The secondary emission of electrons and their interaction with the electromagnetic fields of charged particle beams can lead to the build-up of electron clouds in accelerator beam chambers. The interaction of the electrons with both the beam and the chamber walls leads to detrimental effects, such as transverse instabilities and emittance growth, beam loss, pressure rise and heat load. Such effects are systematically observed in the Large Hadron Collider (LHC) during operation with proton beams with the nominal bunch spacing of 25 ns. Furthermore, the severity of electron cloud effects has increased after each long shutdown period of the machine, due to a degradation of the beam screen surfaces with air-exposure. Consequently, electron cloud is already limiting the total intensity in the collider and is one of the main concerns for the performance of the HL-LHC upgrade. In this contribution, the present understanding of electron cloud in hadron accelerators is reviewed. Measurements and observations at the LHC are presented, the impact on performance is evaluated and mitigation measures are discussed along with lessons for future machines.

In autumn 2023, the FCC Feasibility Study underwent a crucial “mid-term review”. We describe some accelerator performance risks for the proposed future circular electron- positron collider, FCC-ee, identified for, and during, the mid-term review. For the collider rings, these are the collective effects when running on the Z resonance – especially resistive wall, beam-beam, and electron cloud –, the beam lifetime, dynamic aperture, alignment tolerances, and beam-based alignment. For the booster, the primary concern is the vacuum system, with regard to impedance and effects of the residual gas. For the injector, the layout and the linac repetition rate are primary considerations. We discuss the various issues and report the planned mitigations.

Xsuite is a modular simulation package bringing to a single flexible and modern framework capabilities of different tools developed at CERN in the past decades notably MAD-X Sixtrack Sixtracklib COMBI and PyHEADTAIL. The suite consists of a set of Python modules (Xobjects, Xpart, Xtrack, Xcoll, Xfields, Xdeps) that can be flexibly combined together and with other accelerator-specific and general-purpose python tools to study complex simulation scenarios. Different computing platforms are supported including conventional CPUs as well as GPUs from different vendors. The code allows for symplectic modeling of the particle dynamics combined with the effect of synchrotron radiation impedances feedbacks space charge electron cloud beam-beam beamstrahlung and electron lenses. For collimation studies beam-matter interaction is simulated using the K2 scattering model or interfacing Xsuite with the BDSIM/Geant4 library and with the FLUKA code. Methods are made available to compute and optimize the accelerator lattice functions, chromatic properties and equilibrium beam sizes. By now the tool has reached a mature stage of development and is used for simulations studies by a large and diverse user community.

During Run 2 and Run 3 of the Large Hadron Collider (LHC), slow losses from electron cloud (e-cloud) effects have been systematically observed during the full duration of fills with closely-spaced proton bunches. In particular, these effects had been found to depend strongly on the crossing angle of the two beams and the value of the betatron functions in the interaction points. Due to this observation, the main cause of this effect was attributed to the non-linear forces induced by electron clouds forming in the vacuum chamber of the LHC Inner Triplet quadrupole magnets. In this contribution, electron cloud buildup simulations reveal that the induced forces depend strongly on the transverse coordinates of the beam particles, on time, as well as on the longitudinal coordinate within the Inner Triplet. Finally, non-linear maps are generated based on the buildup simulations, and the effect of these forces on the motion of the protons is simulated.