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Hramov A. E. Complex dynamics of coherent structures in two-stream vircator. Izvestiya VUZ. Applied Nonlinear Dynamics, 1998, vol. 6, iss. 2, pp. 42-64.

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Russian
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Complex dynamics of coherent structures in two-stream vircator

Autors: 
Hramov Aleksandr Evgenevich, Immanuel Kant Baltic Federal University
Abstract: 

System of virtual cathode oscillators with electrostatic coupling-vircator оп oncoming streams is investigated with the aid of numerical simulation. The existence of different regimes, including the synchronisation and chaotic generation, is shown. Physical processes in the system are determined by the formation of electron patterns in each beam. The inner structures in the beam are analysed by the orthogonal decomposition by Karhunen-Loeve method. The simplest finite-dimension model-analogy is proposed to illustrate of аn interaction between electron structures in the beam, that leads to chactic dynamics of virtual cathode oscillation.

Key words: 
Acknowledgments: 
The author is grateful to V. G. Anfinogentov for his attention to this work, repeated discussions and useful critical comments. The work was supported by the RFBR (project 98-02-16541).
Reference: 
  1. Sze Н, Harteneck В, Price D. Phase locking оf two strongly coupled vircators. J. Appl. Phys. 1990;67(5):2278-2282. DOI: 10.1063/1.345521.
  2. Woo W, Benford J, Fittingoff D, Harteneck B, Price D, Smith R, Sze H. Phase locking оf high—power microwave oscillators. J. Appl. Phys. 1989;65(2):861-866. DOI: 10.1063/1.343079.
  3. Selemir VD, Alekhin VV, Vatrunin VK, Dubinov AE, Stepanov NV, Shamro OA, Shibalko KV. Theoretical and experimental studies of microwave devices with a virtual cathode. Plasma Physics Reports. 1994;20(7-8):689-708. (in Russian).
  4. Hendricks K, Richard А, Noggle R. Experimental results оf phase locking two virtual cathode oscillator. J. Appl. Phys. 1990;68(2):820-825. DOI: 10.1063/1.346762.
  5. Magda II, Prokopenko YuV. Co-operative high—power radiation оf two beams at the dual vircator complex. In: Proc. оf 11th International Conference оn High Power Particle Beams. 10-14 June 1996, Prague, Czech Republic. Р. 422–425.
  6. Granatstein VL, Alexeff I, editors. High Power Microwave Sources. Boston: Artech House, 1987. 564 p.
  7. Artyukh IG, Sadalov AI, Sulakshin AS, Fomenko GP, Shtein YuG. Relativistic devices of ultra-high power. Reviews on Electronic Technology. Ser. 1. Microwave Electronics. 1989;17(1490):70. (in Russian).
  8. Grigorjev VP, Zherlitsyn AG, Koval TV, Kuznetsov SI, Melnikov GV. On the possibility of changing the frequency of radiation by an external signal in a microwave triode with a virtual cathode. Tech. Phys. Lett. 1988;14(23):2164-2168. (in Russian).
  9. Hramov AE. Influence of external action оn chaotic dynamics оf virtual cathode oscillations. In: Proc. оf 5th Int. Specialist Workshop оn Nonlinear Dynamics оf Electronic Systems (NDES’97). 26-27 June, 1997. Moscow, Russia. P. 443.
  10. Anfinogentov VG, Hramov AE. Non-autonomous oscillations of the electron flux with a virtual cathode in a flat diode gap. Izvestiya VUZ. Applied Nonlinear Dynamics. 1997;5(6):61-75. (in Russian).
  11. Ginzburg NS, Kuznetsov SP. Periodic and stochastic automodulation modes in electronic generators with distributed interaction. In: Relativistic High-frequency Electronics. Gorky: Institute of Applied Physics AS USSR Press; 1981. P. 101-144. (in Russian).
  12. Afanasjeva VV, Trubetskov DI. Dynamic chaos in electronic ultra-high-frequency devices.  Reviews on Electronic Technology. Ser. 1. Microwave Electronics. 1991;4(1615):32.
  13. Trubetskov DI, Mchedlova ES, Anfinogentov VG, Ponomarenko VI, Ryskin NM. Nonlinear waves, chaos and patterns in microwave devices. Chaos. 1996;6(3):358-367. DOI: 10.1063/1.166179.
  14. Madon А, Klinger Т. A model for the bifurcations to plasma drift—waves. Physica D. 1997;102(3-4):335-342. DOI: 10.1016/S0167-2789(96)00194-7.
  15. Akhromeeva TS, Kurdyumov SP, Malinetskii GG, Samarskii AA. Non-stationary Structures and Diffusion Chaos.М.:Nauka; 1992. 541 p. (in Russian).
  16. Kaneko K. Simulating Physics with Coupled Map Lattices. In: Kawasaki K, Suzuki M, Onuki A, editors. Formation, Dynamics and Statistics of Patterns. Vol. 1. Singapore: Word Scientific; 1990. P. 1-54. DOI: 10.1142/9789814368223_0001.
  17. Privezentsev AP, Fomenko GP. Complex dynamics of charged particle flow with virtual cathode. Izvestiya VUZ. Applied Nonlinear Dynamics. 1994;2(5):56-68. (in Russian).
  18. Brandt HE. The turbutron. IEEE Trans. Plasma Sci. 1985;13(6):513-519. DOI: 10.1109/TPS.1985.4316466.
  19. Afonin AM, Didenko AN, Pautkin АF, Roshal AS. Nonlinear dynamics of the virtual cathode in triode systems. Sov. J. Comm. Tech. Electron. 1992;37(10):1889.
  20. Anfinogentov VG, Khramov AE. Mechanism of chaotic dynamics and interaction of coherent structures in a vacuum microwave generator on a virtual cathode. In: Materials of the scientific conference “Modern Problems of Electronics and Radiophysics of Microwave”. 4-8 September 1997, Saratov, Russia. Saratov: College; 1997. P. 4-6.
  21. Anfinogentov VG. Interaction of coherent structures and chaotic dynamics in the electronic flow with the virtual cathode. Tech. Phys. Lett. 1995;21(8):70-75.
  22. Anfinogentov VG. Nonlinear dynamics аnd chaotic behaviour оf electron beam with virtual cathode in the Pierce diode. In: Proc. Зrd Int. Specialist Workshop оn Nonlinear Dynamics in Electronic Systems (NDES’95), 28-29 July, 1995, Dublin, Ireland. Dublin: 1995. Р. 79.
  23. Anfinogentov VG. Chaotic dynamics and structure formation in the plasma diode with virtual cathode. In: Proc. 24th European Physical Society Conference оn Controlied Fusion and Plasma Physics. Vol. 3. 9—13 June 1997. Berchtesgaden, Germany. Berchtesgaden; 1997. P. 1293,
  24. Hramov AE. Oscillations in the system of two connected generators on a virtual cathode of virtual type with controlled communication: a computational experiment. Izvestiya VUZ. Applied Nonlinear Dynamics. 1998;6(1):108-121.
  25. Anfinogentov VG, Hramov AE. Complex behavior of an electron stream with a virtual cathode and generation of chaotic signals in virtual systems. Bulletin of the Russian Academy of Sciences: Physics. 1997;61(12):2391-2401.
  26. Gadetskii NN, Magda II, Najsteter SN, Prokopenko YuV, Chumakov VI. Generator on supercritical REP current with controlled feedback - virtod. Plasma Physics Reports. 1993;19(4):530-537.
  27. Anfinogentov V.G. Chaotic dynamics of electron beam with virtual cathode in the bounded systems. In: Proc. of 11th International Conference on High-Power Particle Beams. 10-14 June 1996, Prague, Czech Republic. P. 381-384.
  28. Anfinogentov VG, Hramov AE. Influence of distributed feedback on chaotic virtual cathode oscillation. Izvestiya VUZ. Applied Nonlinear Dynamics. 1998;6(1):93-107. (in Russian).
  29. Kwan TJT, Thode LE. Formation of virtual cathodes and microwave generation in relativistic electron beams. Phys. Fluids. 1984;27:1570-1572. DOI: 10.1063/1.864811.
  30. Didenko AN, Rashchikov VI. Generation of powerful microwave oscillations in systems with a virtual cathode. Plasma Phys. Rep. 1992;18(9):1182-1190.
  31. Birdsall CK, Langdon АB. Plasma Physics Via Computer Simulation. N.Y.: McGraw-Hill; 1985. 479 p.
  32. Roache PJ. Computational Fluid Dynamics. Socorro: Hermosa Publishers; 1976. 446 p.
  33. Takens F.  Detecting strange attractors in turbulence. In: Rand D, Young LS, editors. Dynamical Systems and Turbulence, Warwick 1980. Lecture Notes in Mathematics. Vol 898. Berlin: Springer; 1980. P. 366-381. DOI: 10.1007/BFb0091924.
  34. Grassberger Р, Procaccia I. Characterization оf strange attractors. Phys. Rev. Lett. 1983;50(5):346-349. DOI: 10.1103/PhysRevLett.50.346.
  35. Berge P, Pomeau Y, Vidal C. Order Within Chaos. Towards a Deterministic Approach to Turbulence. N.Y.: Wiley; 1987. 329 p.
  36. Watanabe S. Karunen-Loeva decomposition and factor analysis. Theory and applications. In: Braverman EM, editor. Automatic Analysis of Complex Images. M.: Mir; 1969. P. 251-273.
  37. Lumley JL. The structure оf ingomogeneous turbulent flows. In: Yaglom AM, Tutarsky VI, editors. Atmospheric Turbulence and Radio Wave Propagation: Proc. of the International Colloquim. Moscow: Nauka, 1967. P. 166.
  38. Wilkinson JH. The Algebraic Eigenvalue Problem. Oxford: Clarendon Press; 1965. 662 p.
  39. Privezentsev AP, Fomenko GP, Filipenko NM. Fluctuations of the electron flow in a flat span. Sov. Phys. Tech. Phys. 1981;26(6):659.
  40. Privezentsev AP, Fomenko GP, Filipenko NM. Phenomenological analysis of the stability of stationary states of intense electron flow in the drift space. Sov. J. Comm. Tech. Electron. 1983;28(5):1011.
  41. Matsumoto T, Chua LO, Tanaka S. Simplest chaotic nonautonomous circuits. Phys. Rev. A. 1984;30(2):1155-1157. DOI: 10.1103/PhysRevA.30.1155.
  42. Andrushkevich AV, Kipchatov AA, Krasichkov LV, Koronovskii AA. The path to chaos in a piecewise linear model of a tunnel diode generator. Izvestiya VUZ. Applied Nonlinear Dynamics. 1993;1(1-2):93-103. (in Russian).
  43. Kipchatov AA, Podin SV. Study of the behavior of a non-autonomous relaxation generator in the space of control parameters. Izvestiya VUZ. Applied Nonlinear Dynamics. 1996;4(4-5):30. (in Russian).
Received: 
17.10.1997
Accepted: 
05.06.1998
Published: 
08.07.1998