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

We suggest a novel technique of measuring subpicosecond electron bunch length based on coherent Smith-Purcell radiation (SPR). We predict an electron beam traversing near the surface of a grating will emit coherent SPR if the electron bunch length is less than the grating period. The coherent SPR will be emitted at large angles with respect to the beam propagation direction and its intensity will be greatly enhanced compared to incoherent SPR. By measuring the angular position of the coherent SPR peak or the ratio of its intensity relative to the incoherent SPR, we can determine the electron bunch length. This technique appears to be scaleable to femtosecond electron bunch measurements.