A non-destructive electron beam diagnostic for a SASE FEL using coherent off-axis undulator radiation

We show that by observing coherent off-axis undulator radiation (COUR) from a short diagnostic wiggler, it may be possible to determine the length and structure of a short electron bunch. Typically the on-axis undulator radiation is incoherent, but at angles of a few degrees, the wavelength of the emitted radiation may be comparable to the length of a short electron bunch, and thus coherence effects emerge. Due to such coherence effects, the intensity of the emitted radiation may change by up to a factor of 109 as the angle of observation is increased. The radiation becomes coherent in a way which depends on the length and structure of the electron bunch. Observing COUR disturbs the electron bunch negligibly. Thus, COUR can be used as a non-destructive diagnostic which would allow for optimization of FEL performance while an FEL is operating. Such a diagnostic could be used for proposed SASE FELs, which use short electron bunches. We present two methods to describe the theory for COUR, and we use these methods to calculate the expected outcome of a COUR experiment. We propose an experiment to demonstrate COUR effects and their applications to SASE FELs.