Synchronous Waves in the LHC Beam Screen with Ribbed Surface

The problem of the wake field generated by a relativistic particle travelling in a long beam tube with rough surface has been revisited by means of a standard theory based on the hybrid modes excited in a periodically corrugated rectangular waveguide. Slow waves synchronous with the particle can be excited in the structure, producing wake fields whose frequency and amplitude depend on the depth of the corrugation. The main features of the longitudinal wake, especially relevant for very short bunches, and its possible effect on proton bunches in the LHC beam screen with ribbed surface are discussed.