“Self-trapping” of the pre-bunched electron beam in a discrete system of isolated cells of the TBA-driver

Averaged quasi-continuous equations for motion of electrons through a discrete system of isolated cells, consisting of generator (FEL) and re-accelerator sections, are obtained. Conditions of trapping of the electron beam by the RF field excited by this beam inside the cells, are analytically studied for the cases of both low-Q and high-Q generator sections.