Resolution of Longitudinal Profile Measures using Coherent Smith-Purcell Radiation with the Number of Gratings and the Number of Pulses Used

The E-203 collaboration is testing a device on FACET at SLAC to measure the longitudinal profile of electron bunches using Smith-Purcell radiation. At FACET the electron bunches have an energy of 20~GeV and a duration of a few hundred femtoseconds. Smith-Purcell radiation is emitted when a charged particle passes close to the surface of a metallic grating. We have studied the stability of the measurement from pulse to pulse and the resolution of the measure depending on the number of gratings used.