632-2018-26-3-78-98
1. Andronov A.A., Flyagin V.A., Gaponov A.V., Gol’denberg A.L., Petelin M.I., Usov V.G., Yulpatov V.K. The gyrotron: High-power source of millimetre and submillimetre waves // Infrared Phys. 1978. Vol. 18, no. 5-6. Pp. 385–393.
2. Nusinovich G.S. Introduction to the Physics of Gyrotrons. Baltimore: J. Hopkins Univ. Press, 2004. 341 p.
3. Thumm M. State-of-the-art of high power gyro-devices and free electron masers. Update 2016 // KIT Scientific Reports. 2017. Band-Nr. 7735.
4. Zasypkin E.V., Gachev I.G., Antakov I.I. Experimental study of a W-band gyroklystron amplifier operated in the high order TE021 cavity mode. Radiophys. Quant.El., 2012, vol. 55, no. 5, pp. 309–317.
5. Zaitsev N.I., Gvozdev A.K., Zapevalov S.A., Kuzikov S.V., Manuilov V.N., Moiseev M.A., Plotkin M.E. Experimental study of a multimegawatt pulsed gyroklystron. Journal of Communications Technology and Electronics, 2014, vol.59, no.2, pp.164–168.
6. Zaitsev N.I., Abubakirov E.B., Guznov Yu.M., Denisov G.G., Zavolskii N.A., Zapevalov V.E., Zapevalov S.A., Plankin O.P., Rozental R.M., Sedov A S., Semenov E.S., Chirkov A.V., Shevchenko A.S. Book of abstracts of 25th Int. Crimean Conf.
7. Swati M.V., Chauhan M.S., Jain P.K. Design methodology and beam-wave interaction study of a second-harmonic D-band gyroklystron amplifier // IEEE Trans. Plasma Sci. 2016. Vol. 44, no. 11. Pp. 2844–2851.
8. Kuznetsov S.P., Perelman A.Yu., Trubetskov D.I. Technical Physics, 1983, vol. 53, no. 1, pp. 163–166.
9. Grishin S.V., Dmitriev B.S., Zharkov Y.D., Skorohodov V.N., Sharaevskii Y.P. Gene- ration of chaotic microwave pulses in a ring system based on a klystron power amplifier and a nonlinear delay line on magnetostatic waves. Technical Physics Letters, 2010, vol. 36, iss. 2, pp. 76–79
10. Emelyanov V.V., Girevoy R.A., Yakovlev A.V., Ryskin N.M. Time-domain particle-in-cell modeling of delayed feedback klystron oscillators // IEEE Trans. Electron. Dev. 2014. Vol. 61, no. 6. Pp. 1842–1847.
11. Ергаков В.С., Моисеев М.А. Двухрезонаторный генератор с запаздывающей обратной связью // Радиотехника и электроника. 1986. Т. 31, вып. 5. С. 962–967.
12. Afanasieva V.V., Lazerson A.G. Chaotic dynamics of two-cavity clystron oscillators with delayed feedback. Izvestiya VUZ. Applied Nonlinear Dynamics, 1995, vol. 3, no. 5, pp. 88–99. (in Russian).
13. Ginzburg N.S., Rozental R.M., Sergeev A.S., Zotova I.V. Time-domain model of gyroklystrons with diffraction power input and output // Physics of Plasmas. 2016. Vol. 23. 033108–033112.
14. Zasypkin E.V., Moiseev M.A., Gachev I.G., Antakov I.I. Study of high-power Kaband second-harmonic gyroklystron amplifier // IEEE Trans. Plasma Sci. 1996. Vol. 24, no. 3. Pp. 666–670.
15. Tolkachev A.A., Levitan B.A., Solovjev G.K., Veytsel V.V., Farber V.E. A megawatt power millimeter-wave phased-array radar // IEEE Aerospace and Electronic Systems Magazine. 2000. Vol. 15. Pp. 25–31.
16. Antakov I.I., Gachev I.G., Zasypkin E.V. Experimental studies of a gyroklystron operating in the field of a permanent magnet. Radiophys. Quant. El., 2011, vol. 54, no. 3, pp. 166–173.
17. Ginzburg N.S., Zavolsky N.A., Nusinovich G.S. Theory of non-stationary processes in gyrotrons with low-Q resonators // Int. J. Electron. 1986. Vol. 61. Pp. 881–894.
18. Ginzburg N.S., Sergeev A.S., Zotova I.V. Time-domain self-consistent theory of frequency-locking regimes in gyrotrons with low-Q resonators // Phys. Plasmas. 2015. Vol. 22. 033101–033105.
19. Katz V.A. Appearance of chaos and its evolution in a distributed oscillator with delay (experiment). Radiophys. Quant. El., 1985, vol. 28, no. 2, pp. 107–119.
20. Ustinov A.B., Kondrashov A.V., Kalinikos B.A. A microwave photonic generator of chaotic and noise signals. Technical Physics Letters, 2016, vol.42, no.4, pp.403–406.
21. Vlasov S.N., Zhislin G.M., Orlova I.M., Petelin M.I., Rogacheva G.G. Irregular wa- veguides as open resonators. Radiophys. Quant. El., 1969, vol.12, no.8, pp.972–978.
22. Ryskin N.M. Study of the nonlinear dynamics of a traveling-wave-tube oscillator with delayed feedback. Radiophysics and Quantum Electronics, 2004, vol. 47, no. 2, pp. 116–128.
23. Kuznetsov S.P. Complex dynamics of oscillators with delayed feedback (review). Radiophys. Quant. El., 1982, vol. 25, no. 12, pp. 996–1009.
24. Dmitrieva T.V., Ryskin N.M., Titov V.N., Shigaev A.M. Complex dynamics of the simple models of distributed electron-wave systems. Izvestiya VUZ, Applied Nonlinear Dynamics, 1999, vol. 7, no. 6, pp. 66–81 (in Russian).
25. Tarakanov V.P. The Universal Electromagnetic Code KARAT. Math. Modeling. Problems and Results. Moscow: Nauka, 2003, 456 p. (in Russian).
26. Tarakanov V.P. Code KARAT in simulations of power microwave sources including Cherenkov plasma devices, vircators, orotron, E-fieldsensor, calorimeter etc. EPJ Web of Conferences, 2017, vol. 149, 04024.
27. Ergakov V.S., Moiseev M.A. Electronnaya Tekhnica, Ser I, Electronica SVCH, 1977, no. 5, pp. 9–15 (in Russian).
28. Ergakov V.S., Moiseev M.A., Erm R.E. Electronnaya Tekhnica. Ser I. Electronica SVCH, 1980, no. 4, pp. 29–37 (in Russian).
29. Zasypkin E.V., Moiseev M.A. Efficiency enhancement in gyroklystrons with a nonu- niform static magnetic field. Radiophys. Quant. El., 1994, vol.37, no.10, pp.853–862.
30. Kuznetsov S.P. Dynamical Chaos. Moscow: Fizmatlit, 2006. 356 p. (in Russian).
31. Bezruchko B.P., Smirnov D.A. Extracting Knowledge from Time Series. An In- troduction to Nonlinear Empirical Modeling. Heidelberg–Dordrecht–London–New York: Springer, 2010. 420 p.
32. Bradley E., Kantz H. Nonlinear time-series analysis revisited. Chaos, 2015, vol. 25, 097610–097619.
33. Lyapunov A.M. General Problem of the Motion Stability. Moscow–Leningrad: GITTL, 1950, 472 p. (in Russian).
34. Eckmann J.-P., Ruelle D. Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems. Physica D, 1992, vol. 56, pp. 185–187.
35. Bezruchko B.P., Bulgakova L.V., Kuznetsov S.P., Trubetskov D.I. Radiotekhnica i Electronica, 1983, vol. 28, no. 6, pp. 1136–1139 (in Russian).
36. Kuznetsov S.P., Trubetskov D.I. Chaos and hyperchaos in a backward-wave oscillator. Radiophys. Quant. El., 2004, vol. 47, no. 5–6, pp. 341–355.
37. Blokhina E.V., Rozhnev A.G. Chaos and hyperchaos in a gyrotron. Radiophysics and Quantum Electronics, 2006, vol. 49, no. 10, pp. 799–810.
38. Blokhina E.V., Kuznetsov S.P., Rozhnev A.G. High-dimensional chaos in a gyrotron. IEEE Trans. Electron. Dev., 2007, vol. 54, no. 2, pp. 188–193.
39. Balyakin A.A., Ryskin N.M. Peculiarities of calculation of the Lyapunov exponents set in distributed self-oscillated systems with delayed feedback. Izv. VUZ. Applied Nonlinear Dynamics, 2007, vol. 15, no. 6, pp. 3–21 (in Russian).
40. Benettin G., Galgani L., Giorgilli A., Strelcyn J.-M. Lyapunov characteristic expo- nents for smooth dynamical systems and for Hamiltonian systems; A method for computing all of them. Part 1: Theory. Meccanica, 1980, vol. 15, pp. 9–20.
41. Benettin G., Galgani L., Giorgilli A., Strelcyn J.-M. Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; A method for computing all of them. Part 2: Numerical application // Meccanica. 1980. Vol. 15. Pp. 21–30.
42. Wolf A., J.Swift B., Swinney H.L., Vastano J.A. Determining Lyapunov exponents from a time series // Physica D. 1985. Vol. 16. Pp. 285–317.
43. Eckmann J.-P., Kamphorst S.O., Ruelle D., Gilberto D. Lyapunov exponents from a time series // Phys. Rev. A. 1986. Vol. 34. Pp. 4971–4979.
44. Brown R., Bryant P., Abarbanel H.D.I. Computing the Lyapunov spectrum of a dynamical system from an observed time series // Phys. Rev. A. 1991. Vol. 43. Pp. 2787–2806.
45. Sano M., Sawada Y. Measurement of the Lyapunov spectrum from a chaotic time series // Phys. Rev. Lett. 1985. Vol. 55. Pp. 1082–1085.
46. Zeng X., Eykholt R., Pielke R.A. Estimating the Lyapunov exponent spectrum from short time series of low precision // Phys. Rev. Lett. 1991. Vol. 66. Pp. 3229–3232.
47. Rozental R.M., Isaeva O.B., Ginzburg N.S., Zotova I.V., Sergeev A.S., Rozhnev A.G. Characteristics of chaotic regimes in a space-distributed gyroklystron model with delayed feedback // Rus. J. Nonlin. Dyn. 2018. No. 2. (in press).
48. Ginzburg N.S., Rozental R.M., Sergeev A.S., Zotova I.V. Generation of ultrashort microwave pulses in the sub-THz and THz range based on the cyclotron superradiance effect. Technical Physics Letters, 2017, vol. 43, no. 9, pp. 831–834.
49. Frolov N.S., Kurkin S.A., Koronovskii A.A., Hramov A.E. Nonlinear dynamics and bifurcation mechanisms in intense electron beam with virtual cathode. Phys. Lett. A, 2017, vol. 381, no. 28, pp. 2250–2255.
50. Rozental R.M., Ginzburg N.S., Sergeev A.S., Zotova I.V., Fedotov A.E., Taraka- nov V.P. Gyrotron generation of broadband chaotic radiation under overlapping of high- and low-frequency resonances. Technical Physics, 2017, vol. 62, no. 10, pp. 1562–1568.
BibTeX
author = {R. M. Rozental and O. B. Isaeva and N. S. Ginzburg and I. V. Zotova and А. G. Rozhnev and V. P. Tarakanov and A. S. Sergeev},
title = {AUTOMODULATION AND CHAOTIC REGIMES OF GENERATION IN A TWO-RESONATOR GYROKLYSTRON WITH DELAYED FEEDBACK },
year = {2018},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {26},number = {3},
url = {https://old-andjournal.sgu.ru/en/articles/automodulation-and-chaotic-regimes-of-generation-in-two-resonator-gyroklystron-with-delayed},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2018-26-3-78-98},pages = {78--98},issn = {0869-6632},
keywords = {gyroklystron,delayed feedback,strong chaos},
abstract = {Topic and aim. The dynamics of a double-resonator gyroklystron of the 93 GHz band with delayed feedback is studied. A comparative analysis of the dynamical regimes of amplifier generation obtained in the numerical experiment both on the basis of averaged equations and in the framework of direct numerical simulation by the «particle-in-cells» method using the KARAT code is carried out. Method. To identify the dynamical properties of system behavior we apply the spectrum of of statistical methods from the theory of chaos: the calculation of fractal dimensions, Lyapunov exponents, etc. To find the Lyapunov exponents we apply a method of estimating them from dynamical time series. This method is extremely convenient, since it requires only the single scalar time realization in a fixed in space point of spatially distributed system, for example, the amplitude of output radiation. Moreover, this method imitates the processing of the data that can be obtained in natural experiment. Results. The analysis of the time series obtained in numerical simulation showed the existence of hyperchaotic regimes for both approaches to the modeling of gyroklystron. Such regimes correspond to attractors with a high correlation dimension and more than one positive Lyapunov exponents. It was found that mentioned hyperchaotic regimes occur, for example, with an increase in the transmission factor for the feedback loop. The multimode «strong» hyper-chaos arises from chaos resulting from the sequence of period doubling bifurcations of the periodic automodulation mode intensity of output radiation gyroklystron. Discussion. UHF chaotic and noise generators are extremely important for various technical applications. One can note, for example, radars and wideband communication. Thus, the production of multimode, chaotic and hyper-chaotic regimes of gyro-amplifiers generation is a priority branch of microwave electronics. Being proposed in this paper the mathematical modeling methods allow to detect complex regimes for gyroklystron. Being proposed in this paper the approaches to amplifier generations analysis can be applied in a physical experiment. DOI: 10.18500/0869-6632-2018-26-3-78-98 References: Automodulation and chaotic regimes of generation in a two-resonator gyroklystron with delayed feedback. Izvestiya VUZ, Applied Nonlinear Dynamics, 2018, vol. 26, no. 3, pp. 78–98. DOI: 10.18500/0869-6632-2018-26-3-78-98 }}