Cyclotron radiation cooling of a short electron bunch kicked in an undulator with guiding magnetic field

We propose to use of an undulator with the guiding axial magnetic field as a “kicker” forming a bunch of electron gyro-oscillators with a small spread in the axial velocity. The cyclotron emission from the bunch leads to losing oscillatory velocity of electron gyrorotation, but it does not perturb the axial electron velocity. This effect can be used for transformation of minimization of the spread in electron axial velocity in the undulator section into minimization of the spread in electron energy in the cyclotron radiation section.