  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.
