Theory of group synchronism regime in waveguide FEL driven by short electron bunches

A theory of group synchronism regime in a FEL driven by a train of short electron bunches is described. We suggest that translational velocity of particles coincides with group velocity of electromagnetic pulses and the period between neighboring bunches is equal to the period of electromagnetic pulse round trip through the resonator. The dispersion of electromagnetic pulse provides mutual synchronization of radiation inside an electron bunch. On the other hand, due to the guiding properties of electron bunch, the field is localized close to it. These two factors allow one to realize the stationary generation regime. Under the assumption of high Q-factor resonator a parabolic equation for the description of evolution of electromagnetic pulse profile has been used. The self-excitation conditions and the characteristics of stationary generation regime are determined.