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Colliders are essential research tools for particle physics. Numerous future collider proposal were discussed in the course of the US high energy physics community strategic planning exercise Snowmass'21. The Implementation Task Force (ITF) has been established to evaluate the proposed future accelerator projects for performance, technology readiness, schedule, cost, and environmental impact. Corresponding metrics has been developed for uniform comparison of the proposals ranging from Higgs/EW factories to multi-TeV lepton, hadron and ep collider facilities, based on traditional and advanced acceleration technologies. This article describes the metrics and approaches, and presents evaluations of future colliders performed by the ITF.

The Snowmass 2021 Implementation Task Force has been established to evaluate the proposed future accelerator projects for performance, technology readiness, schedule, cost, and environmental impact. Corresponding metrics has been developed for uniform comparison of the proposals ranging from Higgs/EW factories to multi-TeV lepton, hadron and ep collider facilities, based on traditional and advanced acceleration technologies. This report documents the metrics and processes, and presents evaluations of future colliders performed by Implementation Task Force., Comment: 68 pages; Submitted to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021)

The FCC-ee, with its unprecedented luminosity goal and high energy reach, creates challenges and requires solutions to many issues in order to produce a realistic design for the complex machine detector interface. The interaction region design for the FCC-ee adopts the crab-waist collision scheme and proposes an elegant local chromaticity correction system. An asymmetric layout of nearby dipoles suppresses the critical energy of synchrotron radiation incoming to the detector at the interaction point to a maximum value of 100 keV. The main challenge of the FCC-ee machine detector interface design is to combine the many conflicting accelerator and 2 T detector constraints, aiming for the optimal trade-off choices that simultaneously allow for a best machine performance in terms of integrated luminosity and data taking efficiency. Much of the success of the FCC-ee will be related to the interaction region design, as a result of the ingredients coming from areas of accelerator physics, mechanical engineering and detector optimization.

SuperKEKB is an electron–positron asymmetric-energy double-ring collider, which was built in Japan. It has been operated to explore new phenomena in B-meson decays. Hence, extremely higher luminosity is required. A collision scheme of low emittance with a large Piwinski angle called a “nano-beam scheme” has been adopted to achieve higher luminosity by squeezing the vertical beta function at the interaction point to be smaller than the bunch length. A “crab waist collision scheme” proposed by P. Raimondi et al. has also been adopted to improve the luminosity performance. The article presents an overview of the operation of the nano-beam and crab waist collision schemes at SuperKEKB.

After 10 years of physics at the Large Hadron Collider (LHC), the particle physics landscape has greatly evolved. Today, a staged Future Circular Collider (FCC), consisting of a luminosity-frontier highest-energy electron–positron collider (FCC-ee) followed by an energy-frontier hadron collider (FCC-hh), promises the most far-reaching physics program for the post-LHC era. FCC-ee will be a precision instrument used to study the Z, W, Higgs, and top particles, and will offer unprecedented sensitivity to signs of new physics. Most of the FCC-ee infrastructure could be reused for FCC-hh, which will provide proton–proton collisions at a center-of-mass energy of 100 TeV and could directly produce new particles with masses of up to several tens of TeV. This collider will also measure the Higgs self-coupling and explore the dynamics of electroweak symmetry breaking. Thermal dark matter candidates will be either discovered or conclusively ruled out by FCC-hh. Heavy-ion and electron–proton collisions (FCC-eh) will further contribute to the breadth of the overall FCC program. The integrated FCC infrastructure will serve the particle physics community through the end of the twenty-first century. This review combines key contents from the first three volumes of the FCC Conceptual Design Report.

The positron linac of SuperKEKB contains accelerating structures surrounded by quadrupoles without nearby beam-position-monitors (BPMs) or steering magnets. In this situation, standard techniques for beam steering or beam-based-alignment are not efficient. We here present a method to determine the magnetic centers of individual SuperKEKB linac quadrupoles. This method is independent of any BPM offsets. The beam position at the quadrupole under study is scanned, and for each position the quadrupole strength is varied, so as to find the location of zero deflection. Unlike other method used in the past, this technique does not rely on any transfer matrices. Interpolation is possible even to quadrupoles without BPM by assigning ‘virtual BPMs’. We show that the misalignment of the quadrupoles with BPM in the bore can be determined with an rms error of ≤ 37 μ m; for quadrupoles without proper BPMs the error is σ ≤ 112 μ m.

International audience; Injectors and in particular the positron production systems are a crucial element in linear and circular colliders. The proposed FCC-ee injector linac accelerates both electrons and positrons up to 6 GeV in order to be injected into the Pre-Booster Ring (PBR) with a high intensity of 3.5 nC per bunch for the Z running mode. The current design baseline of the FCC-ee injector linac is based on the SuperKEKB scheme, in which the electron and the positron beams share the same linacs with a fixed target configuration on-axis hole for electron beam passage. One of the main drawbacks of this scheme is the positron production efficiency at the exit of the injector linac. In order to achieve a better performance and a higher positron yield, in this paper we study different bypass injection options. Start-to-end design and optimization for beam production, acceleration and transport from the feeding electron source to the positron damping ring are also being presented.

The Future Circular e+/e- Collider (FCC-ee) presents an appreciable challenge for emittance tuning due to the strong final focusing and chromaticity correction, required to achieve high luminosities in the order of 10$^{36}$cm$^{-2}$s$^{-1}$. The proposed 100 km e+/e circular collider, FCC-ee is being designed to undertake precision studies and rare decay observations in the range of 90 to 350 GeV center of mass energy, with luminosities ranging from 1.7x10$^{35}$cm$^{-2}$s$^{-1}$ to 230x10$^{35}$cm$^{-2}$s$^{-1}$. In order to reach these luminosities, large beta values are encountered preceding to the IP, increasing the susceptible to misalignments and field errors. In this paper, we describe a comprehensive correction strategy used for the low emittance tuning. The strategy includes programs that have been developed to optimise the lattice based on Dispersion Free Steering, linear coupling compensation based on Resonant Driving Terms and beta beat correction utilising response matrices.

The Study Group for a GeV-scale Proton Synchrotron was launched in 1952 at CERN. Initially, an up-scaled version of the 3 GeV Cosmotron was considered but soon a new design based on the newly discovered alternating-gradient principle and promising a proton energy of 30 GeV was adopted by the CERN Council in the same year. In order to limit cost the energy was subsequently limited to 25 GeV and the project led by J.B. Adams was approved in 1953. The final parameters were fixed in 1954 and construction started in 1955. The CPS [1] became operational towards the end of 1959 reaching an energy of 28 GeV [2, 3]. It has turned out to be an extremely versatile facility [4] (Table 10.1).

Within the Future Circular Collider (FCC) design study launched at CERN in 2014, it is envisaged to construct hadron (FCC-hh) and lepton (FCC-ee) ultra-high-energy machines aimed to replace the LHC upon the conclusion of its research program. The Budker Institute of Nuclear Physics is actively involved in the development of the FCC-ee electron–positron collider. The Crab Waist (CR) scheme of the collision region that has been proposed by INP and will be implemented at FCC-ee is expected to provide high luminosity over a broad energy range. The status and development of the FCC project are described, and its parameters and limitations are discussed for the lepton collider in particular.

This paper introduces a new approach to measure the muon magnetic moment anomaly $a_{\mu} = (g-2)/2$, and the muon electric dipole moment (EDM) $d_{\mu}$ at the J-PARC muon facility. The goal of our experiment is to measure $a_{\mu}$ and $d_{\mu}$ using an independent method with a factor of 10 lower muon momentum, and a factor of 20 smaller diameter storage-ring solenoid compared with previous and ongoing muon $g-2$ experiments with unprecedented quality of the storage magnetic field. Additional significant differences from the present experimental method include a factor of 1,000 smaller transverse emittance of the muon beam (reaccelerated thermal muon beam), its efficient vertical injection into the solenoid, and tracking each decay positron from muon decay to obtain its momentum vector. The precision goal for $a_{\mu}$ is statistical uncertainty of 450 part per billion (ppb), similar to the present experimental uncertainty, and a systematic uncertainty less than 70 ppb. The goal for EDM is a sensitivity of $1.5\times 10^{-21}~e\cdot\mbox{cm}$., Comment: 24 pages, 14 figures

A newly developed three-dimensional spiral injection scheme for beam insertion into a solenoidal storage ring is reported. A new planned muon g−2/EDM experiment at J-PARC aims to measure g − 2 to a factor of 5 better statistical precision and a factor of 100 better sensitivity for the electric dipole moment (EDM) measurement compared to previous experiments. The J-PARC experiment will use a 3-T MRI solenoid magnet as the muon storage ring with a 0.66 m diameter to achieve a 1-ppm level of local uniformity. The previous g − 2 injection scheme is not applicable for beam injection into a small ring. The new scheme provides a smooth injection utilizing a radial solenoidal fringe field, without causing an error field in the storage volume. The expected storage efficiency is 80% and over, which is to be compared to 3.5% for the previous g − 2 experiment. In addition, the ability to control the storage plane is important for the EDM measurement. In this paper, we introduce the conceptual design and required beam parameters in terms of Twiss functions and the expected injection efficiency.

In the frame of the FCC study we are designing a 27 TeV hadron collider in the LHC tunnel, called the High Energy LHC (HE-LHC). The HE-LHC can be realized by replacing the LHC’s 8.33 T niobium-titanium dipole magnets with 16 T niobium-tin magnets developed for FCC-hh. A high-quality beam available from the upgraded LHC injector complex and significant radiation damping allow achieving the challenging target values for both peak and integrated luminosity required by particle physics. Tunnel integration determines the maximum outer size of the magnet cryAPCostat. The HE-LHC arc optics maximizes the dipole filling factor and optimizes the dynamic aperture, while limiting the field strengths of quadrupoles and sextupoles. The low-beta optics for the experimental insertions features a shielded quadrupole triplet even longer than the HL-LHC’s, which can support an interaction-point beta function of 25 cm, and survive an integrated luminosity above 10/ab. Other challenges include collimation and extraction. The choice of injection energy and injector is another important element, and so are various collective effects. We here report the HE-LHC design status. In the frame of the FCC study we are designing a 27 TeV hadron collider in the LHC tunnel, called the High Energy LHC (HE-LHC).

This paper discusses novel coherent beam-beam instability in collisions with a large crossing angle. The instability appears in the correlated head-tail motion of two colliding beams. A cross-wake force, which is localized at the collision point, is introduced to represent the head-tail correlation between colliding beams. A mode-coupling theory based on this localized cross-wake force enables us to explain the correlated heal-tail instability. The use of a collision scheme with a large crossing angle is becoming popular in the design of electron--positron colliders. An example thereof is the SuperKEKB project, in which a collision with a large crossing angle is performed to boost the luminosity to $0.8\ifmmode\times\else\texttimes\fi{}{10}^{36}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}2}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$. Future circular colliders will also be designed with a large crossing angle. Strong-strong simulations, which have shown the first coherent head-tail instability, can limit the performance of proposed future colliders. The mechanism whereby this instability occurs is mode coupling due to the cross-wake force. This instability may affect all collider designs based on the crab waist scheme.

International audience; Top-up injection is an essential ingredient for the future circular lepton collider (FCC-ee) to maximize the integrated luminosity and it determines the design performance. In ttbar operation mode, with a beam energy of 175 GeV, the design lifetime of ∼ 1 h is the shortest of the four anticipated operational modes, and the beam lifetime may be even shorter in actual operation. A highly robust top-up injection scheme is consequently imperative. Various top-up methods are investigated and a number of suitable schemes are considered in developing alternative designs for the injection straight section of the collider ring. For the first time, we consider multipole-kicker off-energy injection, for minimizing detector background in top-up operation, and the use of a thin wire septum in a lepton storage ring, for maximizing the luminosity.

In recent years the “crab-waist collision” scheme [P. Raimondi, Proceedings of 2nd SuperB Workshop, Frascati, 2006.; M. Zobov et al., Phys. Rev. Lett. 104, 174801 (2010)] has become popular for circular eþ e− colliders. The designs of several future colliders are based on this scheme. So far the beam-beam effects for collisions under a large crossing angle with or without crab waist were mostly studied using weak- strong simulations. We present here strong-strong simulations showing a novel strong coherent head-tail instability, which can limit the performance of proposed future colliders. We explain the underlying instability mechanism starting from the “cross-wake force” induced by the beam-beam interaction. Using this beam-beam wake, the beam-beam head tail modes are studied by an eigenmode analysis. The instability may affect all collider designs based on the crab-waist scheme. We suggest an experimental verification at SuperKEKB during its commissioning phase II.

The design of a 100 km circular e⁺e⁻ collider with extremely high luminosity is an important component of the global Future Circular Collider (FCC) study hosted by CERN. FCC-ee is being designed to serve as Z, W, H and top factory, covering beam energies from 45.6 to 175 GeV. For the injectors, the Z-operation is the most challenging mode, due to the high total charge and low equilibrium emittance in the collider at this energy. Thus, fulfilling the Z-mode will also meet the demands for all other modes of FCC-ee. This goal can be achieved by using a 6 GeV NC linac with an S-band RF frequency of 2.856 GHz and a repetition rate of 100 Hz. This linac will accelerate two bunches per RF pulse, each with a charge of 6.5 nC. Positrons will be generated by sending 4.46 GeV e⁻ onto a hybrid target so that the e⁺ created can still be accelerated to 1.54 GeV in the remaining part of the same linac. The emittance of the e⁺ beam will then shrink to the nm level in a 1.54 GeV damping ring. After damping, the e⁺ will be reinjected into the linac and accelerated to 6 GeV. The e⁻ and e⁺ will then be accelerated alternately to 45.6 GeV in the booster, before they are injected into the collider., Proceedings of the 8th Int. Particle Accelerator Conf., IPAC2017, Copenhagen, Denmark

This article describes the fundamental limitations on the performance of electron–positron circular colliders. After introducing the subject from its end use parameter, the luminosity, we discuss in detail the various accelerator physics limitations and the evolution of several ingenious frontier ideas to ever increase the luminosity of these colliders.

A beam optics scheme has been designed for the Future Circular Collider-e+e- (FCC-ee). The main characteristics of the design are: beam energy 45 to 175 GeV, 100 km circumference with two interaction points (IPs) per ring, horizontal crossing angle of 30 mrad at the IP and the crab-waist scheme [1] with local chromaticity correction. The crab-waist scheme is implemented within the local chromaticity correction system without additional sextupoles, by reducing the strength of one of the two sextupoles for vertical chromatic correction at each side of the IP. So-called "tapering" of the magnets is applied, which scales all fields of the magnets according to the local beam energy to compensate for the effect of synchrotron radiation (SR) loss along the ring. An asymmetric layout near the interaction region reduces the critical energy of SR photons on the incoming side of the IP to values below 100 keV, while matching the geometry to the beam line of the FCC proton collider (FCC-hh) [2] as closely as possible. Sufficient transverse/longitudinal dynamic aperture (DA) has been obtained, including major dynamical effects, to assure an adequate beam lifetime in the presence of beamstrahlung and top-up injection. In particular, a momentum acceptance larger than +/-2% has been obtained, which is better than the momentum acceptance of typical collider rings by about a factor of 2. The effects of the detector solenoids including their compensation elements are taken into account as well as synchrotron radiation in all magnets. The optics presented in this paper is a step toward a full conceptual design for the collider. A number of issues have been identified for further study.

構成：塚﨑朝子

Toward to the next generation experimental investigation of neutrino physics, the J-PARC accelerator group is now considering several candidates to extend the proton beam power to multi-MW region. One of the major candidates is the adoption of a superconducting proton linac. A neutrino is generated by bombarding a proton beam to a target. In Monte-Carlo simulations with GCALOR or FLUKA2011 package, the generated neutrino flux per proton beam energy monotonously increases with the energy reaching to around 9 GeV, and then saturation is seen in higher energy [1]. Therefore, if we only focus on the efficiency of neutrino generation, it is efficient to improve the average beam current with staying the beam energy to 9 GeV. It motivated us to consider the 9 GeV proton linac for neutrino beam generation. For the study on the design, we assume that the linac is constructed in the KEKB tunnel. As shown in Fig.1, the tunnel is fourfold symmetric structure and its circumference is 3 km. The accelerator cavities are placed only in the straight sections. In the each straight section, beam energy reaches 1.2, 3.8, 6.4 and 9 GeV, respectively. From 1.2 GeV to 9 GeV, ILC type superconducting cavities with two kinds of geometrical beta (βg) are placed. The 2 straight is βg = 0.93, and the 3 to 4 straights are βg = 1.0. In this presentation, we introduce the present accelerator design under the term of construction in the KEKB tunnel.

A beam duct coated with NEG materials (Ti, Zr, V), which had been known to have a low secondary electron yield (SEY), was studied for the first time under intense photon irradiation using a positron beam at the KEK B-Factory (KEKB) to investigate a way to suppress the electron cloud instability (ECI). A 2.56 m test copper chamber was coated with the NEG materials (we call it NEG coating here) by magnetron sputtering. It was installed at an arc section of the KEKB positron ring, where the chamber was irradiated by direct photons with a line density of 6.5×10 14 photons m −1 s −1 mA −1 . The vacuum pressure around the test chamber during a usual beam operation was lower than the case of non-coated copper chambers by a factor of 4–5. The number of electrons around positron bunches was measured by a special electron monitor up to a stored beam current of 1600 mA. The measured electron current, however, was almost the same as a non-coated copper chamber, especially at low-beam currents, and the effect of the NEG coating was smaller than expected. A simulation explained the result that abundant photoelectrons in the positron ring reduce the effect of the low SEY. The maximum SEYs of the NEG coating and non-coated copper were evaluated using a simulation as about 0.9–1.0 and 1.1–1.3, respectively, which were consistent with the values after a sufficient electron bombardment. Their photoelectron yields were also estimated as 0.22–0.28 and 0.26–0.34, respectively, and were in good agreement with the previous experimental results. The study indicates that the suppression of photoelectrons, by a beam duct with an antechamber, for example, is indispensable to make effective use of a surface with a low SEY, such as the NEG coating.

A beam duct with an antechamber scheme for high-current accelerators was designed and the test chambers were studied experimentally. The duct consists of two channels, i.e., a beam channel where a beam circulates and a Synchrotron Radiation (SR) channel (antechamber) aside where the SR passes through. By using the antechamber scheme, the maximum power density of SR can be diluted at the side wall. The impedance is small owing to the pumping ports not being at the beam channel, but at the SR channel. Photoelectrons inside the beam channel are also expected to be reduced, which would be a big merit for a positron ring to suppress the electron cloud effect since the photoelectron is a major source of electrons composing the cloud. Two copper test chambers were manufactured with different methods, by pressing and by drawing. These chambers showed a good static vacuum property, i.e., gas desorption rates with less than 3.5 × 10 - 9 Pa m 3 s - 1 m - 2 after baking. After the installation to the positron ring of the KEK B-factory (KEKB), electron numbers in the beam channel, temperatures and pressures were measured during beam operation. The electrons in the beam channel were found to be reduced by a factor of 4 at 1.5 A compared to the case of the usual circular chamber. The reduction, however, was much larger, about 1/300, at a beam current of about 20 mA where the photoelectrons were dominant and the multiplication of electrons by the multipactoring was small. The temperatures were almost in agreement with the expectation. Vacuum scrubbing by photons proceeded almost smoothly, although pressure bursts were sometimes observed, especially for one test chamber, which was possibly due to discharges at the transverse joints in the beam chamber. Various instructive information had been obtained for future practical beam ducts for high-intensity accelerators.

An 8-GeV electron/3.5-GeV positron injector for KEKB was completed in 1998 by upgrading the existing 2.5-GeV electron/positron linac. The main goals were to upgrade its accelerating energy from 2.5 to 8 GeV and to increase the positron intensity by about 20 times. This article describes not only the composition and features of the upgraded linac, but also how these goals were achieved, by focusing on an optics design and commissioning issues concerning especially high-intensity single-bunch acceleration to produce positron beams.

KEKB has been operated since December, 1998, to deliver BB pairs for a physics detector. In this paper,we describe the commissioning procedure of KEKB.

The discovery by the ATLAS and CMS experiments of a new boson with mass around 125 GeV and with measured properties compatible with those of a Standard-Model Higgs boson, coupled with the absence of discoveries of phenomena beyond the Standard Model at the TeV scale, has triggered interest in ideas for future Higgs factories. A new circular e+e- collider hosted in a 80 to 100 km tunnel, TLEP, is among the most attractive solutions proposed so far. It has a clean experimental environment, produces high luminosity for top-quark, Higgs boson, W and Z studies, accommodates multiple detectors, and can reach energies up to the t-tbar threshold and beyond. It will enable measurements of the Higgs boson properties and of Electroweak Symmetry-Breaking (EWSB) parameters with unequalled precision, offering exploration of physics beyond the Standard Model in the multi-TeV range. Moreover, being the natural precursor of the VHE-LHC, a 100 TeV hadron machine in the same tunnel, it builds up a long-term vision for particle physics. Altogether, the combination of TLEP and the VHE-LHC offers, for a great cost effectiveness, the best precision and the best search reach of all options presently on the market. This paper presents a first appraisal of the salient features of the TLEP physics potential, to serve as a baseline for a more extensive design study., Comment: 43 pages, 18 figures, 11 tables, 85 references. Changes with respect to version V2: The comments from the JHEP referee are now included

A three-dimensional (3D) laser cooling method of fast stored ion beams based on a linear coupling mechanism is explored. We extensively study two approaches proposed in previous publications, i.e., the dispersive coupling scheme and the coupling-cavity scheme, confirming how much one can improve the transverse cooling efficiency. A possible design of a coupling cavity is presented. We employ the tracking code SAD and the molecular dynamics code SOLID to carry out reliable numerical experiments where realistic lattice structures of storage rings and particle Coulomb interactions are taken into account. Through systematic simulations, it is demonstrated that resonant coupling remarkably enhances transverse cooling rates for any initial beams, making it feasible to reach an equilibrium temperature far below the current achievable level. We further emphasize the crucial importance of avoiding the Mathieu instability. We also discuss the minimum cooling power required for beam crystallization as well as on an interpretation of past experimental results in the TSR and ASTRID storage rings.

The LHC experiments have discovered a new particle with a mass around 125 GeV that is a strong candidate for the scalar Higgs boson expected in the Standard Model. An e+e− collider operating close to the ZH threshold (at a centre-of-mass energy of 240 GeV) could be the tool of choice for studying this unique particle in detail. We present here the concept of a storage ring collider, which we call LEP3. Preliminary studies show that at a centre-of-mass energy of 240 GeV, near-constant luminosities of 1034 cm-2s-1 are possible in up to four collision points, while respecting a number of constraints including beamstrahlung limits. With an integrated luminosity of 100fb-1 per year and per interaction point, 20,000 e+e- - ZH events would be produced per year and per experiment. LEP3 could also operate in multi-bunch mode at the Z resonance, with luminosities of several×1035cm-2s-1, yielding O(1011) Z decays per year, as well as just above the WW threshold, potentially improving our knowledge of W and Z properties by large factors. The short luminosity lifetime requires the use of top-up injection, which, in turn calls for a full-energy injector. Thus the present design uses two rings (as in theBB factories): a low-emittance collider storage ring operating at a constant energy, and a separate “accelerator” ring that tops up the collider ring every few minutes. The LHeC lattice design has been used as a basis for our studies. Maximum luminosity is achieved with four bunches per beam. The estimated beam lifetime is about 8 minutes (for four simultaneous experiments) dominated by e+e− Bhabha interactions. Finally the synchrotron radiation losses are 50 MW per beam. Further optimization of the design is possible. LEP3 could be installed in the LHC tunnel, serving the two LHC general-purpose detectors ATLAS and CMS, and possibly up to two dedicated ILC-type detectors. Alternatively, it could be installed in a new, longer tunnel; using a tunnel circumference of 80km, a machine operating up to thett threshold can be conceived. This preliminary study has identified no show-stoppers for the concept of the design. A number of basic questions about LEP3 are discussed and we have tried to identify the areas where R&D will be needed. We consider the concept to be highly interesting and deserving of a detailed study.

During 2008 and 2009 dedicated beam experiments with crab cavities were performed in the KEKB. The goal was to measure the impact of crab-cavity radio frequency (rf ) noise on the beam quality. These experiments were performed as a validation of the crab-cavity beam dynamics models in view of the possible use of crab cavities in the upgrade of the CERN Large Hadron Collider (LHC). An unexpected strong beam-beam instability was observed during the course of the experiments as a kind of frequency response. Understanding this finding required extensive multiparticle and single particle simulations plus an extra experimental session to consolidate the observations. Published in PRST-AB 14:111003 (2011)

The results of calculations and simulations of the vertical emittance in the KEK Accelerator Test Facility damping ring are described. Both systematic and random alignment tolerances and a skew correction scheme are presented which limit the normalized vertical emittance to γϵ y −8 m rad. The effect of intrabeam scattering on the vertical emittance is calculated.

We have measured and corrected chromatic $X\mathrm{\text{\ensuremath{-}}}Y$ coupling at an interaction point to improve the luminosity of KEKB. We have measured the beam position of betatron oscillations induced by the kicker using turn-by-turn beam position monitors. A phase space structure reconstructed by the beam position provides us not only the Twiss parameters but also information regarding $X\mathrm{\text{\ensuremath{-}}}Y$ coupling. We have also determined chromatic $X\mathrm{\text{\ensuremath{-}}}Y$ coupling using the measured $X\mathrm{\text{\ensuremath{-}}}Y$ coupling at each momentum deviation from the designed beam energy. Skew sextupole magnets are used to correct the chromatic $X\mathrm{\text{\ensuremath{-}}}Y$ coupling.

Microwave instability in the low energy ring of KEKB was studied using a broadband impedance model. The model gave excellent descriptions of longitudinal dynamics for both positive and negative momentum compactions. Moreover, it predicted that the threshold of microwave instability was a factor of 2 lower than the machine nominal operating bunch current. The prediction was confirmed by a measurement using the Belle detector. Furthermore, we integrated the longitudinal wakefield into the beam-beam simulation and applied it to study the combined effects in KEKB. As a result, the beam-beam simulation became truly three dimensional with emittance growth in all three dimensions simultaneously as the beam currents increase. In addition, an observed mystery of asymmetry in the horizontal scan could also be explained by our simulations.

With the advent of the LHC, we will be able to probe New Physics (NP) up to energy scales almost one order of magnitude larger than it has been possible with present accelerator facilities. While direct detection of new particles will be the main avenue to establish the presence of NP at the LHC, indirect searches will provide precious complementary information, since most probably it will not be possible to measure the full spectrum of new particles and their couplings through direct production. In particular, precision measurements and computations in the realm of flavour physics are expected to play a key role in constraining the unknown parameters of the Lagrangian of any NP model emerging from direct searches at the LHC. The aim of Working Group 2 was twofold: on one hand, to provide a coherent, up-to-date picture of the status of flavour physics before the start of the LHC; on the other hand, to initiate activities on the path towards integrating information on NP from high-pT and flavour data., Comment: Report of Working Group 2 of the CERN Workshop ``Flavour in the era of the LHC'', Geneva, Switzerland, November 2005 -- March 2007

An orbit feedback system around the interaction point (IP) has been developed and successfully employed at KEKB for more than 6 years. The purpose of the system is to maintain an optimum geometrical relationship of orbits of two beams at the IP and to prevent a luminosity degradation due to orbit drifts. The feedback system is based on orbit measurements around the IP rather than a direct measurement of the luminosity. Owing to the system, the luminosity degradation due to the orbit drifts is suppressed to around or less than 1%.

In KEKB, synchrotron radiation interferometers (SRMs) are used for measuring the transverse beam sizes. There is also a tool for enlarging the vertical beam size intentionally by making an asymmetric bump, called an ``iSize'' bump, at one of the strongest non-interleaved sextupole magnets in each KEKB ring. The calibrations of the SRMs were checked by comparing the measured vertical beam sizes with those calculated using the computer code ``SAD''. The obtained correction factors are 1.000$\pm$0.045 for HER and 0.971$\pm$0.060 for LER, which are consistent with the calibration factors of SRMs\cite{SRMcalib} within errors. Using the obtained calibration factor, x-y coupling of each ring was calculated ., Comment: 3 pages, 4 figures, Particle Accelerator Conference 07, Albuquerque

J-PARC is a high intensity proton facility which is constructing as a joint project JAEA-KEK in Japan. J-PARC equips two proton ring accelerators, rapid cycle synchrotron (RCS) and Main Ring (MR). We discuss the space charge effect of MR in this paper. The proton beam with the population of 4.15 times 1013 times 8 bunches is accelerated from 3 GeV to 50 GeV and extracted with 0.3 Hz in MR. Beam loss during the acceleration is caused by an incoherent emittance growth due to the space charge force. We discuss the emittance growth and halo formation using a computer simulation based on the particle in cell method.

The present operational status of the Photon Factory storage ring (PF-ring) and the Photon Factory advanced ring (PF-AR) in KEK is reported. The scheduled user times of them were more than 4000 hours in FY2006. In the last summer shutdown, new undulators were installed in both of the rings and have been stably operated. A top-up operation in a single-bunch mode was demonstrated for six days in February 2007 druring the shutdown of KEKB at the PF-ring.