Journal of Radio Electronics. eISSN 1684-1719. 2023. 11

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Yu.V. Novozhilova, A.A. Bogdashov, M.Yu. Glyavin, G.G. Denisov,

A.P. Fokin, A.V. Nazarovsky, R.M. Rozental


Federal Research Center A.V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences

603950, Nizhny Novgorod, Ul'yanov St., 46


The paper was received November 27, 2023


Abstract. The possibility of frequency stabilization of two gyrotrons with similar parameters when part of their radiation is reflected from an external high-Q cavity is shown analytically, and the stability of stabilized states is investigated. Analysis of stationary states in which the generators radiate coherently shows that the radiation frequency can be stabilized if the quality factor of the external resonator is high enough. In this case, changing the parameters of the system leads to significantly smaller changes in the generation frequency than in the absence of reflections: in a fairly wide range of parameters, the gyrotron radiation frequency can be kept within the band of the external resonator. As the eigen frequencies of gyrotron resonators increase and decrease, hysteresis and jumps in the radiation frequency can be observed. A study of stability at the optimal delay phase shows that frequency-stabilized states are stable. When the deviation from these states is small, the disturbances in the amplitudes of the gyrotrons decrease most quickly. At the next stage, over a longer period of time, stationary values of the gyrotron phases are settled. At the last, longest stage, stationary values of the amplitude and phase of the external resonator are formed.

Key words: gyrotron, coupled oscillators, frequency stabilization, external resonator.

Financing: The work was supported by the Russian Science Foundation, grant No. 19-79-30071,

Corresponding author: Novozhilova Yulia Vladimirovna,



1. Egorov S. V. et al. Implementation of rapid microwave sintering using a 24 GHz gyrotron system // Review of Scientific Instruments. 2022. . 93. . 6.

2. Thumm M. K. A. et al. High-power gyrotrons for electron cyclotron heating and current drive // Nuclear Fusion. 2019. . 59. . 7. . 073001.

3. Nusinovich G. S., Thumm M. K. A., Petelin M. I. The gyrotron at 50: Historical overview // Journal of Infrared, Millimeter, and Terahertz Waves. 2014. . 35. . 325-381.

4. Denisov G. G. New trends in gyrotron development // EPJ Web of Conferences. EDP Sciences, 2017. . 149. . 01001.

5. Jory H. Network for pulling a microwave generator to the frequency of its resonant load: . 3714592 . 1973.

6. Kozorezov G. G. Ferrite-decoupled magnetrons for electron accelerators // Vacuum Microwave Electronics: Collected Review Papers. Institute of Applied Physics, 2002. . 67-70.

7. Kazakevitch G. M. et al. Stabilization of the microtron-injector for a wide-band compact FIR FEL // Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment. 2004. . 528. . 1-2. . 115-119.

8. Li H., Abraham N. B. Analysis of the noise spectra of a laser diode with optical feedback from a high-finesse resonator // IEEE journal of quantum electronics. 1989. . 25. . 8. . 1782-1793.

9. Oraevsky A. N., Yarovitsky A. V., Velichansky V. L. Frequency stabilisation of a diode laser by a whispering-gallery mode // Quantum Electronics. 2001. . 31. . 10. . 897.

10. Liang W. et al. Ultralow noise miniature external cavity semiconductor laser // Nature communications. 2015. . 6. . 1. . 7371.

11. Zolotovskii I. O. et al. Frequency locking of a semiconductor laser by a ring fibre resonator // Quantum Electronics. 2017. . 47. . 10. . 871.

12. Seel S. et al. Cryogenic optical resonators: a new tool for laser frequency stabilization at the 1 Hz level // Physical review letters. 1997. . 78. . 25. . 4741.

13. Novozhilova Y. V., Ishenko A. S. Analytical theory of an RF generator phase-locked by the resonant load with delayed reflection // Journal of Infrared, Millimeter, and Terahertz Waves. 2011. . 32. . 1394-1406.

14. Glyavin M. Y. et al. Stabilization of gyrotron frequency by reflection from nonresonant and resonant loads // Technical Physics Letters. 2015. . 41. . 628-631.

15. Glyavin M. Y. et al. Gyrotron frequency stabilization by a weak reflected wave // Radiophys. Quantum Electron. 2016. . 58. . 9. . 673-683.

16. Zotova I. V. et al. Time-domain theory of low-Q gyrotrons with frequency-dependent reflections of output radiation // Physics of Plasmas. 2018. . 25. . 1.

17. Fokin A. P. et al. Experimental demonstration of gyrotron frequency stabilization by resonant reflection // IEEE Electron Device Letters. 2021. . 42. . 7. . 1077-1080.

18. Komurasaki K., Tabata K. Development of a novel launch system microwave rocket powered by millimeter-wave discharge // International Journal of Aerospace Engineering. 2018. . 2018. . 1-9.

19. Rozental R. M. et al. Mutual synchronization of weakly coupled gyrotrons // Physics of Plasmas. 2015. . 22. . 9.

20. Adilova A. B., Ryskin N. M. Influence of the delay on mutual synchronization of two coupled gyrotrons // Radiophysics and Quantum Electronics. 2021. . 63. . 703-715.

21. Adilova A. B., Ryskin N. M. Theory of peer-to-peer locking of high-power gyrotron oscillators coupled with delay // Electronics. 2022. . 11. . 5. . 811.

22. Novozhilova Yu.V., Bogdashov A.A., Nazarovsky A.V., Fokin A.P., Glyavin M.Yu., Denisov G.G. Numerical simulation of operation of two gyrotrons with a common resonant reflector // Journal of Radio Electronics. 2023. . 11. (In Russian)

For citation:

Novozhilova Yu.V., Bogdashov A.A., Glyavin M.Yu., Denisov G.G., Fokin A.P., Nazarovsky A.V., Rozental R.M. Studying the possibility of frequency stabilization of two gyrotrons under the influence of reflection from an external high-Q resonator // Journal of Radio Electronics. 2023. . 11. (In Russian)