Density modulation of the thin slab beam over a metal grating

Summary form only given, as follows. Summary form only given. We present the density modulation of a relativistic slab beam by a traveling surface wave propagating along the beam over a metal grating. A dispersion relation of the surface wave is derived from boundary conditions on two interfaces, the slab beam and the metal grating. The interaction between the thin slab beam and the surface wave is described in a cold beam limit. A self-modulation of the beam density is amplified with propagation due to a feedback offered by the grating. The analysis is expanded to a warm beam with a relative velocity spread.