Mechanisms of coherent spontaneous cyclotron and undulator radiations of short dense bunches, in which electrons move along the same stationary helical trajectories, but have different dynamic properties, have been compared in detail. The results are based on the simplest 1D model in the form of a plane consisting of uniformly distributed synchronously moving and in-phase emitting particles, as well as numerical 3D codes developed to study the dynamics of bunches in waveguides taking into account the effects of the radiation and spatial charge fields. For cyclotron radiation under group synchronism conditions, the Coulomb expansion of a bunch occurs along the surface of a constant wave phase with the formation of an effectively radiating coherent structure. A significantly higher radiation frequency, but with a lower efficiency, can be obtained in the regime of simultaneous excitation of high-frequency (autoresonant) and low-frequency waves; in the field of the latter, stabilization of the bunch phase size can be achieved. Such a two-wave generation is much more efficient when the bunches radiate in the combined undulator and strong guiding magnetic fields under conditions of the negative mass instability, when both the Coulomb interaction of the particles and the radiation field stabilize the longitudinal size of the bunch.
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