In response to the 2013 Update of the European Strategy for Particle Physics (EPPSU), the Future Circular Collider (FCC) study was launched as a world-wide international collaboration hosted by CERN. The FCC study covered an energy-frontier hadron collider (FCC-hh), a highest-luminosity high-energy lepton collider (FCC-ee), the corresponding 100km tunnel infrastructure, as well as the physics opportunities of these two colliders, and a high-energy LHC, based on FCC-hh technology. This document constitutes the third volume of the FCC Conceptual Design Report, devoted to the hadron collider FCC-hh. It summarizes the FCC-hh physics discovery opportunities, presents the FCC-hh accelerator design, performance reach, and staged operation plan, discusses the underlying technologies, the civil engineering and technical infrastructure, and also sketches a possible implementation. Combining ingredients from the Large Hadron Collider (LHC), the high-luminosity LHC upgrade and adding novel technologies and approaches, the FCC-hh design aims at significantly extending the energy frontier to 100TeV. Its unprecedented centre of-mass collision energy will make the FCC-hh a unique instrument to explore physics beyond the Standard Model, offering great direct sensitivity to new physics and discoveries.

We consider the numerical evolution of the Bloch equations of Derbenev and Kondratenko (DK) for the polarization density in high-energy electron storage rings, such as the proposed FCC-ee and CEPC. Equilibrium spin polarization is well characterized by the DK formulas for current rings (see [1] and [2]), but deviations may be important at the high energies we have in mind. We believe these Bloch equations, in three degrees of freedom (DOF), derived in [3] give a more complete description at all energies. The equations are a system of three coupled linear partial differential equations for the three components of the polarization density and include the spin flip polarization effect. Following [4] we formulate the equations in action-angle variables and approximate the Fokker-Planck terms. Our goal is to integrate these equations numerically in order to approximate the equilibrium and compare with the DK formulas. For 3 DOF the polarization density has 6+ 1 independent variables. For simplicity, suppose that each of the space-like variables has been discretized on a grid with N grid-points, then the computational cost of each time step will scale no better than O(N6). The presence of parabolic terms in the governing equations necessitates implicit time stepping and thus solutions of linear systems of equations. For a fully coupled problem this will bring the per time step cost to O(N6q), with 1 ≤ q ≤ 3, depending on the algorithms used for the linear solve. However, only algorithms with q ≈ 1 are feasible (for Gaussian elimination q = 3). Fortunately, as we outline below, the structure of the equations allow us to group the space-like variables into two groups resulting in a cost that, to leading order, scales as O(M N3q). In the next section we present the full and the reduced Bloch equations and the underlying physics. Then we discuss the details of the numerical algorithm outlined above and the issue of complexity in higher dimensions. Finally we present two numerical results showing a depolarization calculation in 1DOF and spectral convergence in a 2DOF example.

The design of an electron polarization scheme in the Jefferson Lab Electron-Ion Collider (JLEIC) aims to attain a high longitudinal electron polarization (over 70%) at collision points as required by the nuclear physics program. Comprehensive strategies for achieving this goal have been considered and developed including injection of highly polarized electrons from CEBAF, mechanisms for manipulation and preservation of the polarization in the JLEIC collider ring and measurement of the electron polarization. In particular, maintaining a sufficiently long polarization lifetime is crucial for accumulation of adequate experimental statistics. The chosen electron polarization configuration, based on the unique figure-8 geometry of the ring, removes the electron spin-tune energy dependence. This significantly simplifies the control of the electron polarization and suppresses the synchrotron sideband resonances. This paper reports recent studies and simulations of the electron polarization dynamics in the JLEIC electron collider ring.

We give an informal summary of ongoing work which uses tools distilled from the theory of fibre bundles to classify and connect invariant fields associated with spin motion in storage rings. We mention four major theorems. One ties invariant fields with the notion of normal form, the second allows comparison of different invariant fields and the two others tie the existence of invariant fields to the existence of certain invariant sets. We explain how the theorems apply to the spin dynamics of spin-1/2 and spin-1 particles. Our approach elegantly unifies the spin-vector dynamics from the T-BMT equation with the spin-tensor dynamics and other dynamics and suggests an avenue for addressing the question of the existence of the invariant spin field.

I extend and update earlier work, summarised in [1], whereby the invariant polarisation-tensor field (ITF) for deuterons in storage rings was introduced to complement the invariant spin field (ISF). Taken together, the ITF and the ISF provide a definition of the equilibrium spin density-matrix field which, in turn, offers a clean framework for describing equilibrium spin-1 ensembles in storage rings. I show how to construct the ITF by stroboscopic averaging, I give examples, I discuss adiabatic invariance and I introduce a formalism for describing the effect of noise and damping.

This is an addendum to the paper "Some models of spin coherence and decoherence in storage rings" by one of the authors [1] in which spin diffusion in simple electron storage rings is studied. In particular, we illustrate in a compact way, a key implication in the Epilogue of [1], namely that the exact formalism of [1] delivers a rate of depolarisation which can differ from that obtained by the conventional treatments of spin diffusion which rely on the use of the derivative ∂n̂/∂η [2,3,4]. As a vehicle we consider a ring with a Siberian Snake and electron polarisation in the plane of the ring (Machine II in [1]). For this simple setup with its one-dimensional spin motion, we avoid having to deal directly with the Bloch equation [5,6] for the polarisation density. Our treatment, which is deliberately pedagogical, shows that the use of ∂n̂/∂η provides a very good approximation to the rate of spin depolarisation in the model considered. But it then shows that the exact rate of depolarisation can be obtained by replacing ∂n̂/∂η by another derivative as suggested in the Epilogue of [1], while giving a heuristic justification for the new derivative.

Researchers have envisioned an electron-ion collider with ion species up to heavy ions, high polarization of electrons and light ions, and a well-matched center-of-mass energy range as an ideal gluon microscope to explore new frontiers of nuclear science. In its most recent Long Range Plan, the Nuclear Science Advisory Committee (NSAC) of the US Department of Energy and the National Science Foundation endorsed such a collider in the form of a 'half-recommendation.' As a response to this science need, Jefferson Lab and its user community have been engaged in feasibility studies of a medium energy polarized electron-ion collider (MEIC), cost-effectively utilizing Jefferson Lab's already existing Continuous Electron Beam Accelerator Facility (CEBAF). In close collaboration, this community of nuclear physicists and accelerator scientists has rigorously explored the science case and design concept for this envisioned grand instrument of science. An electron-ion collider embodies the vision of reaching the next frontier in Quantum Chromodynamics - understanding the behavior of hadrons as complex bound states of quarks and gluons. Whereas the 12 GeV Upgrade of CEBAF will map the valence-quark components of the nucleon and nuclear wave functions in detail, an electron-ion collider will determine the largely unknown role sea quarks play andmore » for the first time study the glue that binds all atomic nuclei. The MEIC will allow nuclear scientists to map the spin and spatial structure of quarks and gluons in nucleons, to discover the collective effects of gluons in nuclei, and to understand the emergence of hadrons from quarks and gluons. The proposed electron-ion collider at Jefferson Lab will collide a highly polarized electron beam originating from the CEBAF recirculating superconducting radiofrequency (SRF) linear accelerator (linac) with highly polarized light-ion beams or unpolarized light- to heavy-ion beams from a new ion accelerator and storage complex. Since the very beginning, the design studies at Jefferson Lab have focused on achieving high collider performance, particularly ultrahigh luminosities up to 10{sup 34} cm{sup -2}s{sup -1} per detector with large acceptance, while maintaining high polarization for both the electron and light-ion beams. These are the two key performance requirements of a future electron-ion collider facility as articulated by the NSAC Long Range Plan. In MEIC, a new ion complex is designed specifically to deliver ion beams that match the high bunch repetition and highly polarized electron beam from CEBAF. During the last two years, both development of the science case and optimization of the machine design point toward a medium-energy electron-ion collider as the topmost goal for Jefferson Lab. The MEIC, with relatively compact collider rings, can deliver a luminosity above 10{sup 34} cm{sup -2}s{sup -1} at a center-of-mass energy up to 65 GeV. It offers an electron energy up to 11 GeV, a proton energy up to 100 GeV, and corresponding energies per nucleon for heavy ions with the same magnetic rigidity. This design choice balances the scope of the science program, collider capabilities, accelerator technology innovation, and total project cost. An energy upgrade could be implemented in the future by adding two large collider rings housed in another large tunnel to push the center-of-mass energy up to or exceeding 140 GeV. After careful consideration of an alternative electron energy recovery linac on ion storage ring approach, a ring-ring collider scenario at high bunch repetition frequency was found to offer fully competitive performance while eliminating the uncertainties of challenging RD the third is for low energy ion beams stored in a dedicated low-energy compact storage ring, as a possible follow-on project.« less

The physics programme and the design are described of a new collider for particle and nuclear physics, the Large Hadron Electron Collider (LHeC), in which a newly built electron beam of 60 GeV, to possibly 140 GeV, energy collides with the intense hadron beams of the LHC. Compared to the first ep collider, HERA, the kinematic range covered is extended by a factor of twenty in the negative four-momentum squared, Q2 , and in the inverse Bjorken x, while with the design luminosity of 1033 cm-2 s-1 the LHeC is projected to exceed the integrated HERA luminosity by two orders of magnitude. The physics programme is devoted to an exploration of the energy frontier, complementing the LHC and its discovery potential for physics beyond the Standard Model with high precision deep inelastic scattering measurements. These are designed to investigate a variety of fundamental questions in strong and electroweak interactions. The LHeC thus continues the path of deep inelastic scattering (DIS) into unknown areas of physics and kinematics. The physics programme also includes electron-deuteron and electron-ion scattering in a (Q 21/x) range extended by four orders of magnitude as compared to previous lepton-nucleus DIS experiments for novel investigations of neutron's and nuclear structure, the initial conditions of Quark-Gluon Plasma formation and further quantum chromodynamic phenomena. The LHeC may be realised either as a ring-ring or as a linac-ring collider. Optics and beam dynamics studies are presented for both versions, along with technical design considerations on the interaction region, magnets including new dipole prototypes, cryogenics, RF, and further components. A design study is also presented of a detector suitable to perform high precision DIS measurements in a wide range of acceptance using state-of-the art detector technology, which is modular and of limited size enabling its fast installation. The detector includes tagging devices for electron, photon, proton and neutron detection near to the beam pipe. Civil engineering and installation studies are presented for the accelerator and the detector. The LHeC can be built within a decade and thus be operated while the LHC runs in its high-luminosity phase. It so represents a major opportunity for progress in particle physics exploiting the investment made in the LHC.

SuperB, the 2nd-generation B-Factory with a luminosity of 10{sup 36}/cm{sup 2}/s proposed for LNF, is being designed from the start to be capable of providing a spin-polarized electron beam in the low-energy ring (LER) with longitudinal polarization at the interaction point. Due to the high luminosity at moderate beam current the beam lifetime is short (a few minutes), and a polarized injector will be used. Spin rotators have been designed and the equilibrium polarization evaluated. It will be shown that an average polarization of about 70% can be expected.

This paper will report the recent progress in the conceptual design of MEIC, a high luminosity medium energy polarized ring-ring electron-ion collider at Jefferson lab. The topics and achievements that will be covered are design of the ion large booster and the ERL-circulator-ring-based electron cooling facility, optimization of chromatic corrections and dynamic aperture studies, schemes and tracking simulations of lepton and ion polarization in the figure-8 collider ring, and the beam-beam and electron cooling simulations. A proposal of a test facility for the MEIC electron cooler will also be discussed.

This report presents a brief summary of the science opportunities and program of a polarized medium energy electron-ion collider at Jefferson Lab and a comprehensive description of the conceptual design of such a collider based on the CEBAF electron accelerator facility.

The present note relies on the recently published conceptual design report of the LHeC and extends the first contribution to the European strategy debate in emphasising the role of the LHeC to complement and complete the high luminosity LHC programme. The brief discussion therefore focuses on the importance of high precision PDF and alpha_s determinations for the physics beyond the Standard Model (GUTs, SUSY, Higgs). Emphasis is also given to the importance of high parton density phenomena in nuclei and their relevance to the heavy ion physics programme at the LHC.

A proposal to add 60-GeV electron and positron beams to the LHC at CERN (LHeC) is currently being prepared. The provision of electron and positron longitudinal polarisation is an important component of the proposal and we are examining the feasibility of Sokolov-Ternov self-polarisation at energies up to 60 GeV in a storage ring in the LHC tunnel. But at this energy the attainable polarisation can be very strongly limited by depolarising effects. This paper summarises first calculations of the attainable polarisation including estimates of the efficacy of Siberian Snakes for weakening synchrotron sideband resonances

The joint IPPP Durham/Cockcroft Institute/ICFA workshop on advanced QED methods for future accelerators took place at the Cockcroft Institute in early March 2009. The motivation for the workshop was the need for a detailed consideration of the physics processes associated with beam–beam effects at the interaction points of future high-energy electron-positron colliders.

We complement the concept of the invariant spin field (ISF) in storage rings by defining the invariant polarisation‐tensor field (ITF) for spin‐1 particles and we suggest how to calculate it by stroboscopic averaging or directly from the invariant spin field. The ITF the ISF are used to construct equilibrium spin density‐matrix fields, and thereby offer a clean framework for describing equilibrium ensembles of spin‐1 particles such as deuterons in storage rings.

The clean environment of a lepton linear collider allows high-precision measurements for physics analyses. In or- der to exploit this potential, precise knowledge about the polarization state of the beams is also required. In this pa- per we concentrate on depolarization effects caused by the intense beam-beam interaction, which is expected to be the dominant source of depolarization. Higher-ordereffects, as well as critical analyses of the theoretical assumptions used in the past and theoretical improvements in the derivation of suitable equations, are given. Updates on existing sim- ulation programs are reported. Numerical results for the design of the International Linear Collider (ILC) are dis- cussed.

A short overview is given about the potential of polarized beams at future colliders is given. In particular the baseline design for polarized beams at the ILC is presented and the physics case for polarized e− and e+ is discussed. In order to fulfil the precision requirements spin tracking from the source to the interaction point is needed. Updates concerning the theoretical calculations as well as their implementation in simulation codes are reported.