Some properties of coherent smith-purcell radiation from electron bunches and gratings of finite dimensions

There is a strong interest in the development of single shot diagnostics of fs relativistic electron bunches within a number of research areas including compact particle accelerators and THz and X-ray sources of radiation. The goal of this work is to investigate some properties of coherent Smith-Purcell radiation and to use it for the reconstruction of the longitudinal profile of a fs-long electron bunch.