Monochromatization of the beams is presented as a technique to reduce the energy spread and thus improve the CM energy resolution in colliding-beam experiments. Monochromatization consists of generating opposite correlations between a spatial position and the energy deviation in the colliding beams. In beam-optics terms, this can be achieved by generating a nonzero dispersion function of opposite signs for the two beams at the Interaction Points. For the FCC-ee collider monochomatization could enable measurement of the electron Yukawa coupling. This talk will describe the different possible implementation schemes in a high-energy collider as FCC-ee, including the impact of beamstrahlung, and future possible experimental tests at current running colliders.

The ATF2-3 beamline is the only facility in the world for testing the Final Focus Beamline of linear colliders and is essential for the ILC and the CLIC projects. A vertical electron beam size of 41 nm (within 10% of the target), a closed-loop intra-bunch feedback of latency 133 ns, and direct stabilization of the beam position at the Interaction Point to 41 nm (limited by IP BPM resolution) have all been achieved at ATF2. These results fulfilled the two main ATF2 design goals, but were obtained with reduced aberration optics and a bunch population of approximately 10% of the nominal value of 10^10 electrons. Recent studies indicate that the beam degradation with the beam intensity is due to the effects of wakefields. To overcome this intensity limitation, hardware upgrades including new vacuum chambers, magnets, IP-Beam Size Monitor laser, cavity BPMs, wakefield mitigation station, as well as a comprehensive R&D program to maximize the luminosity potential are being pursued in the framework of the ILC Technology Network. This new R&D program focuses on the study of wakefield mitigation techniques, correction of higher-order aberrations, tuning strategies, including AI techniques, as well as beam instrumentation issues, such as the BPMs, advanced Cherenkov Diffractive Radiation monitors, and fast feedback systems, among others. This paper summarizes the hardware upgrades, the R&D program and the results of the Fall 2023-Winter 2024 experimental campaign performed in ATF2-3.

With a circumference of approximately 91 km, the Future Circular electron-positron Collider, FCC-ee, aims for unprecedented luminosities at beam energies from 45.6 to 182.5 GeV. A major challenge is reaching its design performance in the presence of magnet misalignments and field errors. The FCC-ee optics tuning working group studies all related aspects, and applies state-of-the-art techniques for beam-based alignment, commissioning simulations, beam threading, optics measurements and corrections, which are probed at numerous world-leading accelerator physics facilities. Advanced optics correction simulations include interaction-point tuning, magnetic tolerances are studied, and a new optics is under scrutiny. The current status of tuning simulations for different FCC-ee lattices is presented.

The FCC-ee could allow the measurement of the electron Yukawa coupling via direct Higgs s-channel production at ~125 GeV centre-of-mass (CM) energy, provided that the CM energy spread of this channel, can be reduced to about 5–10 MeV to be comparable to the width of the standard model Higgs boson. The natural collision-energy spread at 125 GeV, due only to synchrotron radiation (SR), is about 50 MeV. Its reduction to the desired level can be accomplished by means of “monochromatization”, e.g., through introducing non-zero dispersion of opposite sign at the Interaction Point (IP), for the two colliding beams. This nonzero dispersion at the IP (horizontal or vertical) could be generated by different methods, requiring or not modifications of the Final Focus System (FFS) Local Chromaticity Correction (LCC) system. In this paper we report and compare the different recent Interaction Region (IR) optics design of this new possible collision mode.

The design of the electron-positron Future Circular Collider (FCC-ee) challenges the requirements on optics codes (like MAD-X) in terms of accuracy, consistency, and performance. Traditionally, MAD-X uses a transport formalism by expanding the transfer map about the origin up to second order to compute optics functions and synchrotron radiation integrals in the TWISS and EMIT modules. Conversely, particle tracking uses symplectic maps to propagate particles. These approaches solve the same problem using different approximations, resulting in a mismatch between the models used for tracking and for optics. While in a machine like LHC these differences are not relevant, for FCC-ee, given the size and the sensitivity to phase advance, the different approaches lead to important differences in the models. For instance, a tapering strategy that matches the tunes for optics needs to apply approximations that would mismatch the tune in tracking and vice versa. In this paper, we show the effectiveness of advanced methods that bring the maps used for optics and tracking closer and that will be used to reduce the gap between optics and tracking models to an acceptable level for FCC-ee studies.