The Large Hadron electron Collider (LHeC) is designed to move the field of deep inelastic scattering (DIS) to the energy and intensity frontier of particle physics. Exploiting energy recovery technology, it collides a novel, intense electron beam with a proton or ion beam from the High Luminosity--Large Hadron Collider (HL-LHC). The accelerator and interaction region are designed for concurrent electron-proton and proton-proton operation. This report represents an update of the Conceptual Design Report (CDR) of the LHeC, published in 2012. It comprises new results on parton structure of the proton and heavier nuclei, QCD dynamics, electroweak and top-quark physics. It is shown how the LHeC will open a new chapter of nuclear particle physics in extending the accessible kinematic range in lepton-nucleus scattering by several orders of magnitude. Due to enhanced luminosity, large energy and the cleanliness of the hadronic final states, the LHeC has a strong Higgs physics programme and its own discovery potential for new physics. Building on the 2012 CDR, the report represents a detailed updated design of the energy recovery electron linac (ERL) including new lattice, magnet, superconducting radio frequency technology and further components. Challenges of energy recovery are described and the lower energy, high current, 3-turn ERL facility, PERLE at Orsay, is presented which uses the LHeC characteristics serving as a development facility for the design and operation of the LHeC. An updated detector design is presented corresponding to the acceptance, resolution and calibration goals which arise from the Higgs and parton density function physics programmes. The paper also presents novel results on the Future Circular Collider in electron-hadron mode, FCC-eh, which utilises the same ERL technology to further extend the reach of DIS to even higher centre-of-mass energies.

The CLIC damping rings aim at unprecedented small normalized equilibrium emittances of 3.3 nm vertical and 550 nm horizontal, for a bunch charge of 2.6·10 9 particles and an energy of 2.4 GeV. In this parameter regime the dominant emittance growth mechanism is intra-beam scattering. Intense synchrotron radiation damping from wigglers is required to counteract its effect. Here the overall optimization of the wiggler parameters is described, taking into account state-of-the-art wiggler technologies, wiggler effects on dynamic aperture, and problems of wiggler radiation absorption. Two technical solutions, one based on superconducting magnet technology the other on permanent magnets are presented. Although dynamic aperture and tolerances of this ring design remain challenging, benefits are obtained from the strong damping. For optimized wigglers, only bunches for a single machine pulse may need to be stored, making injection/extraction particularly simple and limiting the synchrotron-radiation power. With a 365 m circumference the ring remains comparatively small.