Effects of the beam loading in the rf deflectors of the CLIC test facility CTF3 combiner ring

In this paper we study the impact of the rf deflectors beam loading on the transverse beam dynamics of the CTF3 combiner ring. A general expression for the single-passage wake field is obtained. Different approximated formulas are derived applying linearization of the rf deflector dispersion curve either on a limited or an unlimited frequency range. A dedicated tracking code has been written to study the multibunch multiturn effects on the transverse beam dynamics. The numerical simulations reveal that the beam emittance growth due to the wake field in the rf deflectors is a small fraction of the design emittance if the trains are injected perfectly on axis. Nevertheless in case of injection errors the final emittance growth strongly depends on the betatron phase advance between the rf deflectors. If the finite bunch length is included in the tracking code, the scenario for the central part of the bunches does not change. However, for some particular injection errors, the tails of the bunches can increase the total transverse bunch emittances.