Design of a Smith-Purcell radiation bunch length diagnostic

We present the design of a Smith-Purcell radiation diagnostic to measure the micro bunch length of a 20MeV, 17 GHz electron bunch train. The bunch length can be determined by measuring the frequency and angular distribution of the emitted radiation as proposed by Nguyen[1]. The beam is produced by a 17 GHz, 50 MeV/m traveling wave (TW) accelerator built by Haimson Research Corporation (HRC). The high operating frequency of this accelerator allows for the production of ultra-short bunches of about 180 femtoseconds. We will present detailed calculations of the optimization of the experimental system and of the expected bunch length resolution.