Coherent spontaneous emission from short electron bunches in free space

We study superradiance of an electron bunch which has a finite transverse size in the frame of a 2-D model. This model includes effects of optical guiding as well as transverse electromagnetic energy dissipation and diffraction. Using a nonstationary parabolic equation we describe SR of a sheet shaped electron bunch in free space. It is shown that the radiation is composed of pulses of electromagnetic radiation which are diffracted after escaping from the channel formed by the electron beam. This process is accompanied by a progressive increase of the electron efficiency. This enhancement is caused by the phenomenon of permanent self supporting resonance due to the variation of the radiation angle and frequency.