Analysis of the particle longitudinal motion during the injection process into the disk loaded traveling wave accelerating structure

We study longitudinal beam motion of the beam with a nonrelativistic energy during the injection into the disk loaded accelerating structure with traveling wave. Analysis of the particle dynamics is carried out with the help of the Hamiltonian formalism. Condition of the particle capture into the acceleration is derived. Trajectories of the particles in the longitudinal phase space are shown. We also discuss the optimal injection phase for the maximum particle energy gain together with beam bunching during the injection.