Skip to main content
SpringerLink
Log in

Influence of the Delay on Mutual Synchronization of Two Coupled Gyrotrons

  • Published:
Radiophysics and Quantum Electronics Aims and scope

We study mutual synchronization in a system of two delay-coupled gyrotrons. The results of the bifurcation analysis are presented in the approximation where the delay time is short compared with the oscillation onset duration. The conditions of the stability of in-phase and antiphase synchronization regimes are analyzed for various values of parameters. Synchronization regions are plotted on the detuning–coupling coefficient parameter plane. Special attention is given to the mechanisms of appearance and disappearance of the bistability of synchronous regimes during parameter variations. A simple and physically justified way to switch between the in-phase and antiphase modes is proposed, which can be useful in many applications.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Zhang, D. Zhang, Y. Fan, et al., Phys. Plasmas, 27, No. 1, 010501 (2020). https://doi.org/https://doi.org/10.1063/1.5126271

  2. N. S. Ginzburg, A. W.Cross, A. A. Golovanov, et al., Phys. Rev. Lett., 115, No. 11, 114802 (2015). https://doi.org/https://doi.org/10.1103/PhysRevLett.115.114802

  3. Y. Li, X. Zhang, J. Zhang, et al., Phys. Plasmas, 21, No. 10, 103302 (2014). https://doi.org/https://doi.org/10.1063/1.4900417

  4. R. Xiao, Y. Deng, C.Chen, et al., Phys. Plasmas, 25, No. 3, 033109 (2018). https://doi.org/https://doi.org/10.1063/1.5022808

  5. J. Benford, H. Sze, W.Woo, et al., Phys. Rev. Lett., 62, No. 8, 969–971 (1989). https://doi.org/https://doi.org/10.1103/PhysRevLett.62.969

  6. W.Woo, J. Benford, D. Fittinghoff, et al., J. Appl. Phys., 65, No. 2, 861–866 (1989). https://doi.org/https://doi.org/10.1063/1.343079

  7. E.P. Bocharov and G.N.Korostelev, Radiophys. Quantum Electron., 24, No. 7, 564–567 (1981). https://doi.org/https://doi.org/10.1007/BF01034553

  8. E. J. Cruz., B. W. Hoff, P. Pengvanich P., et al., Appl. Phys. Lett., 95, No. 19, 191503 (2009). https://doi.org/10.1063/1.3262970

  9. H. Sze, D. Price, and B.Harteneck, J. Appl. Phys., 67, No. 5, 2278–2282 (1990). https://doi.org/https://doi.org/10.1063/1.345521

  10. A. E.Dubinov, V.D. Selemir, and A.V.Tsarev, Radiophys. Quantum Electron., 43, No. 8, 637–642 (2000). https://doi.org/https://doi.org/10.1023/A:1004809403664.

  11. B.G. Repin and A. E.Dubinov, Tech. Phys., 51, No. 4, 489–494 (2006). https://doi.org/https://doi.org/10.1134/S1063784206040153

  12. R. M. Rozental, N. S. Ginzburg, M.Yu.Glyavin, et al., Phys. Plasmas, 22, No. 9, 093118 (2015). https://doi.org/https://doi.org/10.1063/1.4931746

  13. M.Thumm, IEEE Trans. Plasma Sci., 42, No. 3, 590–599 (2014). https://doi.org/https://doi.org/10.1109/TPS.2013.2284026

  14. M.K. A.Thumm, G. G. Denisov, K. Sakamoto, and M.Q.Tran, Nucl. Fusion, 59, No. 7, 073001 (2019). https://doi.org/https://doi.org/10.1088/1741-4326/ab2005

  15. S.Yanchuk and P. Perlikowski, Phys. Rev. E, 79, No. 4, 046221 (2009). https://doi.org/https://doi.org/10.1103/PhysRevE.79.046221

  16. M.Wolfrum and S.Yanchuk, Phys. Rev. Lett., 96, No. 22, 220201 (2006). https://doi.org/https://doi.org/10.1103/PhysRevLett.96.220201

  17. M. I. Balakin and N. M. Ryskin, Rus. J. Nonlin. Dyn., 13, No. 2, 151–164 (2017) https://doi.org/10.20537/nd1702001

    Google Scholar 

  18. M. I. Balakin and N. M. Ryskin, Tech. Phys. Lett., 45, No. 3, 278–280 (2019). https://doi.org/https://doi.org/10.1134/S1063785019030209

  19. V. V.Klinshov and V. I.Nekorkin, Chaos Solitons Fractals, 44, No. 1, 98–107 (2011). https://doi.org/https://doi.org/10.1016/j.chaos.2010.12.007

  20. S. A. Usacheva and N.M.Ryskin, Chaos, 24, No. 2, 023123 (2014). https://doi.org/https://doi.org/10.1063/1.4881837

  21. A. B. Adilova, S.A.Gerasimova, and N.M. Ryskin, Rus. J. Nonlin. Dyn., 13, No. 1, 3–12 (2017). https://doi.org/10.20537/nd1701001

    Google Scholar 

  22. G. S.Nusinovich, Int. J. Electron., 51, No. 4, 457–474 (1981). https://doi.org/https://doi.org/10.1080/00207218108901349

  23. G. S.Nusinovich, Introduction to the Physics of Gyrotrons, Johns Hopkins Univ. Press, Baltimore, London (2004).

    Google Scholar 

  24. V. L. Bakunin, G. G. Denisov, N.A. Zavolsky, and M.A.Moiseev, Izv. Vyssh. Uchebn. Zaved., Prikl. Nonlin. Din., 20, No. 6, 67–81. https://doi.org/10.18500/0869-6632-2012-20-6-67-81

  25. M. A. Moiseev and G. S.Nusinovich, Radiophys. Quantum Electron., 17, No. 11, 1305–1311 (1974). https://doi.org/https://doi.org/10.1007/BF01042032

  26. A. B. Adilova and N.M. Ryskin, Izv. Vyssh. Uchebn. Zaved., Prikl. Nonlin. Din., 26, No. 6, 68–81 (2018). https://doi.org/10.18500/0869-6632-2018-26-6-68-81

  27. M.Yu.Glyavin, G.G. Denisov, M. L.Kulygin, et al., Radiophys. Quantum Electron., 58, No. 9, 639–648 (2015). https://doi.org/https://doi.org/10.1007/s11141-016-9636-3

  28. http://www.math.pitt.edu/∼bard/xpp/xpp.html

  29. A. Pikovsky, M.Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences, Cambridge Univ. Press, Cambridge (2003).

    Book  Google Scholar 

  30. A.P. Kuznetsov, S.P. Kuznetsov, and N.M. Ryskin, Nonlinear Oscillations [in Russian], Fizmatlit, Moscow (2005).

    Google Scholar 

  31. A.P. Kuznetsov, Yu. P. Emelyanova, I. R. Sataev, and L. V.Tyuryukina, Synchronization in Problems [in Russian], Nauka Publ., Saratov (2010).

  32. A.P.Kuznetsov, N. V. Stankevich, and L. V.Turukina, Physica D, 238, No. 14, 1203–1215 (2009). https://doi.org/https://doi.org/10.1016/j.physd.2009.04.001

  33. G.S.Nusinovich, O.V. Sinitsyn, and T.M.Antonsen, Phys. Rev. Lett., 98, No. 20, 205101 (2007). https://doi.org/https://doi.org/10.1103/PhysRevLett.98.205101

  34. K.Kajiwara, K. Sakamoto, Y.Oda, et al., Nucl. Fusion, 53, No. 4, Art. no. 043013 (2013). https://doi.org/https://doi.org/10.1088/0029-5515/53/4/043013

  35. V. L.Bakunin, G.G.Denisov, and Yu.V.Novozhilova, Radiophys. Quantum Electron., 62, No. 7, 490–505 (2019). https://doi.org/https://doi.org/10.1007/s11141-020-09995-x

  36. A. A.Koronovskii and A. E. Hramov, Continuous Wavelet Analysis and its Applications [in Russian], Fizmatlit, Moscow (2003).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. N. G. Chernyshevsky Saratov State University, Saratov, Russia

    A. B. Adilova & N. M. Ryskin

  2. Saratov Branch of V.A.Kotelnikov Institute of Radio Engineering and Electronics of the Russian Academy of Sciences, Saratov, Russia

    N. M. Ryskin

Authors
  1. A. B. Adilova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. M. Ryskin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. B. Adilova.

Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 63, Nos. 9–10, pp. 781–795, September–October 2020.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Adilova, A.B., Ryskin, N.M. Influence of the Delay on Mutual Synchronization of Two Coupled Gyrotrons. Radiophys Quantum El 63, 703–715 (2021). https://doi.org/10.1007/s11141-021-10091-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11141-021-10091-x

Search

Navigation