Abstract
The growth characteristics of a two-dimensional Cherenkov free-electron laser (CFEL) in the small-signal low gain regime are studied for both single-electron and collective models. In the single-electron regime, for a thick enough beam, we prove that the gain of the CFEL can be increased by a factor of 2 than that obtained for an infinitely thin electron beam. Thus, the Cherenkov laser should be considered as a hybrid longitudinal/transverse free-electron laser device in general. In the collective-regime, we demonstrate the damping effects of Coulomb collisions among electrons on the amplification characteristics of a Cherenkov laser.