Rf cavity point-charge wakefield computation through a hybrid analytical and numerical approach

Abstract

We study short-range geometric wakefields of a normal conducting third harmonic cavity, developed by ALBA, which is currently under investigation for the BESSY II main storage ring upgrade. As is commonly done to enhance the shunt impedance, the single cell cavity shape includes smooth nose-cone transitions to the outside beam pipe, which significantly affects the wakefields. Utilizing the general approach developed by the earlier work [B. Podobedov and G. Stupakov, Phys. Rev. ST Accel. Beams 16, 024401 (2013)], a model of point-charge wakefield for cavities of this type is suggested. The wakefield model consists of two parts: the singular part, inherently difficult for numerical codes, is found analytically, and the nonsingular part, which could be retrieved from relatively nondemanding numerical wakefield computations. Based on this hybrid approach, the wakefields due to arbitrary short bunches can be readily obtained both efficiently and accurately. The model was cross-checked against direct numerical simulations and a good agreement was found within the entire range of bunch lengths relevant to potential applications, from sub-millimeter down to $1\text{\ensuremath{-}}\ensuremath{\mu}\mathrm{m}\text{ }\text{ }\mathrm{rms}$. We also observed that the wakefield model of a single cavity applies equally well to a small number of coupled cavities after some straightforward parameter scaling.