Impedance of a Beam Tube with Small Corrugations

In accelerators with very short bunches, such as is envisioned in the undulator region of the Linac Coherent Light Source (LCLS)[1], the wakefield due to the roughness of the beam-tube walls can have important implications on the required smoothness and minimum radius allowed for the beam tube. Of two theories of roughness impedance, one yields an almost purely inductive impedance[2], the other a single resonator impedance[3]; for smooth bunches, whose length is large compared to the wall perturbation size, these two models give comparable results[4]. Using very detailed, time-domain simulations it was found in Ref. [3] that a beam tube with a random, rough surface has an impedance that is similar to that of one with small, periodic corrugations. It was further found that the wake was similar to that of a thin dielectric layer (with dielectric constant 2) on a metallic tube: Wz(s) 2K0 cos k0s, with wave number and loss factor