Dechirper wakefields for short bunches

In previous work (Bane and Stupakov, 2015 [1]) general expressions, valid for arbitrary bunch lengths, were derived for the wakefields of corrugated structures with flat geometry, such as is used in the RadiaBeam/LCLS dechirper. However, the bunch at the end of linac-based X-ray FELs-like the LCLS-is extremely short, and for short bunches the wakes can be considerably simplified. In this work, we first derive analytical approximations to the short-range wakes. These are generalized wakes, in the sense that their validity is not limited to a small neighborhood of the symmetry axis, but rather extends to arbitrary transverse offsets of driving and test particles. The validity of these short-bunch wakes holds not only for the corrugated structure, but rather for any flat structure whose beam-cavity interaction can be described by a surface impedance. We use these wakes to obtain, for a short bunch passing through a dechirper: estimates of the energy loss as function of gap, the transverse kick as a function of beam offset, the slice energy spread increase, and the emittance growth. In the Appendix, a more accurate derivation-than that is found in Bane and Stupakov (2015) [1]-of the arbitrary bunch length wakes is performed; we find full agreement with the earlier results, provided the bunches are short compared to the dechirper gap, which is normally the regime of interest.