Coherent Smith-Purcell radiation as a diagnostic for sub-picosecond electron bunch length

We suggest a novel technique of measuring sub-picosecond electron bunch length base on coherent Smith-Purcell radiation (SPR) emitted when electrons pass close to the surface of a metal grating. With electron bunch lengths comparable to the grating period, we predict that coherent SPR will be emitted at large angles with respect to direction of beam propagation. As the bunch length shortens, the coherent SPR will be enhanced over the incoherent component that is normally observed at small angles. Furthermore, the angular distribution of the coherent SPR will be shifted toward smaller angles as the bunch length becomes much smaller than the grating period. By measuring the angular distribution of the coherent SPR, one can determine the bunch length of sub-picosecond electron pulses. This new technique is easy to implement and appears capable of measuring femtosecond electron bunch lengths