Conversion of an Electromagnetic Wave into a Periodic Train of Solitons under Cyclotron Resonance Interaction with a Backward Beam of Unexcited Electron-Oscillators I. V. Zotova, 1,* N. S. Ginzburg, 1,2 A. S. Sergeev, 1 E. R. Kocharovskaya, 1 and V. Yu. Zaslavsky 1,2 1 Institute of Applied Physics RAS, GSP-120 Nizhny Novgorod, Russia 2 Nizhny Novgorod State University, 603950 Nizhny Novgorod, Russia (Received 13 June 2014; published 1 October 2014) The possibility of the conversion of intense continuous microwave radiation into a periodic train of short pulses by means of resonant interaction with a beam of unexcited cyclotron electron oscillators moving backward is shown. In such a system there is a certain range of parameters where the incident stationary signal splits into a train of short pulses and each of them can be interpreted as a soliton. It is proposed to use this effect for amplitude modulation of radiation of short wavelength gyrotrons. DOI: 10.1103/PhysRevLett.113.143901 PACS numbers: 41.20.Jb, 52.35.Mw The problem of transforming microwave radiation into a sequence of coherent short nanosecond pulses is important for a number of applications including plasma diagnostics, radars, particle accelerators, spectroscopy, etc. In Refs. [1,2] optically controlled switches are used for these purposes; those switches are based on the effect of induced photoconductivity in semiconductor elements implemented in a resonant system. In the present Letter we propose an alternative method based on cyclotron resonance absorp- tion of microwave radiation by an initially rectilinear electron beam interacting with a backward propagating wave. The specifics of the interaction of short electromagnetic pulses with initially rectilinear electron beams under the cyclotron resonance condition has been investigated in Refs. [3,4]. It was shown that, starting from a certain threshold power of an incident pulse, linear cyclotron absorption is replaced by the effect of self-induced trans- parency, when the electromagnetic pulse propagates with- out damping. In fact, similar to optics [5–9], the initial pulse transforms itself into a soliton whose amplitude and duration depend on its velocity. The present Letter deals with the nontrivial dynamics arising when a quasistationary incident signal interacts with a counterpropagating recti- linear electron beam under the cyclotron resonance con- dition. As shown below, in such a system the continuous signal decomposes itself into a train of short pulses, and each of them can be interpreted as a soliton. It is important to note that the described effect occurs only when the relativistic dependence of the gyrofrequency on the particle energy is taken into account [10,11]. Moreover, the phase velocity of the wave should be significantly different from the speed of light in order to avoid mutual compensation of electron phase shifts caused by the changes in gyrofre- quency and the recoil effect, which is typical for autor- esonance regimes [12]. Under such an assumption, an initially rectilinear electron beam could be considered as a nonlinear resonance medium. Let us consider the interaction of an initially rectilinear annular electron beam guided by a homogeneous magnetic field ~ H ¼ ~ z 0 H 0 with a backward electromagnetic wave (Fig. 1) in a cylindrical waveguide with a radius R under the cyclotron-resonance condition ω þ hv 0 ≈ ω H ; ð1Þ where v 0 ¼ β 0 c is the axial velocity of particles, ω H ¼ eH 0 =mcγ is the electron gyrofrequency, and γ is the relativistic mass factor. The electromagnetic field in the situation under study can be presented in the form E ⇀ ¼ Re( ~ E s ð~ r ⊥ ÞAðz; tÞ expðiωt þ ihzÞ); ð2Þ where Aðz; tÞ is the slowly varying wave amplitude and the function ~ E s ð~ r ⊥ Þ describes the transverse structure of radiation corresponding to a TE mn waveguide mode. The electron-wave interaction can be described by the equations [3,4] ∂ a ∂ Z - ∂ a ∂ τ ¼ p; ∂ p ∂ Z þ ipðδ þjpj 2 Þ¼ a: ð3Þ FIG. 1 (color online). Schematic of the interaction space with electron trajectories found in PIC simulation. PRL 113, 143901 (2014) PHYSICAL REVIEW LETTERS week ending 3 OCTOBER 2014 0031-9007=14=113(14)=143901(5) 143901-1 © 2014 American Physical Society