Transition radiation wakefields for a beam passing through a metallic foil

In the x-ray, free-electron laser project, the Linac Coherent Light Source (LCLS), a proposal has been made to generate a shorter light pulse by placing a spoiler foil in the middle of a compressor chicane: The foil has a small slot, which selects out the small fraction of particles passing through it (“target particles”) to lase. In this report, using the method of field matching, we obtain longitudinal and transverse impedances and wakefields for several models of the proposed LCLS spoiler foil. We consider the model of a pencil beam and of a cylindrically symmetric, bi-Gaussian beam that is wider than it is long. Third, we generate a Green function that allows us to consider asymmetric beams also. For target particles of the tilted, tri-Gaussian beam that is found at the LCLS spoiler location we obtain approximate analytical formulas and numerical results for wakefield kicks in the three directions. We find that the kicks, after correction using a simple dipole and quadrupole, are all within tolerances.