On the mechanism of surface roughness wake field excitation

In the manufacturing process beam pipes acquire a structure on their inner walls with a roughness depth in the order of typically 0.5 /spl mu/m rms. This surface structure is polarised by the beam and can be interpreted as an artificial dielectric. The thin dielectric layer model shows, that for rough tubes there is exactly one synchronous mode, the so called "rough tube mode" (normally in the THz region), which couples to the beam. The existence of this mode was proven by 2D and 3D simulations. In 2D the surface roughness is represented by irises. For a special kind of such 2D roughness, namely rectangular irises with random width and distance, there exists an easy way to explicitly calculate their equivalent dielectric properties. Equipped with these we calculate the wave number of the rough tube mode and contrast it to the wave number of the thin dielectric layer mode. In doing so, we present for this geometry a consistent mathematical formulation of rough surface wake fields. In 3D simulations the surface roughness is represented by randomly distributed obstacles. We show two simulations with few obstacles. In one case the wake field turns out to be mainly inductive, whereas in the other case we find again the rough tube mode.