Theory of cyclotron super-radiance from a moving electron bunch under group synchronism condition

A theory of cyclotron super-radiance (SR) from a moving electron bunch under a group synchronism condition has been developed. This regime occurs for the propagation of a radiation field in a waveguide or in other dispersive media such as a plasma when the electron bunch translational velocity coincides with the wave group velocity. In the comoving reference frame such emission corresponds to emission at a quasi-cut-off frequency. For a linear approximation it is shown that a bunch of electrons rotating in the magnetic field can be presented as an active resonator which possesses a spectrum of unstable eigenmodes. The gain of these modes defines the gain of the SR instability. To describe the nonlinear stage of the SR instability a time-domain approach based on a combination of a parabolic equation for wave evolution and a non-isochronous oscillator equation to describe electron azimuthal self-bunching was used. Profiles of SR pulses were found first in the comoving reference frame and then transferred into the laboratory reference frame using a Lorentz transformation. Both linear and nonlinear analyses demonstrated the advantage of SR in the regime of group synchronism as compared to cyclotron SR in free space. The fast drop of the SR pulse amplitude by detuning the magnetic field from the grazing condition was observed using the three-dimensional particle-in-cell code KARAT