The problem of X-ray Free-Electron Laser operating on self-amplified spontaneous emission in irregular microundulator is considered. The case when the spectrum width of spontaneous radiation is conditioned by the spatial distribution of sources creat
ing the undulating field is considered. In this case gain function of the stimulated radiation is dozens of times higher than that of the conventional undulators. We propose a model of irregular microundulator, which can be used to construct a drastically cheap and compact X-ray free-electron laser operating on medium energy electron bunch.
The problem of spontaneous radiation of the electron bunch grazing into a charged metallic surface with randomly distributed needle shaped asperities is considered. Distances between two neighboring asperities have been described by gamma distributio
n. Being repealed by highly charged asperities the electrons of the bunch move along non-regular periodical trajectories in the planes parallel to the metallic surface. The spatial periods of the trajectories are random quantities which are described by the same gamma distribution. The radiation characteristics of the bunch have been obtained. It is shown that the angular distributions of the number of photons radiated from the bunch and from a single electron are the same but the frequency distribution of the bunch is being drastically changed at the hard frequency region. It is proposed to develop a new non-destructive method for investigation of the metal surface roughness. The frequency distribution of the number of photons radiated under the zero angle has been obtained. That allows to find the gain expression of the stimulated radiation.
