Gain of double-slab Cherenkov free-electron laser

A formula is derived for the small-signal gain of a double-slab Cherenkov free-electron laser. The simplified model is composed of a rectangular wave-guide partially filled with two lined parallel dielectric slabs and a sheet electron beam. The theory describes the electron beam as a plasma dielectric moving between the two dielectric slabs. With the help of hydrodynamic approximation, we derived the dispersion equation and the formula of small-signal gain. Through numerical computing, we studied an ongoing experiment of double-slab Cherenkov free-electron laser, and worked out the synchronous frequency and single-pass gain.