On-axis top-up injection with multipole injection kicker in FCC-ee

Top-up injection is required in FCC-ee to maintain high luminosity given the short beam lifetime. The present baseline relies on on-axis off-energy injection with a conventional orbit bump; in this work, an alternative on-axis scheme based on a multipole injection kicker (MIK) is investigated. The FCC-ee beam parameters place challenging demands on the MIK field distribution, which must combine a large field-free region for the circulating beam, a narrow transition region, and a sufficiently uniform field in the injection region across all operation modes. To relax these challenging requirements while limiting the residual kick on the circulating beam, a compensated MIK scheme is proposed, in which a compensation MIK (CMIK) is placed upstream of the main MIK, and the required optics and field-symmetry conditions between the two devices are derived for different phase advances. The pulsed-conductor kicker is adopted as the preferred design, and its influence on the circulating beam and its injection performance are evaluated for the Z operation mode. In the Z mode, the near-zero phase-advance compensated scheme limits the single-pass emittance growth of the circulating beam to about $7\%$ horizontally and below $2\%$ vertically, while the injected beam requires transfer-line pre-compensation to mitigate the field gradient in the injection region. These results indicate that compensated MIK injection is a promising candidate for FCC-ee on-axis top-up injection.