Low level Radio Frequency studies for the Compact Linear Collider Damping Rings

The Compact Linear Collider (CLIC) Damping Rings (DRs) need to generate ultra-low emittance bunches to achieve high luminosity in CLIC. Strong wiggler magnets are required to significantly increase the energy loss per turn. A high total voltage Radio Frequency (RF) system is needed to compensate these losses. The resulting strong beam loading transients affect the bunch position and length. On the other hand, in order to maintain the luminosity loss below 1%, the bunch position has to be regulated within $\pm 1^{\circ }$ at 2 GHz ($\pm$ $400\mu m$) at the DR extraction. These conflicting specifications lead to a challenging design for the Low-Level RF (LLRF) system. In this work, simulations of the LLRF system are presented and validated using theoretical expressions. They are then used to evaluate various potential LLRF architectures, and to estimate and compare their performance to the demanding specifications on bunch longitudinal position in the CLIC DRs.