Very short range wake in strongly tapered disk loaded waveguide structures

Electron bunches are very short in linear colliders but even more in linac based X-FELs. Furthermore, typical disk-loaded waveguide structures used for particle acceleration are tapered. For example in CLIC, in order to achieve high accelerating gradient, the structure is short, 26 cells, which results in strong tapering. In this paper, very short range longitudinal wake is investigated in the regime where the number of cells needed to arrive at steady state is much larger than the number of cells in a single tapered structure. In this case the very short range wake is dominated by the wake from the smallest aperture. The results of an analytical model and numeric solutions are compared.