A formula is derived for the small-signal gain of a Smith-Purcell free-electron laser. The theory describes the electron beam as a moving plasma dielectric. and assumes that the electron beam interacts with an evanescent mode traveling along the surface of a periodic waveguide with a rectangular profile. The phase velocity of the evanescent wave is synchronous with the electron velocity. https://thegreensjunglebeautyshops.shop/product-category/cream-serum/