Study of character of modulation instability in cyclotron resonance interaction of an electromagnetic wave with a counterpropagating rectilinear electron beam

Cover Page

Cite item

Full Text

Abstract

In this paper, the interaction of a monochromatic electromagnetic wave with a counterpropagating electron beam moving in an axial magnetic field is considered. The purpose of this study is to investigate the conditions for occurrence of modulation instability (MI) in such a system and to determine at which parameters of the incident wave the MI is absolute or convective. Methods. Theoretical analysis of the MI character is carried out by studying the asymptotic form of unstable perturbations using the saddle-point analysis. The analytical results are verified by numerical simulations. Results. Theoretically, the boundary of change in the character of MI on the plane of input signal parameters (amplitude and detuning of the frequency from the cyclotron resonance) is determined. Numerical simulations confirm that as the signal frequency increases, the regime of self-modulation, which corresponds to the absolute MI, is replaced by the stationary single-frequency transmission corresponding to the convective MI. The numerical results coincide with the analytical ones for the system, which is matched at the end. The matching is implemented by smooth increasing of the guiding magnetic field in the region of electron beam injection. Conclusion. Determining the analytical conditions for the implementation of the absolute MI is of practical interest, since the emerging self-modulation can lead to the generation of trains of pulses with the spectrum in the form of frequency combs.

About the authors

Alena Aleksandrovna Rostuntsova

Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences; Institute of Applied Physics of the Russian Academy of Sciences; Saratov State University

ORCID iD: 0000-0002-6795-2108
SPIN-code: 2544-8724
Scopus Author ID: 57204902473
ResearcherId: AAA-4540-2022
ul. Zelyonaya, 38, Saratov, 410019, Russia

Nikita Mikhailovich Ryskin

Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences; Saratov State University

ORCID iD: 0000-0001-8501-6658
Scopus Author ID: 7003373306
ResearcherId: K-2549-2012
ul. Zelyonaya, 38, Saratov, 410019, Russia

References

  1. Benjamin T. B. Instability of periodic wavetrains in nonlinear dispersive systems // Proc. R. Soc. Lond. A. 1967. Vol. 299, no. 1456. P. 59–76. doi: 10.1098/rspa.1967.0123.
  2. Додд Р., Эйлбек Дж., Гиббон Дж., Моррис Х. Солитоны и нелинейные волновые уравнения. М.: Мир, 1988. 696 с.
  3. Ньюэлл А. Солитоны в математике и физике. М.: Мир, 1989. 328 с.
  4. Островский Л. А., Потапов А. И. Введение в теорию модулированных волн. М.: Физматлит, 2003. 398 с.
  5. Zakharov V. E., Ostrovsky L. A. Modulation instability: The beginning // Physica D. 2009. Vol. 238, no. 5. P. 540–548. doi: 10.1016/j.physd.2008.12.002.
  6. Рыскин Н. М., Трубецков Д. И. Нелинейные волны. М.: URSS, 2021. 312 с.
  7. Рыскин Н. М. Колебания и волны в нелинейных активных средах. Саратов: Издательство Саратовского университета, 2017. 102 с.
  8. Балякин А. А., Рыскин Н. М. Смена характера модуляционной неустойчивости вблизи критической частоты // Письма в ЖТФ. 2004. Т. 30, № 5. С. 6–13.
  9. Balyakin A. A., Ryskin N. M. Modulation instability in a nonlinear dispersive medium near cut-off frequency // Nonlinear Phenomena in Complex Systems. 2004. Vol. 7, no. 1. P. 34–42.
  10. Rostuntsova A. A., Ryskin N. M., Zotova I. V., Ginzburg N. S. Modulation instability of an electromagnetic wave interacting with a counterpropagating electron beam under condition of cyclotron resonance absorption // Phys. Rev. E. 2022. Vol. 106, no. 1. P. 014214. doi: 10.1103/PhysRevE. 106.014214.
  11. Newell A. C. Nonlinear tunnelling // J. Math. Phys. 1978. Vol. 19, no. 5. P. 1126–1133. doi: 10.1063/1.523759.
  12. Зотова И. В., Гинзбург Н. С., Железнов И. В., Сергеев А. С. Модуляция интенсивного СВЧ-излучения при резонансном взаимодействии со встречным потоком невозбужденных циклотронных осцилляторов // Письма в ЖТФ. 2014. Т. 40, № 12. С. 1–10.
  13. Zotova I. V., Ginzburg N. S., Sergeev A. S., Kocharovskaya E. R., Zaslavsky V. Y. Conversion of an electromagnetic wave into a periodic train of solitons under cyclotron resonance interaction with a backward beam of unexcited electron-oscillators // Phys. Rev. Lett. 2014. Vol. 113, no. 14. P. 143901. doi: 10.1103/PhysRevLett.113.143901.
  14. Гинзбург Н. С., Зотова И. В., Кочаровская Е. Р., Сергеев А. С., Железнов И. В., Заславский В.Ю. Солитоны самоиндуцированной прозрачности и диссипативные солитоны в системах микроволновой электроники // Известия вузов. Радиофизика. 2020. Т. 63, № 9. С. 796–824.
  15. Benirschke D. J., Han N., Burghoff D. Frequency comb ptychoscopy // Nat. Commun. 2021. Vol. 12, no. 1. P. 4244. doi: 10.1038/s41467-021-24471-4.
  16. Hagmann M. J. Scanning frequency comb microscopy–A new method in scanning probe microscopy // AIP Advances. 2018. Vol. 8, no. 12. P. 125203. doi: 10.1063/1.5047440.
  17. Гапонов А. В., Петелин М. И., Юлпатов В. К. Индуцированное излучение возбужденных классических осцилляторов и его использование в высокочастотной электронике // Известия вузов. Радиофизика. 1967. Т. 10, № 9. С. 1414–1453.
  18. Кузелев М. В., Рухадзе А. А. Методы теории волн в средах с дисперсией. М.: Физматлит, 2007. 272 с.
  19. Barletta A., Celli M. Convective to absolute instability transition in a horizontal porous channel with open upper boundary // Fluids. 2017. Vol. 2, no. 2. P. 33. doi: 10.3390/fluids2020033.

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies