Damping bunch oscillations due to off-axis injection

In the FCC-ee pre-injector complex, a slightly modified SPS can serve as pre-booster. The baseline design foresees injecting the low-emittance electron and positron bunches off-axis into the SPS, and deploying strong wigglers to greatly enhance the radiation damping at the injection energy. We here compare the damping of large injection oscillations by means of radiation damping with the effect of other possible damping mechanisms such as a fast bunch-by-bunch feedback system and/or head-tail damping via nonzero chromaticity. As a by-product, we investigate the transverse beam stability.