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The Future Circular e⁺e⁻ Collider (FCC- e⁺e⁻) injector complex needs to produce and to transport a high-intensity e⁺e⁻ beam at a fast repetition rate for topping up the collider at its collision energy. Two different options are under consideration as pre-accelerator before the bunches are transferred to the high-energy booster: using the existing SPS and designing a completely new ring. The purpose of this paper is to explore the needs and parameters of the existing SPS, to investigate wiggler magnet options for SPS, and provide an updated study of alternative accelerator ring design with injection and extraction energies of 6 and 20 GeV, respectively. In this study, the parameters of both choices are established, including the optics design, layout update and considerations for non-linear dynamics optimization., Proceedings of the 10th Int. Particle Accelerator Conf., IPAC2019, Melbourne, Australia

The 100 km FCC-ee e⁺/e⁻ circular collider requires luminosities in the order of 10³⁵ cm⁻² s⁻¹ and very low emittances of 0.27 nm·prad for the horizontal plane and 1 pm·prad in the vertical. In order to reach these requirements, extreme focusing of the beam is needed in the interaction regions, leading to a vertical beta function of 0.8 mm at the IP. These challenges make the FCC-ee design particularly susceptible to misalignment and field errors. This paper describes the tolerance of the machine to magnet alignment errors and the effectiveness of optics and orbit correction methods that were implemented in order to bring the vertical dispersion to acceptable values, which in turn limits the vertical emittance. Thousands of misalignment and error seeds were introduced in MADX simulations and a comprehensive correction strategy, which includes macros based upon Dispersion Free Steering (DFS), linear coupling correction based on Resonant Driving Terms (RDTs) and response matrices, was implemented. The results are summarized in this paper., Proceedings of the 62th ICFA ABDW on High Luminosity Circular e$^+$e$^-$ Colliders, eeFACT2018, Hong Kong, China

Several studies on the beam dynamics at FCC-ee: low emittance tuning, dynamic aperture, beam blowup with/without beam beam, will be introduced., Proceedings of the 62th ICFA ABDW on High Luminosity Circular e$^+$e$^-$ Colliders, eeFACT2018, Hong Kong, China

The Future Circular electron-positron Collider (FCC-ee) requires fast cycling injectors with very low extraction emittances to provide and maintain extreme luminosities at center of mass energy varying between 91.2-385 GeV in the collider. For this reason, the whole injector complex table is prepared by putting into consideration the minimum fill time from scratch, bootstrapping, transmission efficiency as well as store time of the beams in synchrotrons to approach equilibrium emittances. The current injector baseline contains 6 GeV S-band linac, a damping ring at 1.54 GeV, a prebooster to accelerate from 6 to 20 GeV, which is followed by 98-km top up booster accelerating up to final collision energies. Acceleration from 6 GeV to 20 GeV can be provided either by Super Proton Synchrotron (SPS) of CERN or a new synchrotron or C-Band linac, distinctively, which all options are retained. In this paper, the current status of the whole FCC-ee injector complex and injection strategies are discussed., Proceedings of the 62th ICFA ABDW on High Luminosity Circular e$^+$e$^-$ Colliders, eeFACT2018, Hong Kong, China

The Schottky monitors installed at the LHC enable the detection of Schottky noise of the two circulating proton / ion beams. From Schottky noise, beam parameters like tune, chromaticity, and relative emittance, can be extracted in a non-destructive and purely parasitic method of measurement. The primary goal of this MD was to study the Schottky monitors capability to reliably and accurately determine the beam chromaticities at injection energy. Furthermore, the possibility to track the beam emittance has been investigated.

A Robinson wiggler is planned to be installed in the storage ring of the Metrology Light Source (the MLS). The Robison wiggler (RW) is a device consisting of a chain of combined-function magnets (CFMs), intended to manipulate the damping partition numbers and thus adjust the longitudinal emittance. The objective is to lengthen the bunch in order to improve the Touschek lifetime. However, the nonlinear perturbation of the beam dynamics due to the Robinson wiggler could limit the achievable improvement. Therefore, a symplectic method of modeling the wiggler has been established to study these nonlinear effects. Optimized solutions have been developed for both the ramping procedure and the future daily operation of the wiggler and are presented in this paper., Proceedings of the 9th Int. Particle Accelerator Conf., IPAC2018, Vancouver, BC, Canada

The FCC-ee Lepton Collider will provide e⁺e⁻ collisions in the beam energy range of 45.6 GeV to 182.5 GeV. FCC-ee will be a precision measurement tool for Z, W, H and t physics with expected luminosities of 2.07× 10³⁶ cm⁻² s⁻¹ at the Z-pole and 1.3 × 10³⁴ cm⁻² s⁻¹ at the tt⁻ threshold. In order to achieve the foreseen luminosities, a vertical β^{*} of 1 mm to 2 mm is mandatory. Dynamic aperture and frequency map analysis for the 97.75 km machine with such a squeezed accelerator optics are studied. Furthermore, effects of machine misalignments on dynamic and momentum aperture are presented and estimations for the required tolerances are given, Proceedings of the 9th Int. Particle Accelerator Conf., IPAC2018, Vancouver, BC, Canada

This contribution presents the status of the top-up booster synchrotron for the FCC electron-positron collider FCC-ee, which is a 100 km electron-positron collider being designed for precision studies and rare decay observations in the range of 90 to 365 GeV centre-of-mass energy. In order to keep the luminosity at a level of the order of 10³⁵ cm⁻²s⁻¹ continuous top-up injection is required, because of the short beam lifetime of less than one hour. The top-up booster synchrotron will be housed in the same tunnel as the collider rings and will ramp up the beam energy from 20 GeV at injection to the full energy between 45.5 GeV and 182.5 GeV depending on operation mode. The lattice design and two possible optics will be presented. The dynamic aperture was investigated for different sextupole schemes with and without misalignments of the lattice components. In addition, wigglers were installed to decrease the damping time and mitigate intra-beam-scattering., Proceedings of the 9th Int. Particle Accelerator Conf., IPAC2018, Vancouver, BC, Canada

Luminosity leveling by beta* is the baseline operational scenario of HL-LHC, and this leveling technique may be used in 2018 or during run~3 depending on the beam parameters and beta* range. During this MD beta*leveling was commissioned successfully for the first time with the telescopic squeeze over the beta* range of 40 cm to 30 cm. A novel beta* leveling controls technique based on a modification of the LSA trim was also tested during the MD.

FCC-ee is a 100 km e⁺ e⁻ collider, which is being designed within the Future Circular Collider Study (FCC) for precision studies and rare decay observations in the range of 90 to 350 GeV center-of- mass energy. The beam lifetime will be limited to less than one hour, because of radiative Bhaba scattering and beamstrahlung. In order to keep the luminosity on the high level of 10³⁵ cm⁻²s⁻¹ continuous top-up injection is required. Therefore, besides the collider, that will operate at constant energy, a fast cycling booster synchrotron will be installed in the tunnel. The injection energy to the booster synchrotron will be around 6-20 GeV. Such a small energy together with the large bending radius not only creates an ultra-small beam emittance, but also requires very low magnetic fields close to the limit of technical feasibility. This paper will focus on the challenges and requirements for the top-up booster design arising from low magnetic fields and collective instabilities and present the status of the lattice design., Proceedings of the 8th Int. Particle Accelerator Conf., IPAC2017, Copenhagen, Denmark

Im Jahre 1958, schlug Kenneth W. Robinson die Nutzung eines Korrektormagneten vor um den entdämpften radialen Betatronoszillationen im Cambridge electron accelerator entgegen zu wirken. Dieser Korrektormagnet sollte aus kurzen, alternierenden Dipolen mit einem starken Gradienten bestehen, sodass die Verluste durch Synchrotronstrahlung mit zunehmendem Trajektorienradius abnehmen. Diese Transversal-Gradienten-Wiggler werden auch "Robinson Wiggler" (RW) genannt. Die Metrology Light Source (MLS), welche Eigentum der Physikalisch-Technischen Bundesanstalt (PTB) ist und vom Helmholtz-Zentrum Berlin (HZB) entworfen und betrieben wird, ist ein Elektronen-Synchrotron, optimiert für die Produktion von Synchrotronstrahlung im Spektralbereich zwischen THz und EUV. Da die MLS eine gerampte Maschine ist, nimmt der gespeicherte Elektronenstrom mit der Zeit ab und die Strahllebensdauer ist von Bedeutung für die Nutzer der Synchrotronstrahlung. Es wird vorgeschlagen einen RW bei der MLS zu installieren um die Strahllebensdauer zu erhöhen. Mit RW wäre es möglich, Dämpfung aus der longitudinalen in die horizontale Ebene zu verschieben sodass sich die Energiebreite um einen Faktor 3 erhöht und die Emittanz sich um ungefähr einen Faktor 2 reduziert. Die Länge der Elektronenpakete wird dadurch stärker verlängert als die mittlere horizontale Paketbreite reduziert wird. So nimmt die Elektronendichte im Paket ab und die Verlustrate sinkt. Dies hat zu Folge dass sich die Lebensdauer verbessert und die Aktivierung von Komponenten reduziert wird. Mit erhöhter Energiebreite und verringerter Emittanz, wird der Beitrag der Dispersion zur horizontalen Quellgröße stärker. Durch geeignete Wahl der Magnetoptik kann die Brillianz am Quellpunkt erhöht werden bei gleichzeitiger Verbesserung der Lebensdauer. Simulationen zeigen dass die Lebensdauer an der MLS durch die Installation eines solchen RW um einen Faktor 2.3 ansteigt, was einem Zugewinn an integriertem Photonenfluss von 30 % entspricht. In 1958, Kenneth W. Robinson proposed the usage of a magnetic correction device to reduce the antidamping of radial betatron oscillations in the Cambridge electron accelerator. The essence of this correction device are short, alternating dipoles with a strong gradient, such that the radiation loss decreases with increasing radius of trajectory. These transverse gradient wigglers are also called "Robinson Wigglers" (RW). The Metrology Light Source (MLS), owned by the Physikalisch-Technische Bundesanstalt (PTB) and designed and operated by Helmholtz-Zentrum Berlin (HZB), is an electron synchrotron, optimized for the production of synchrotron radiation in the THz to the EUV spectral region. Being a ramped machine, Top-Up operation is not possible. With a decaying beam current, the lifetime of the stored beam is of importance for the user community, for reasons of temporal stability and integrated photon flux. It is proposed to install a RW at the MLS in order to improve the beam lifetime. With a RW, it is possible to transfer damping from the longitundinal to the horizontal plane in a way, that the energy spread increases by a factor of 3 and the emittance reduces by a factor of 2. Doing so, the bunch length is increased by a larger fraction than the average bunch width is decreased. Thereby the electron density is reduced which results in a lower loss rate of electrons. This improves the beam lifetime and reduces induced radioactivity of accelerator components and shielding. With an increased energy spread and a reduced emittance, the contribution of the dispersion to source size becomes more important. By carefully choosing the magnet optics, the brilliance at the source point can be improved simultaneously to increasing the lifetime. Simulations indicate that a RW is able to increase the lifetime in the standard user operation mode at the MLS by a factor of 2.3, corresponding to an increase in photon flux for one standard user run of approximately 30 %.

The Metrology Light Source (MLS) is a dedicated elec-tron storage ring for metrology applications with three families of sextupoles. The existing setting of the three independently powered sextupole families respective to lifetime were roughly determined by scanning their strengths against each other. As a flexible machine the sextupole families of the MLS can be regrouped into new families, which increase the complexity of the scan pro-cedure. Consequently the former strategy would be too time-consuming for refined global scan and it has to be complemented with physical constraints. Therefore a scheme has been developed to keep the chromaticity in a reasonable range during the scan and to reduce the degree of freedom, which is even more important at BESSY II with increasing number of independent sextupole cir-cuits. This paper presents the principle of sextupole scan and the experimental results at the MLS and preliminary test at BESSY II., Proceedings of the 7th Int. Particle Accelerator Conf., IPAC2016, Busan, Korea