The Future Circular Electron-Positron Collider (FCC-ee) represents a cutting-edge particle physics facility designed to further investigate the Z, W± and Higgs boson in addition to the top quark. The implementation of Nested Magnets (NMs) in the FCC-ee arc cells would maintain high luminosity and reduce its energy consumption. The use of these special magnets induces changes in the damping partition numbers. To mitigate this the dipole fields in focusing and defocusing quadrupoles have to be different. This solution gives rise to incompatibility problems for the machine layout between the different energy configurations as the optics is also changed. This problem is tackled by defining different bending and geometric angles for the NMs. The beam dynamics and performance aspects of the new lattice are studied in this paper.

Schottky monitors serve as non-invasive tools for beam diagnostics, providing insights into crucial bunch characteristics such as tune, chromaticity, bunch profile, or synchrotron frequency distribution. However, octupole magnets commonly used in circular storage rings to mitigate instabilities through the Landau damping mechanism, can significantly affect the Schottky spectrum. Due to the amplitude-dependent incoherent tune shift of individual particles, the satellites of the Schottky spectrum are smeared out as the octupolar field increases. This study investigates the impact of octupoles and their incorporation into theory, with the goal of improving beam and machine parameter evaluation from measured spectra. Theoretical findings are validated through macro-particle simulations conducted across a range of octupole strengths, encompassing typical operational conditions at the Large Hadron Collider.

Schottky monitors are valuable non-invasive tools used for beam diagnostics, providing insights into crucial bunch characteristics such as tune, chromaticity, bunch profile, or synchrotron frequency distribution. This study investigates Schottky spectra at the Large Hadron Collider (LHC) through a combination of simulations and measurements. Experimental data from lead ion bunches are compared with simulated spectra derived from time-domain, macro-particle simulations. In particular, amplitude detuning due to the octupole magnets, known to influence the Schottky spectra, is incorporated into the simulations. These simulations are performed for various octupoles currents with the goal of better understanding the interplay between octupoles and the Schottky spectrum. Finally, measured spectra are compared to simulations performed using the best available knowledge of the parameters impacting the spectra.

Schottky monitors serve as non-invasive tools for beam diagnostics, providing insights into crucial bunch characteristics such as tune, chromaticity, bunch profile, or synchrotron frequency distribution. However, octupole magnets commonly used in circular storage rings to mitigate instabilities through the Landau damping mechanism, can significantly affect the Schottky spectrum. Due to the amplitude-dependent incoherent tune shift of individual particles, the satellites of the Schottky spectrum are smeared out as the octupolar field increases. This study investigates the impact of octupoles and their incorporation into theory, with the goal of improving beam and machine parameter evaluation from measured spectra. Theoretical findings are validated through macro-particle simulations conducted across a range of octupole strengths, encompassing typical operational conditions at the Large Hadron Collider.

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.

This paper provides updates on two essential toolsets designed to facilitate the tuning and commissioning processes of the Future Circular Collider (FCC): relaxed optics and linear tuning knobs specifically for the experimental insertion regions. Motivated by the imperative need for efficient tuning strategies, we outline the construction methodology for both toolsets and present initial studies demonstrating their efficacy. The paper discusses the significance of these tools in enhancing the operational capabilities of the FCC and presents early results showcasing their potential impact on the collider's performance during tuning and commissioning phase.

The determination of equilibrium emittance stands as a critical factor in optimizing the luminosity of the Future Circular Collider (FCC). In order to have accurate simulations and understanding of the emittance, multiple effects have to be taken into consideration including errors in the machine, solenoid effects, synchrotron radiation and beam-beam effects. The novel X-Suite software aims to encompass many of these effects. In this paper we present benchmark studies and first results for determining equilibrium emittances using X-Suite and other simulation codes.

Precise determination of the center-of-mass energy in the Future Circular Collider e+e- (FCC-ee) at Z and W energies can be achieved by employing resonant spin depolarization techniques, for which a sufficient level of transverse beam polarization is demanded under the presence of machine imperfections. In this study, the FCC-ee lattice has been modeled and simulated with a variety of realistic lattice imperfections, including misalignments, angular deviations, BPM errors, long-range errors, etc., along with refined orbit correction and tune matching procedures. The equilibrium polarization is calculated within the context of realistic machine models, aiming to understand the underlying reason for polarization loss and potentially improve polarization by lattice manipulation.

The Future Circular Electron-Positron Collider (FCC-ee) represents a cutting-edge particle physics facility designed to further investigate the Z, W± and Higgs boson in addition to the top quark. The implementation of Nested Magnets (NMs) in the FCC-ee arc cells would maintain high luminosity and reduce its energy consumption. The use of these special magnets induces changes in the damping partition numbers. To mitigate this the dipole fields in focusing and defocusing quadrupoles have to be different. This solution gives rise to incompatibility problems for the machine layout between the different energy configurations as the optics is also changed. This problem is tackled by defining different bending and geometric angles for the NMs. The beam dynamics and performance aspects of the new lattice are studied in this paper.

The Future Circular Collider (FCC-ee) is designed to explore the Z and W± bosons, along with the Higgs boson and top quark, achieving exceptionally high luminosity. In order to minimize the energy lost per turn due to Synchrotron Radiation (SR) we explore the use of Nested Magnets (NMs) into the arcs cell. For this, it is necessary to explore the possible combinations of the different magnet types in the cell, namely: dipoles, quadrupoles and sextupoles. Specifications in terms of strength and alignment tolerances are reviewed in this paper.

A significant project such as the FCC-ee (with 91.17 km circumference) entails numerous challenges to ensure the stability and performance of the machine. In the pursuit of contributing to the improvement of energy consumption during its operation, the exploration of Nested Magnets (NMs) as a means to reduce synchrotron radiation has been undertaken. This paper presents first studies on the Dynamic Aperture (DA) and the Momentum Acceptance (MA) of this novel design to guide the next developments.

In autumn 2023, the FCC Feasibility Study underwent a crucial “mid-term review”. We describe some accelerator performance risks for the proposed future circular electron- positron collider, FCC-ee, identified for, and during, the mid-term review. For the collider rings, these are the collective effects when running on the Z resonance – especially resistive wall, beam-beam, and electron cloud –, the beam lifetime, dynamic aperture, alignment tolerances, and beam-based alignment. For the booster, the primary concern is the vacuum system, with regard to impedance and effects of the residual gas. For the injector, the layout and the linac repetition rate are primary considerations. We discuss the various issues and report the planned mitigations.

The FCC-ee collider physics program requires a precise determination of the center-of-mass energy. The average energies of the two colliding beams can be measured by resonant depolarization (RDP) of polarized electron and positron bunches. The depolarization is achieved by an electromagnetic device, e.g., a strip line, excited at a sweeping frequency. Once the excitation frequency is equal to the spin precession frequency, which is directly proportional to the beam energy, the polarization is lost or reduced. At KARA the resonant frequency is routinely measured via the change of the Touschek lifetime. We report on an RDP beam measurement campaign at the Karlsruhe Research Accelerator (KARA), exploring how this technique could be applied at the FCC-ee. In particular, we examine the sensitivity of the inferred value of beam energy to various parameters, such as the depolarize scan speed, the scan direction, and the beam operation energy.

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.

Xsuite is a modular simulation package bringing to a single flexible and modern framework capabilities of different tools developed at CERN in the past decades notably MAD-X Sixtrack Sixtracklib COMBI and PyHEADTAIL. The suite consists of a set of Python modules (Xobjects, Xpart, Xtrack, Xcoll, Xfields, Xdeps) that can be flexibly combined together and with other accelerator-specific and general-purpose python tools to study complex simulation scenarios. Different computing platforms are supported including conventional CPUs as well as GPUs from different vendors. The code allows for symplectic modeling of the particle dynamics combined with the effect of synchrotron radiation impedances feedbacks space charge electron cloud beam-beam beamstrahlung and electron lenses. For collimation studies beam-matter interaction is simulated using the K2 scattering model or interfacing Xsuite with the BDSIM/Geant4 library and with the FLUKA code. Methods are made available to compute and optimize the accelerator lattice functions, chromatic properties and equilibrium beam sizes. By now the tool has reached a mature stage of development and is used for simulations studies by a large and diverse user community.