Aplication of Frequency Map Analysis to Beam-Beam Effects Study in Crab Waist Collision Scheme

We applied Frequency Map Analysis (FMA) - a method that is widely used to explore dynamics of Hamiltonian systems - to beam-beam effects study. The method turned out to be rather informative and illustrative in the case of a novel Crab Waist collision approach, when "crab" focusing of colliding beams results in significant suppression of betatron coupling resonances. Application of FMA provides visible information about all working resonances, their widths and locations in the planes of betatron tunes and betatron amplitudes, so the process of resonances suppression due to the beams crabbing is clearly seen.Comment: 11 pages, 10 figure

Recent Beam-Beam Effects at VEPP-2000 and VEPP-4M

Budker INP hosts two e+e- colliders, VEPP-4M operating in the beam energy range of 1-5.5 GeV and the low-energy machine VEPP-2000, collecting data at 160-1000 MeV per beam. The latter uses a novel concept of round colliding beams. The paper presents an overview of observed beam-beam effects and obtained luminosities.Comment: Presented at the ICFA Mini-Workshop on Beam-Beam in Hadron Colliders, CERN, Geneva, Switzerland, 18-22 March 201

Machine detector interface for the e+e−e^+e^- future circular collider

The international Future Circular Collider (FCC) study aims at a design of $pp$, $e^+e^-$, $ep$ colliders to be built in a new 100 km tunnel in the Geneva region. The $e^+e^-$ collider (FCC-ee) has a centre of mass energy range between 90 (Z-pole) and 375 GeV (tt_bar). To reach such unprecedented energies and luminosities, the design of the interaction region is crucial. The crab-waist collision scheme has been chosen for the design and it will be compatible with all beam energies. In this paper we will describe the machine detector interface layout including the solenoid compensation scheme. We will describe how this layout fulfills all the requirements set by the parameters table and by the physical constraints. We will summarize the studies of the impact of the synchrotron radiation, the analysis of trapped modes and of the backgrounds induced by single beam and luminosity effects giving an estimate of the losses in the interaction region and in the detector.Comment: 6 pages, 7 figures, 62th ICFA ABDW on High Luminosity Circular $e^+e^-$ Colliders, eeFACT2018, Hong Kong, Chin

The status of the energy calibration, polarization and monochromatization of the FCC-ee

The Future Circular electron-positron Collider, FCC- ee, is designed for unprecedented precision for particle physics experiments from the Z-pole up to above the top-pair-threshold, corresponding to a beam energy range from 45.6 to 182.5 GeV. Performing collisions at various particle-physics resonances requires precise knowledge of the centre-of-mass energy (ECM) and collision boosts at all four interaction points. Measurement of the ECM by resonant depolarization of transversely polarized pilot bunches in combination with a 3D polarimeter, aims to achieve a systematic uncertainty of 4 and 100 keV for the Z-pole and W-pair-threshold energies respectively. The ECM itself depends on the RF-cavity locations, beamstrahlung, longitudinal impedance, the Earth’s tides, opposite sign dispersion and possible collision offsets. Application of monochromatization schemes are envisaged at certain beam energies to reduce the energy spread. The latest results of studies of the energy calibration, polarization and monochromatization are reported here

Momentum acceptance optimization in FCC-ee lattice (CERN)

The part of the ongoing study of the future circular collider (FCC) is an electron positron machine with center of mass energy from 90 to 350 GeV. Crab waist collision scheme and small (1 mm) vertical beta function at the interaction point (IP) provide superior luminosity. At the top energy, radiation in the field of the opposite bunch (beamstrahlung) limits the beam lifetime and therefore achievable luminosity. Beamstrahlung influence depends on momentum acceptance of the lattice, the value of 2% provides acceptable lifetime. The small value of vertical beta function enhances effects of nonlinear chromaticity. The present work describes principles used in design and optimization of FCC-ee momentum acceptance optimization

Final focus designs for crab waist colliders

The crab waist collision scheme promises significant luminosity gain. The successful upgrade of the DA$\Phi$NE collider proved the principle of crab waist collision and increased luminosity 3 times. Therefore, several new projects try to implement the scheme. The paper reviews interaction region designs with the crab waist collision scheme for already existent collider DA$\Phi$NE and SuperKEKB, presently undergoing commissioning, for the projects of SuperB in Italy, CTau in Novosibirsk and FCC-ee at CERN

Application of frequency map analysis to beam-beam effects study in crab waist collision scheme

We applied frequency map analysis (FMA)—a method that is widely used to explore dynamics of Hamiltonian systems—to study beam-beam effects in a novel crab waist collision approach. The “crab” focusing of colliding beams results in significant suppression of betatron coupling resonances induced by beam-beam interaction. Application of FMA provides visible information about all working resonances, their widths, and locations in the planes of betatron tunes and betatron amplitudes, so the process of resonances suppression due to the beams crabbing is clearly seen. However, our numerical simulations and further analysis showed that effectiveness of crab waist is considerably restricted in the cases when the colliding beams are not flat. The FMA technique turned out to be very helpful in these studies, as it gave us the key information which would be difficult to obtain in a different way

Beam Dynamics Challenges for FCC-ee

The goals of FCC-ee include reaching luminosities of up to a few 1036 cm-2s-1 per interaction point at the Z pole or some 1034 cm-2s-1 at the ZH production peak, and pushing the beam energy up to ≥175 GeV, in a ring of 100 km circumference, with a total synchrotron-radiation power not exceeding 100 MW. A parameter baseline as well as high-luminosity crab-waist options were described in [1] and [2], respectively. The extremely high luminosity and resulting short beam lifetime (due to radiative Bhabha scattering) are sustained by top-up injection. The FCC-ee design status and typical beam parameters for different modes of operation are reported in [3]. One distinct feature of the FCC-ee design is its conception as a double ring, with separate beam pipes for the two counter-rotating (electron and positron) beams, resembling, in this aspect, the high-luminosity B factories PEP-II, KEKB and SuperKEKB as well as the LHC. The two separate rings do not only permit operation with a large number of bunches, up to a few 10,000’s at the Z pole, but also allow for a well-centered orbit all around the ring as well as for a nearly perfect mitigation of the energy sawtooth, e.g. by tapering the strength of all magnets according to the local beam energy, and for an independent optics control for the two beams. A side benefit at low energies is a reduction of the machine impedance by a factor of twos. A long list of optics and beam dynamics challenges for FCC-ee includes the following: (1) final focus optics design with a target vertical IP beta function of 1 or 2 mm, 50 or 25 times smaller than for LEP2, incorporating sextupoles for crab-waist; (2) synchrotron radiation in the final focus systems and the arcs, with effects on the detector (background, component lifetime) and on the beam (vertical emittance blow up and dynamic aperture); (3) beam-beam effects, including single-turn and multi-turn beamstrahlung; (4) design of the interaction region with a strong detector solenoid with possible compensation solenoids, a large crossing angle and a pair of final-focusing quadrupoles; (5) compatibility of the layout with the design of the hadron collider sharing the same tunnel; (6) RF acceleration system for high voltage (ZH, tt) and high current (Z, WW) with possible staging scenario; (7) impedance, HOM losses and instabilities, especially for high-current “low-energy” operation at the Z pole; (8) the top-up injection scheme; (9) achieving the dynamic aperture required for adequate beam lifetime and for the top-up injection, comprising the optimization of the arc optics; (10) vertical emittance control, including alignment and field errors, lattice nonlinearities, as well as beam-beam effects; (11) energy calibration and transverse polarization; (12) adapting to a non-planar tunnel; and (13) the development of a mono-chromatization for direct H production in the s channel. In the following we consider some of these challenges

Combined Operation and Staging Scenarios for the FCC-ee Lepton Collider

FCC-ee is a proposed high-energy electron positron circular collider that would initially occupy the 100-km FCC tunnel that will eventually house the 100 TeV FCC-hh hadron collider. The parameter range for the e⁺/e⁻ collider is large, operating at a cm energy from 90 GeV (Z-pole) to 350 GeV (t-tbar production) with the maximum beam current ranging from 1.5 A to 6 mA for each beam, corresponding to a synchrotron radiation power of 50 MW and a radiative energy loss varying from ~30 MeV/turn to ~7500 MeV/turn. This presents challenges for the rf system due to the varying rf voltage requirements and beam loading conditions. In this paper we present a possible gradual evolution of the FCC-ee complex by step-wise expansion, and possibly reconfiguration, of the superconducting RF system. The performance attainable at each step is discussed, along with the possible advantages and drawbacks