Influence of a finite length of a dielectric waveguide on the acceleration of electrons by wake fields of a train of bunches

The excitation of wake fields by a train of relativistic electron bunches in a cylindrical waveguide partially filled with dielectric is considered. The waveguide finiteness along the longitudinal direction is accounted for by the introduction of the wake field trailing edge which propagates at the velocity equal to the group velocity of the resonance wave. The numerical simulation of self-consistent dynamics for particles and for the acceleration of electrons in wake fields is carried out.