Conversion of an Electromagnetic Wave into a Periodic Train of Solitons under Cyclotron Resonance Interaction with a Backward Beam of Unexcited Electron-Oscillators

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.

Figure 1

Schematic of the interaction space with electron trajectories found in PIC simulation.

Figure 2

Zones of different interaction regimes of cw radiation with backward rectilinear electron beam under the exact cyclotron resonance condition $\delta =0$. I: zone of stationary regimes with monotonic dependence of the field intensity on the normalized longitudinal coordinate (zone of normal cyclotron absorption). II: zone of stationary regimes with periodic dependence of the field intensity on the normalized longitudinal coordinate; dashed line 1,2,3 corresponds to the regime of nonlinear bleaching with the indicated number of longitudinal variations. III: zone of periodic self-modulation regimes. IV: zone of chaotic self-modulation regimes.

Figure 3

Longitudinal distributions of normalized field intensity $I$, absolute value of transverse momentum $|p|$, and mutual phase difference $\chi$ between signal and electron rotation momentum. (a) Regime of stationary cyclotron absorption (zone I, for $L=3.7$, $I_{\text{in}}=3.24$). (b) Regime of stationary nonlinear bleaching with two longitudinal variations (dashed curve 2 in zone II, for $L=3.7$, $I_{\text{in}}=9$).

Figure 4

Regime of periodic self-modulation (zone II, for $L=6$, $I_{\text{in}}=4.1$). (a) Output signal at the cross section $Z=0$. (b) Single soliton profile inside the interaction space in comparison with analytical solution (4) (dashed line). (c) Soliton propagation on the plane $Z$, $\tau$.

Figure 5

PIC simulations of the regime of nonlinear bleaching. Radiation power emitted in (a) negative $P^{-}(z=0)$ and (b) positive $P^{+}(z=l)$ directions of the $z$ axis. The inset shows the longitudinal distribution of transverse electron velocities.

Figure 6

Same as in Fig. 5 for the regime of periodic self-modulation.