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

For citation:

Kurkin S. A., Koronovskii A. A., Egorov E. N., Levin Y. I., Filatov R. A. Mathematical model and its numerical realization for the investigation and optimization of generators with electron feedback. Izvestiya VUZ. Applied Nonlinear Dynamics, 2010, vol. 18, iss. 6, pp. 106-137. DOI: 10.18500/0869-6632-2010-18-6-106-137

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: 199)
Article type: 

Mathematical model and its numerical realization for the investigation and optimization of generators with electron feedback

Kurkin Semen Andreevich, Innopolis University
Koronovskii Aleksei Aleksandrovich, Saratov State University
Egorov Evgenij Nikolaevich, Saratov State University
Levin Yurij Ivanovich, Saratov State University
Filatov Roman Andreevich, Saratov State University

It was stated in the paper the mathematical model and its numerical realization for the investigation of wideband chaotic oscillations and of physical processes in the electron beams with virtual cathode at the generators with electron feedback. Also it was briefly described the developed program package for the modeling of non­stationary nonlinear physical processes at the electron generators with virtual cathode and for calculating of output characteristics of devices. It was described the numerical methods and its features used in the program package. Results of some calculations and optimizations of various configurations of the systems with virtual cathode were presented in the paper.

  1. Dmitriev AS, Panas AI. Dynamic Chaos: Novel Type of Information Carrier for Communications Systems. Moscow: Fizmatlit; 2002.
  2. Dronov V, Hendrey MR, Antonsen TM, Ott E. Communication with a chaotic traveling wave tube microwave generator. Chaos. 2004;14(1):30–37. DOI: 10.1063/1.1622352.
  3. Dmitriev BS, Hramov AE, Koronovskii AA, Starodubov AV, Trubetskov DI, Zharkov YD. First experimental observation of generalized synchronization phenomena in microwave oscillators. Physical Review Letters. 2009;102(7):074101. DOI: 10.1103/PhysRevLett.102.074101.
  4. Koronovskii AA, Moskalenko OI, Hramov AE. On the use of chaotic synchronization for secure communication. Phys. Usp. 2009;52(12):1213–1238.
  5. Narayanan RM, Dawood M. Doppler estimation using a coherent ultrawide-band random noise radar. IEEE Trans. Antennas and Propagation. 2000;48(6):868–878. DOI: 10.1109/8.865218.
  6. Zalogin NN, Kislov VV. Broadband Chaotic Signals in Radio Engineering and Information Systems. Moscow: Radiotekhnika; 2006. (in Russian).
  7. Meadows BK, Heath TH, Ne JD, et al. Nonlinear antenna technology. Proceedings IEEE. 2002;90(5):882–897. DOI: 10.1109/JPROC.2002.1015012.
  8. Shalfeev VD, Matrosov VV, Korzinova MV. Dynamic chaos in ensembles of coupled phase systems. Zarubezh. Radioelektron. Usp. Sovrem. Radioelektron. 1998;11:44–56  (in Russian).
  9. Didenko AN, Krasik YE, Perelygin SF, Fomenko GP. Generation of powerful microwave radiation by a relativistic electron beam in a triode system. Tech. Phys. Lett. 1979;5(6):321–324 (in Russian).
  10. Trubetskov DI, Khramov AE. Lectures on Microwave Electronics for Physicists. Vol. 2. Moscow: Fizmatlit; 2004. 648 p. (in Russian).
  11. Dubinov AE, Selemir VD. Electronic devices with a virtual cathode (review). Journal of Communications Technology and Electronics. 2002;47(6):575–600.
  12. Granatstein VL, Alexeff I. High Power Microwave Sources. Artech House Microwave Library; 1987.
  13. Benford J, Swegle JA, Schamiloglu E. High Power Microwaves. Taylor and Francis: CRC Press; 2007.
  14. Shevchik VN, Shvedov GN, Soboleva AN. Wave and oscillatory phenomena in electron flows at ultrahigh frequencies. Saratov: Sarat. State Univ. Publ.; 1962. 334 p. (in Russian).
  15. Kalinin YuA, Koronovskii AA, Khramov AE, Egorov EN, Filatov RA. Experimental and theoretical investigations of stochastic oscillatory phenomena in a nonrelativistic electron beam with a virtual cathode. Plasma Physics Reports. 2005;31(11):938–952. DOI: 10.1134/1.2131130.
  16. Egorov EN, Kalinin YuA, Levin YuI, Trubetskov DI, Khramov AE. Vacuum generators of broadband chaotic oscillations based on nonrelativistic electron beams with virtual cathode. Bulletin of the Russian Academy of Sciences: Physics. 2005;69(12):1921–1924.
  17. Gursharn S, Shashank C. Secondary virtual-cathode formation in a low-voltage vircator: Pic simulations. IEEE Transactions on Plasma Science. 2008;36(3):694–700. DOI: 10.1109/TPS.2008.922499.
  18. Kalinin YuA, Hramov AE. Experimental and theoretical investigation into the effect of the electron velocity distribution on chaotic oscillations in an electron beam under virtual cathode formation conditions. Technical Physics. 2006;51(5):558–566. DOI: 10.1134/S1063784206050045.
  19. Filatov RA, Khramov AE, Kalinin YuA. RF Patent (Useful Model) RU59323U1. Microwave generator of chaotic broadband signal on virtual cathodes. Official Bulletin of the Federal Service for Intellectual Property, Patents and Trademarks; No. 34. Moscow: FIPS. (December 10, 2006). (in Russian).
  20. Kalinin YuA, Kurkin SA, Trubetskov DI, Hramov AE. Microwave generators of chaotic oscillations based on the beam with virtual cathode. Telecommunications and Radio Engineering. 2008;9:53–55 (in Russian).
  21. Egorov EN, Kalinin YA, Koronovskii AA, et al. Analysis of the formation of structures and chaotic dynamics in a nonrelativistic electron beam with a virtual cathode in the presence of a decelerating field. J. Commun. Technol. Electron. 2007;52:45–57. DOI: 10.1134/S106422690701007X.
  22. Egorov EN, Kalinin YuA, Koronovskii AA, Hramov AE. Analysis of the dependence of the microwave generation power of a low-voltage vircator on controlling parameters. Technical Physics. 2007;52(10):1387–1390. DOI: 10.1134/S1063784207100258.
  23. Filatov RA, Hramov AE, Bliokh YP, Koronovskii AA, Felsteiner J. Influence of background gas ionization on oscillations in a virtual cathode with a retarding potential. Physics of Plasmas. 2009;16(3):033106. DOI: 10.1063/1.3080200.
  24. Kalinin YA, Starodubov AV, Volkova LN. Ultrabroadband generators of noiselike high-frequency and microwave oscillations with electron feedback. Tech. Phys. Lett. 2010;36:112–114. DOI: 10.1134/S1063785010020069.
  25. Roshal AS. Modeling of charged beams. Moscow: Atomizdat; 1979. 224 p. (in Russian).
  26. Sveshnikov AG, Yakunin SA. Numerical models of collisionless plasma dynamics. Matem. Mod. 1989;1(4):1–25 (in Russian).
  27. Anderson TM, Mondelli AA, Levush B, Verboncoeur JP, Birdsall CK. Advances in modelling and simulation of vacuum electron devices. Proceedings IEEE. 1999;87(5):804–839. DOI: 10.1109/5.757256.
  28. Birdsall CK, Langdon AB. Plasma physics, via computer simulation. New-York: McGrawHill; 1985.
  29. Warren G, Ludeking L, Nguyen K, Smithe D, Goplen B. Advances/applications of MAGIC and SOS. Computational Accelarator Physics. AIP Conf. Proc. 1994;297:313–322.
  30. Tarakanov VP. User’s manual for code KARAT. Springfield, VA: BRA; 1992.
  31. A software suite with total synergy. Microwave Journal. 2006;49(1):19.
  32. Verboncoeur JP, Langdon AB, Gladd NT. An object-oriented electromagnetic PIC code. Comput. Phys. Commun. 1991;64:252–266.
  33. Antoshkin MYu, Grigoryev VP, Koval TV, Sablin NI. An electromagnetic code in the polar coordinates system for mathematical simulation of microwave radiation in a coaxial triode with a virtual cathode. Matem. Mod. 1995;7(8):25–35 (in Russian).
  34. Alimovskii IV. Electron Beams and Electron Guns. Moscow: Sov. Radio; 1966. (in Russian).
  35. Koronovskii AA, Trubetskov DI, Hramov AE. Methods of nonlinear dynamics and chaos in problems of microwave electronics. Vol. 2. Unsteady and chaotic processes. Moscow: Fizmatlit; 2009. (in Russian).
  36. Kalinin YA, Kozhevnikov VN, Lazerson AG, et al. Dynamical chaos in a charged-particle flow produced by a magnetron injection gun: Numerical simulation and experiment. Tech. Phys. 2000;45:896–904. DOI: 10.1134/1.1259745.
  37. Kalinin YuA, Kuznetsov NN, Ukrainskaya TN. Investigation of wide-band stochastic oscillations produced by virtual cathode in intensive beams of charged particles. Izvestiya VUZ. Applied Nonlinear Dynamics. 2002;10(5):32–36 (in Russian).
  38. Tsimring SE. Electron beams and microwave vacuum electronics. John Wiley and Sons, Inc., Hoboken, New Jersey; 2007.
  39. Kalinin YA, Koronovskii AA, Hramov AE. Chaotic wideband microwave oscillations in a hybrid system consisting of a traveling wave tube and a collector oscillator. Tech. Phys. 2008;53:614–619. DOI: 10.1134/S1063784208050149.
  40. Kalinin YuA, Esin AD. Methods and Means of Physical Experiment in Vacuum Microwave Electronics. Saratov: Sarat. State Univ. Publ.; 1991. (in Russian).
  41. Kalinin YuA, Panin AF, Ukrainskaya TN. Experimental study of the spectrum of the longitudinal components of the electron velocity during the RF field period. Electronic equipment. Ser. 1. 1976;2:111 (in Russian).
  42. Trubetskov DI, Hramov AE. Lectures on microwave electronics for physicists. Vol. 1. Moscow: Fizmatlit; 2003. 496 p. (in Russian).
  43. Roach P. Computational Fluid Dynamics. Albuquerque: Hermosa; 1972.
  44. Boris JP, Lee R. Optimization of particle calculations in 2 and 3 dimensions. Commun. Math. Phys. 1969;12:131.
  45. Yao RL, Striffler CD. Numerical simulation of collective ion acceleration in an intense electron beam-localized gas cloud system. J. Appl. Phys. 1990;67(4):1650–1658. DOI: 10.1063/1.345632.
  46. Sena LA. Collisions of electrons and ions with gas atoms. Leningrad: OGIZ; 1948. (in Russian).
  47. Morey IJ, Birdsall CK. Travelling-wave-tube simulation: the IBC code. IEEE Trans. Plasma Sci. 1990;18(3):482–489. DOI: 10.1109/27.55918.
  48. Egorov EN, Kalinin YuA, Koronovskii AA, Hramov AE, Morozov MYu. Microwave generation power in a nonrelativistic electron beam with virtual cathode in a retarding electric field. Technical Physics Letters. 2006;32:402–405.
  49. Batura MP, Kuraev AA, Sinitsyn AK. Fundamentals of theory and optimization of modern electronic microwave devices. Minsk: BSUIR; 2007. 245 p. (in Russian).
  50. Morozov MYu, Hramov AE. Effect of the external magnetic field on the critical current for the onset of a virtual cathode in an electron beam. Plasma Physics Reports. 2007;33(7):553–561. DOI: 10.1134/S1063780X07070045.
  51. Hramov AE, Koronovskii AA, Morozov M, Mushtakov AV. Effect of external magnetic field on critical current for the onset of virtual cathode oscillations in relativistic electron beams. Phys. Lett. A. 2008;372:876–883. DOI: 10.1016/j.physleta.2007.08.039.
  52. Kurkin SA, Hramov AE. Virtual cathode formation in annular electron beam in an external magnetic field. Technical Physics Letters. 2009;35(1):23–25. DOI: 10.1134/S1063785009010076.
  53. Kurkin SA, Koronovskii AA, Hramov AE. External magnetic field influence on the forming and dynamics of virtual cathode. Izvestiya VUZ. Applied Nonlinear Dynamics. 2008;16(4):182–200 (in Russian). DOI: 10.18500/0869-6632-2008-16-4-182-200.
  54. Kurkin SA, Koronovskii AA, Hramov AE. Nonlinear dynamics and chaotization of oscillations of a virtual cathode in an annular electron beam in a uniform external magnetic field. Plasma Phys. Rep. 2009;35:628–642. DOI: 10.1134/S1063780X09080029.
  55. Kurkin SA. The influence of the noise spread of electron velocities on the dynamics of an electron flow with a virtual cathode. Journal of Communications Technology and Electronics. 2010;55(5):572–579. DOI: 10.1134/S106422691005013X.
  56. Filatov RA, Kalinin YuA, Khramov AE, Trubetskov DI. Influence of positive ions on oscillatory processes in an electron beam with virtual cathode. Radiophysics and Quantum Electronics. 2006;49(10):769–778. DOI: 10.1007/s11141-006-0111-4.
  57. Atanov NV, Dmitriev AS, Efremova EV, Maksimov NA. Chaotic RF pulses generated by a periodically driven oscillator. Tech. Phys. Lett. 2006;32:645–646. DOI: 10.1134/S1063785006080013.
  58. Filatov RA, Kalinin YuA, Hramov AE. Effect of Positive Ions on the Microwave Generation in a Low-Voltage Vircator. Tech. Phys. Lett. 2006;32(6):492–494. DOI: 10.1134/S1063785006060125.
Short text (in English):
(downloads: 89)