Charge density harmonics generation in free-electron relativistic parametric devices.

A single-particle theory of the evolution of the harmonic content of a bunched beam in a relativistic optical klystron is reported. The equations of motion of the electrons in the dispersive-magnetic-drift space are solved analytically, including the effects of the energy and angular spreads of the beam. The theory enables one to predict the optical efficiency of a coherent relativistic scatterer designed for the generation of the third harmonics of the charge density wave (lambda(sc) = 1766 A) induced on the electron beam of the Frascati storage ring, Adone, with gamma = 1200.