Radiation by a relativistic charged particle in self-wakefield in   periodic structure
  A new elementary mechanism of radiation due to the oscillatory character of a radiation reaction force appearing when a relativistic charged particle moves along a periodic structure without external fields is investigated. It is shown that the non-synchronous spatial harmonics of Cherenkov-type radiation (CR) can give rise to the oscillation of a particle which consequently generates undulator-type radiation (UR). In the spectral region, where the diffraction of generated waves is essential, the radiation manifests itself in the coherent interference of CR and UR. A pure undulator -type radiation takes place only in the wavelength range where the wave diffraction can be neglected. In the case of coherent UR by a bunch of N electrons, the UR power is proportional to N in the forth degree. 
Anatoliy Opanasenko