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The Linear Collider Facility (LCF) at CERN

In this paper we outline a proposal for a Linear Collider Facility as the next flagship project for CERN. It offers the opportunity for a timely, cost-effective and staged construction of a new collider that will be able to comprehensively map the Higgs boson's properties, including the Higgs field potential, thanks to a large span in centre-of-mass energies and polarised beams. A comprehensive programme to study the Higgs boson and its closest relatives with high precision requires data at centre-of-mass energies from the Z pole to at least 1 TeV. It should include measurements of the Higgs boson in both major production mechanisms, ee -> ZH and ee -> vvH, precision measurements of gauge boson interactions as well as of the W boson, Higgs boson and top-quark masses, measurement of the top-quark Yukawa coupling through ee ->ttH, measurement of the Higgs boson self-coupling through HH production, and precision measurements of the electroweak couplings of the top quark. In addition, ee collisions offer discovery potential for new particles complementary to HL-LHC.

43 PARTICLE ACCELERATORS↗

ESPPU INPUT: C$^3$ within the "Linear Collider Vision"

The Linear Collider Vision calls for a Linear Collider Facility with a physics reach from a Higgs Factory to the TeV-scale with $e^+e^{-}$ collisions. One of the technologies under consideration for the accelerator is a cold-copper distributed-coupling linac capable of achieving high gradient. This technology is being pursued by the C$^3$ collaboration to understand its applicability to future colliders and broader scientific applications. In this input we share the baseline parameters for a C$^3$ Higgs-factory and the energy reach of up to 3 TeV in the 33 km tunnel foreseen under the Linear Collider Vision. Recent results, near-term plans and future R&D needs are highlighted.

43 PARTICLE ACCELERATORS↗

The science case for an intermediate energy advanced and novel accelerator linear collider facility

It is widely accepted that the next lepton collider beyond a Higgs factory would require center-of-mass energy of the order of up to 15 TeV. Since, given reasonable space and cost restrictions, conventional accelerator technology reaches its limits near this energy, high-gradient advanced acceleration concepts are attractive. Advanced and novel accelerators (ANAs) are leading candidates due to their ability to produce acceleration gradients on the order of 1–100 GV/m, leading to compact acceleration facilities. However, intermediate energy facilities (IEF) are required to test the critical technology elements on the way towards multi-TeV-class colliders. Here a science case for a 20–100 GeV center-of-mass energy ANA-based lepton collider that can be a candidate for an intermediate energy facility is presented. The IEF can provide numerous opportunities for high energy physics studies including precision Quantum Chromodynamics and Beyond the Standard Model physics measurements, investigation of charged particle interactions with extreme electromagnetic fields, and exploring muon and proton beam acceleration. Possible applications of this collider include the studies of γγ and electron beam-fixed target/beamdump collider designs. Thus, the goal of the proposed IEF is to both carry out particle physics measurements in the 20-100 GeV ranges as well as to serve as an ANA demonstrator facility.

43 PARTICLE ACCELERATORS↗

Development work for a superconducting linear collider

For future linear e(+)e(-) colliders in the TeV range several alternatives are under discussion. The TESLA approach is based on the advantages of superconductivity. High Q values of the accelerator structures give high efficiency for converting RF power into beam power. A low resonance frequency for the RF structures can be chosen to obtain a large number of electrons (positrons) per bunch. For a given luminosity the beam dimensions can be chosen conservatively which leads to relaxed beam emittance and tolerances at the final focus. Each individual superconducting accelerator component (resonator cavity) of this linear collider has to deliver an energy gain of 25 MeV/m to the beam. Today s.c. resonators are in use at CEBAF/USA, at DESY/Germany, Darmstadt/Germany KEK/Japan and CERN/Geneva. They show acceleration gradients between 5 MV/m and 10 MV/m. Encouraging experiments at CEA Saclay and Cornell University showed acceleration gradients of 20 MV/m and 25 MV/m in single and multicell structures. In an activity centered at DESY in Hamburg/Germany the TESLA collaboration is constructing a 500 MeV superconducting accelerator test facility (TTF) to demonstrate that a linear collider based on this technique can be built in a cost effective manner and that the necessary acceleration gradients of more than 15 MeV/m can be reached reproducibly. The test facility built at DESY covers an area of 3.000 m2 and is divided into 3 major activity areas: (1) The testlinac, where the performance ofthe modular components with an electron beam passing the 40 m long acceleration section can be demonstrated. (2) The test area, where all individual resonators are tested before installation into a module. (3) The preparation and assembly area, where assembly of cavities and modules take place. We report here on the design work to reach a reduction of costs compared to actual existing superconducting accelerator structures and on the facility set up to reach high acceleration gradients in a reproducible way.

Matheisen, Axel↗

Simulation Studies of Intra-Train, Bunch-by-Bunch Feedback Systems at the International Linear Collider

The International Linear Collider (ILC) is a proposed electron-positron collider targeting collision energies from 250 GeV to 1 TeV. With design luminosities of order 10³⁴ cm²s⁻¹, a beam-based, intra-train feedback system would be required near the Interaction Point (IP) to provide nanometre-level stabilisation of the beam overlap in the collisions. Here we present results from beam-tracking simulations of the 500 GeV ILC, including the impact of beam-trajectory imperfections on the luminosity, and the capability of the IP feedback system to compensate for them. Effects investigated include the position jitter introduced by the damping ring extraction kicker, short-range and long-range wakefields, and ground motion. The feedback system was shown to be able to correct for beam-beam offsets of up to 200 nm and stabilise the collision overlap to the nanometre level, within a few bunch crossings.

Ramjiawan, R. L.↗

Summary of Working Group 7: Linear colliders

The contributions presented during the Working Group 7: Linear Colliders (WG7) sessions at the 2024 Advanced Accelerator Concepts Workshop are briefly summarized, as well as the discussions regarding a design initiative for a linear collider based on wakefield accelerator technology.

Advanced Accelerator Concepts↗

Damping-Ring-Free Injector Design for Linear Colliders

The current designs of future electron-positron linear colliders incorporate large and complex damping rings to produce asymmetric beams for beamstrahlung mitigation at the interaction point. This paper presents the design of an damping-ring-free electron injector capable of delivering flat electron beams with phase-space partition comparable to the electron-beam parameters produced downstream of the damping ring in the proposed international linear collider (ILC) design. The performance of the proposed configuration, its sensitivity to jitter along with its impact on spin-polarization is discussed.

43 PARTICLE ACCELERATORS↗

Status of the International Linear Collider

This paper is not a proposal for a CERN future project but provides information on the International Linear Collider (ILC) considered for Japan in order to facilitate the European Strategy discussion in a global context. It describes progress to date, ongoing engineering studies, updated cost estimate for the machine at $\sqrt{s}=250~\rm GeV$ and the situation in Japan. The physics of the ILC is not presented here, but jointly for all Linear Collider projects in a separate document ``A Linear Collider Vision for the Future of Particle Physics'' submitted for the forthcoming European Strategy deliberations.

Abe, Y. [KEK, Tsukuba]↗

Statement from the American Linear Collider Committee to the P5 subpanel

This statement from the American Linear Collider Committee to the P5 subpanel has three purposes. It presents a brief summary of the case for an $e^+e^-$ Higgs factory that has emerged from Snowmass 2021. It highlights the special virtues of the ILC that are shared with other linear colliders but not with circular colliders. Finally, it calls attention to the resources available in the ILC White Paper for Snowmass (arXiv:2203.07622). The ALCC urges P5 to move the Higgs factory forward as a global project by assigning the idea of an $e^+e^-$ Higgs factory high priority, initiating a global discussion of the technology choice and cost sharing, and offering the option of siting the Higgs factory in the U.S.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Beam delivery and beamstrahlung considerations for ultra-high energy linear colliders

As part of the Snowmass'21 community planning excercise, the Advanced Accelerator Concepts (AAC) community proposed future linear colliders with center-of-mass energies up to 15 TeV and luminosities up to 50 × 1034 cm -2 s -1 in a compact footprint. In addition to being compact, these machines must also be energy efficient. We identify two challenges that must be addressed in the design of these machines. First, the Beam Delivery System (BDS) must not add significant length to the accelerator complex. Second, beam parameters must be chosen to mitigate beamstrahlung effects and maximize the luminosity-per-power of the machine. In this paper, we review advances in plasma lens technology that will help to reduce the length of the BDS system, and we detail new Particle-in-Cell simulation studies that will provide insight into beamstrahlung mitigation techniques. We apply our analysis to both $e$ + $e$ - and $γγ$ colliders. The challenges and solutions described in this paper are considered independently. In conclusion, a unified, self-consistent concept for a BDS system for a 15 TeV linear collider will be the subject of future work.

47 OTHER INSTRUMENTATION↗

Linear colliders based on laser-plasma accelerators

Laser-plasma accelerators are capable of sustaining accelerating fields of 10–100 GeV/m, 100–1000 times that of conventional technology and the highest fields produced by any of the widely researched advanced accelerator concepts. Laser-plasma accelerators also intrinsically accelerate short particle bunches, several orders of magnitude shorter than that of conventional technology, which leads to reductions in beamstrahlung and, hence, savings in the overall power consumption to reach a desired luminosity. These properties make laser-plasma accelerators a promising accelerator technology for a more compact, less expensive high-energy linear collider providing multi-TeV polarized leptons. In this submission to the Snowmass 2021 Accelerator Frontier, we discuss the motivation for a laser-plasma-accelerator-based linear collider, the status of the field, and potential linear collider concepts up to 15 TeV. Herein, we outline the research and development path toward a collider based on laser-plasma accelerator technology, and highlight near-term and mid-term applications of this technology on the collider development path. The required experimental facilities to carry out this research are described. We conclude with community recommendations developed during Snowmass.

43 PARTICLE ACCELERATORS↗

A linear collider vision for the future of particle physics

In this paper we review the physics opportunities at linear e + e - colliders with a special focus on high centre-of-mass energies and beam polarisation, take a fresh look at the various accelerator technologies available or under development and, for the first time, discuss how a facility first equipped with a technology that is mature today could be upgraded with technologies of tomorrow to reach much higher energies and/or luminosities. In addition, we discuss detectors, alternative collider modes, as well as opportunities for beyond-collider experiments and R&D facilities as part of a linear collider facility (LCF). The material of this paper supports all plans for e + e - linear colliders and the additional opportunities they offer, independently of technology choice or proposed site, as well as R&D for advanced accelerator technologies. This joint perspective on the physics goals, early technologies and upgrade strategies has been developed by the LCVision team based on an initial discussion at LCWS2024 in Tokyo and a follow-up at the LCVision Community Event at CERN in January 2025. It heavily builds on decades of achievements of the global linear collider community, in particular in the context of CLIC and ILC.

43 PARTICLE ACCELERATORS↗

The positron arm of a plasma-based linear collider

Plasma-based acceleration of electrons has produced high-energy beams at high accelerating gradients with a narrow energy spread and high efficiency both in experiments and simulations. Furthermore, it is now being considered as a complementary approach to the use of radiofrequency cavities in next-generation lepton accelerators. However, compared with electrons, plasma-based positron acceleration is at the present time much less advanced. Although high-gradient positron acceleration in a plasma has been achieved, we are one to three orders of magnitude away from delivering the high-quality positron beams needed for a future high-energy linear collider. Here we review the status of plasma-based acceleration of electrons and positrons and discuss the prospects for substantial progress towards developing the positron arm of a plasma-based electron–positron linear collider in the next decade.

Plasma-based accelerators↗

Superconducting radio frequency linear collider HELEN

This article discusses a proposed Higgs-Energy LEptoN (HELEN) $e^+e^-$ linear collider based on advanced traveling wave superconducting radio frequency technology. Here, the proposed collider offers cost and AC power savings, smaller footprint (relative to the ILC), and could be built at Fermilab. After the initial physics run at 250 GeV, the collider could be upgraded either to higher luminosity or to higher, up to 500 GeV, energies.

43 PARTICLE ACCELERATORS↗

Beam delivery and final focus systems for multi-TeV advanced linear colliders

The Beam Delivery System (BDS) is a critical component of a high-energy linear collider. It transports the beam from the accelerator and brings it to a focus at the Interaction Point. The BDS system includes diagnostic sections for measuring the beam energy, emittance, and polarization, as well as collimators for machine protection. The length of the BDS increases with collision energy. Higher collision energies also require higher luminosities, and this is a significant constraint on the design for energy-frontier machines. Here, we review BDS designs based on traditional quadrupole magnets and examine the challenges involved in extending these to the Multi-TeV regime consistent with requirements for advanced accelerator concepts.

43 PARTICLE ACCELERATORS↗

HELEN: A Linear Collider Based On Advanced SRF Technology

This paper discusses recently proposed Higgs Energy LEptoN (HELEN) $e+e-$ linear collider based on advances in superconducting radio frequency technology. The collider offers cost and AC power savings, smaller footprint (relative to the ILC), and could be built at Fermilab with an interaction region within the site boundaries. After the initial physics run at 250 GeV, the collider could be upgraded either to higher luminosity or to higher (up to 500 GeV) energies.

43 PARTICLE ACCELERATORS↗

Beam dynamics challenges in linear colliders based on laser-plasma accelerators

In this paper we discuss design considerations and beam dynamics challenges associated with laser-driven plasma-based accelerators as applied to multi-TeV-scale linear colliders. Plasma accelerators provide ultra-high gradients and ultra-short bunches, offering the potential for compact linacs and reduced power requirements. We show that stable, efficient acceleration with beam quality preservation is possible in the nonlinear bubble regime of laser-plasma accelerators using beam shaping. Ion motion, naturally occuring for dense beams (i.e., low emittance and high energy) severely damps transverse beam instabilities. Coulomb scattering by the background ions is considered and it is shown that the strong focusing in the plasma strongly suppresses scattering-induced emittance growth. Finally, Betatron radiation emission from the transverse motion of the beam in the plasma will result in beam power loss and energy spread growth; however for sub-100 nm emittances, the beam power loss and energy spread growth will be sub-percent for multi-TeV-class plasma linacs.

47 OTHER INSTRUMENTATION↗

Fully plasma-based electron injector for a linear collider or XFEL

We demonstrate through high-fidelity particle-in-cell (PIC) simulations a simple approach for efficiently generating 20 + GeV electron beams with the necessary charge, energy spread, and emittance for use as an injector in a future linear collider or a next generation XFEL. A high quality injected bunch is generated by self-focusing an unmatched electron driver in a nonlinear plasma wakefield. Over pump depletion distances, the drive beam dynamics and self-loading effects lead to high energy, low-energy spread output beams. For plasma densities of 10 18 c⁢m −3 , PIC simulation results indicate that self-injected beams with 0.52 n⁢C charge can be accelerated to 20 GeV with projected core energy spreads of ≲ 1%, normalized slice emittances of 110n⁢m, peak normalized brightness of ≳ 10 19 A/m 2 /rad 2 , and transfer efficiencies of ≳ 44%.

Particle acceleration in plasmas↗