Radiation by self-oscillating relativistic charged particle moving along periodic structure

The new elementary radiation mechanism due to the oscillatory character of a radiation friction force appearing when a relativistic charged particle moves along a periodic structure without external fields is studied by analytical methods. The equation of motion for the charged particle driven by the radiation friction force is solved by the perturbation method. It is shown that the non-synchronous spatial harmonics of the Cherenkov-type radiation (CR) can cause an oscillatory motion of the particle, which therefore generates an undulator-type radiation (UR). In the frequency range where the diffraction of the generated waves is essential, the radiation manifests itself in the interference of CR and UR. The undulator radiation takes place only in that spectral region where the wave diffraction can be neglected.