Effect of reflections and losses in Smith–Purcell free-electron lasers

We have included the effects of losses in the grating surface and reflections at the ends of the grating in the theory of Smith-Purcell free-electron lasers. Computations show that losses typically increase the start current by about 10%. The complex reflection coefficient for the evanescent wave is computed using numerical simulations, and is found to have a magnitude on the order of 30%. This typically increases or decreases the start current by about 10%, depending on the phase of the round-trip reflection.