APPLIED PROBLEMS OF NONLINEAR OSCILLATION AND WAVE THEORY
Modulation instability and soliton formation under interaction of an electromagnetic wave with a beam of unexcited non-isochronous electron–oscillators
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.
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