Theory of group synchronism in free-electron waveguide lasers fed a sequence of short electron pulses

A theory of free-electron lasers fed a sequence of short electron pulses is developed. It is assumed that the group velocity of the electromagnetic pulse that develops in the cavity is the same as the translational velocity of the particles, and the repetition period of the electron pulses equals the transit time of the electromagnetic radiation in the cavity. Under these conditions of group synchronism, the principal factors governing the feasibility of establishing a stationary pulsed lasing regime are found to be the dispersive spread of the electromagnetic pulse and the channeling properties of an electron bunch. The conditions for self-excitation are found, and the characteristics of the stationary lasing regimes are determined assuming that the cavity has a high Q and using a parabolic equation for the evolution of the electromagnetic pulse shape. Zh. Tekh. Fiz. 69, 78–83 (February 1999)