The spatial growth rate of a negative material involved Cherenkov free-electron laser

An electron beam flying near a dielectric slab plays an important part in the study of Cherenkov free-electron laser (CFEL). In this paper, an electron beam travelling along the surface of a slab made of negative-index materials (NIM) are theoretically studied. The dispersion equation with beam loaded is derived and the spatial growth rate is obtained which is proportional to the cube root of the beam current.