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

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.