The high precision measurement of the centre-of-mass energy in the Future Circular Collider e+e- (FCC-ee) at Z and W energies can be realized through resonant spin depolarization utilizing transversely polarized beams. This requires a guaranteed sufficiently-high spin polarization in the presence of lattice imperfections. Investigations of the impact of misalignments on the equilibrium polarization are conducted using analytical and Monte-Carlo spin simulations with Bmad. Potential optimization schemes to ensure high polarization using orbit bumps have been explored.

The future upgrade to the High-Luminosity Large Hadron Collider (HL-LHC) will impose tight tolerances on IP optics measurements. k-modulation is currently the preferred method in the LHC for IP optics measurements and will play a critical role in the HL-LHC. As such, Run 3 of the LHC provides an ideal test-bench for addressing challenges in k-modulation. In the first commissioning year of Run 3, this method was used to measure and validate optics with beta ranging from 30cm to 24m. However unsatisfactory reproducibility was observed for low beta measurements. This paper presents the k-modulation results for the start of Run 3 with in depth analyses and it highlights the sensitivity of this method in view of the challenging HL-LHC runs.

The high precision measurement of the centre-of-mass energy in the Future Circular Collider e+e- (FCC-ee) at Z and W energies can be realized through resonant spin depolarization utilizing transversely polarized beams. This requires a guaranteed sufficiently-high spin polarization in the presence of lattice imperfections. Investigations of the impact of misalignments on the equilibrium polarization are conducted using analytical and Monte-Carlo spin simulations with Bmad. Potential optimization schemes to ensure high polarization using orbit bumps have been explored.