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

For citation:

Ginzburg N. S., Zaslavsky V. Y., Zotova I. V., Rostuntsova A. A., Ryskin N. M., Sergeev A. S., Yurovskiy L. A. Modulation instability and soliton formation under interaction of an electromagnetic wave with a beam of unexcited non-isochronous electron–oscillators. Izvestiya VUZ. Applied Nonlinear Dynamics, 2025, vol. 33, iss. 6, pp. 823-842. DOI: 10.18500/0869-6632-003187, EDN: CDEQIR

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Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
530.182
DOI: 
10.18500/0869-6632-003187
EDN: 
CDEQIR

Modulation instability and soliton formation under interaction of an electromagnetic wave with a beam of unexcited non-isochronous electron–oscillators

Autors: 
Ginzburg Naum Samuilovich, Institute of Applied Physics of the Russian Academy of Sciences
Zaslavsky Vladislav Yurevich, Institute of Applied Physics of the Russian Academy of Sciences
Zotova Irina Valeryevna, Institute of Applied Physics of the Russian Academy of Sciences
Rostuntsova Alena Alexandrovna, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Ryskin Nikita Mikhailovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Sergeev Alexander Sergeevich, Institute of Applied Physics of the Russian Academy of Sciences
Yurovskiy Lev Aleksandrovich, Institute of Applied Physics of the Russian Academy of Sciences
Abstract: 

This paper develops the theory of modulation instability (MI) in the interaction of an electromagnetic wave with a counterpropagating beam of unexcited electron-oscillators under the cyclotron resonance conditions. The purpose of this study is to establish the pattern of possible wave propagation regimes in such a system.

Methods. The theoretical analysis is based on the nonlinear Schrodinger equation, which enables to determine the conditions for occurrence of MI and obtain a simple analytical expression for the boundary between the absolute and convective MI on the wave frequency – wave amplitude parameter plane. The theoretical conclusions about possible regimes of wave propagation are verified by direct 3-D particle-in-cell (PIC) simulation of the electronwave interaction.

The obtained results show that above the boundary of cyclotron absorption band non-stationary self-modulation regimes occur. These regimes are caused by absolute MI and can lead to the formation of solitonlike pulse trains. As the frequency of the input signal increases, self-modulation is replaced by a stationary
single-frequency regime of wave propagation. This transition is due to the change of MI character from absolute to convective. The results of 3-D PIC simulation are consistent with the theoretical analysis of the averaged equations, and the same sequence of transitions between different dynamic regimes occurs as the input frequency
increases.

Conclusion. 3-D PIC simulation provided an opportunity to study a model that approximates the conditions of a potential experiment. The possibility of converting the 241.3-GHz signal into a close-to-periodic train of nanosecond pulses was demonstrated. Such an effect is useful for the generation of microwave frequency
combs.
 

Key words: 
modulation instability
self-induced transparency
microwave solitons
cyclotron resonance
Acknowledgments: 
This work was supported by Russian Science Foundation under Grant No. 23-12-00291.
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Received: 
14.05.2025
Accepted: 
10.06.2025
Available online: 
09.07.2025
Published: 
28.11.2025
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