Wakefields in the LCLS Undulator Transitions

We have studied longitudinal wakefields of very short bunches in non-cylindrically symmetric (3D) vacuum chamber transitions using analytical models and the computer program ECHO. The wake (for pairs of well-separated, non-smooth transitions) invariably is resistive, with its shape proportional to the bunch distribution. For the example of an elliptical collimator in a round beam pipe we have demonstrated that--as in the cylindrically symmetric (2D) case--the wake can be obtained from the static primary field of the beam alone. We have obtained the wakes of the LCLS rectangular-to-round transitions using indirect (numerical) field integration combined with a primary beam field calculation. For the LCLS 1 nC bunch charge configuration we find that the total variation in wake-induced energy change is small (0.03% in the core of the beam, 0.15% in the horns of the distribution) compared to that due to the resistive wall wakes of the undulator beam pipe (0.6%)