Wake fields effects due to surface roughness in a circular pipe

The problem of the wake field generated by a relativistic particle travelling in a long beam pipe with rough surface has been studied by means of a standard theory based on the hybrid modes excited in a periodically corrugated waveguide with circular cross-section. 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. An analytical expression of the wake field is given for very small corrugations.