Cyclotron-undulator cooling of a free-electron-laser beam

We propose methods of fast cooling of an electron beam, which are based on wiggling of particles in an undulator in the presence of an axial magnetic field. We use a strong dependence of the axial electron velocity on the oscillatory velocity, when the electron cyclotron frequency is close to the frequency of electron wiggling in the undulator field. The abnormal character of this dependence (when the oscillatory velocity increases with the increase of the input axial velocity) can be a basis of various methods for fast cooling of moderately relativistic (several MeV) electron beams.