Impedance of a Beam Tube with Small Corrugations
  In accelerator projects involving the use of very short bunches, such as the Linac Coherent Light Source (LCLS)-where the rms bunch length in the undulator section is 30 micron-, it appears that even submicron imperfections in the beam tube surface can generate an impedance that is unacceptably large. We consider two periodic models of an imperfect, rough surface, one with small rectangular corrugations, the other with smooth sinusoidal oscillations. We compare the impedance of these two models. 
K. L. F. Bane and V. V. Stupakov