The Future Circular Collider (FCC) study aims at designing different options of a post-LHC collider. The high luminosity electron-positron collider FCC-ee based on the crab waist concept is considered as an intermediate step on the way towards FCC-hh, a 100 TeV hadron collider using the same tunnel of about 100 km. Due to a high intensity of circulating beams the impact of collective effects on FCC-ee performance has to be carefully analyzed. In this paper we evaluate beam coupling impedance of the FCC-ee vacuum chamber, estimate thresholds and rise times of eventual single- and multibunch beam instabilities and discuss possible measures to mitigate them.

The ALS-U upgrade promises to deliver diffraction limited performance throughout the soft x-ray range by lowering the horizontal emittance to about 50 pm resulting in 2-3 orders of brightness increase for soft x-rays compared to the current ALS. The design utilizes a multi bend achromat lattice with on-axis swap-out injection and an accumulator ring. One central design goal is to install and commission ALS-U within a short dark period. This paper summarizes the status of the conceptual design of the accelerator, as well as some results of the R&D program that has been ongoing for the last 3 years.

In the framework of the Future Circular Collider (FCC) design studies at CERN [1], the high luminosity electron-positron collider FCC-ee is considered as a possible first step towards FCC-hh, a 100 TeV hadron collider in the same tunnel of about 100 km. Table 1 summarizes the main beam parameters at four different center-of-mass energies from 45.6 GeV (Z pole) to 175 GeV (top pair threshold). One of the major issues for such a kind of machine is represented by collective effects due to electromagnetic fields generated by the interaction of the beam with the vacuum chamber, which could produce instabilities, thus limiting the machine operation and performance. An impedance model is needed to study these instabilities, to predict their effects on the beam dynamics and to find a possible solution for their mitigation. Another critical aspect for the future lepton collider is represented by the electron cloud which will be discussed in the last section of this contribution, together with possible strategies to suppress its effects.

The Future Circular Collider study, hosted by CERN to design post-LHC particle accelerator options in a worldwide context, is focused on proton-proton high-energy and electron-positron high-luminosity frontier machines. This new accelerator complex represents a great challenge under several aspects, which involve R&D on beam dynamics and new technologies. One very critical point in this context is represented by collective effects, generated by the interaction of the beam with self-induced electromagnetic fields, called wake fields, which could produce beam instabilities, thus reducing the machines performance and limiting the maximum stored current. It is therefore very important to be able to predict these effects and to study in detail potential solutions to counteract them. In this paper the resistive wall and some other important geometrical sources of impedance for the FCC electron-positron accelera- tor are identified and evaluated, and their impact on the beam dynamics, which in some cases could lead to unwanted instabilities, is discussed.

Instabilities driven by the transverse impedance are proven to be one of the limitations for the high intensity reach of the CERN PS. Since several years, fast single bunch vertical instability at transition energy has been observed with the high intensity bunch serving the neutron Time-of-Flight facility (n-ToF). In order to better understand the instability mechanism, a dedicated measurement campaign took place. The results were compared with macro-particle simulations with PyHEADTAIL based on the new impedance model developed for the PS. Instability threshold and growth rate for different longitudinal emittances and beam intensities were studied.

The current knowledge of the transverse beam coupling impedance of the CERN Proton Synchrotron (PS) has been established with beam-based measurements at different energies. The transverse coherent tune shift as a function of the beam intensity has been measured in order to evaluate the total effective imaginary part of the transverse impedance in the accelerator at the energies of 7, 13 and 25 GeV. Measurements have been performed changing the vertical chromaticity for each vertical tune scan with intensity. The data analysis revealed an increase of impedance with chromaticity for all the considered energies. The transverse impedance can be compared with the previously evaluated theoretical impedance budget taking into account the individual contribution of several machine devices.

The current knowledge of the transverse impedance of the CERN Proton Synchrotron (PS) has been established by theoretical computations, electromagnetic simulations and beam-based measurements at different energies. The transverse coherent tune and phase advance shifts as a function of intensity have been measured in order to evaluate the total effective transverse impedance and its distribution in the accelerator. In order to understand the beam dynamics, the frequency dependence of the impedance budget has also been evaluated considering the individual contribution of several machine devices. 3D models of many PS elements have been realized to perform accurate impedance simulations, while resistive wall and indirect space charge impedances have been evaluated with theoretical and numerical computations. Finally comparisons between the total budget and the measurement results are presented.

The impedance of the Finemet® loaded longitudinal damper cavity, installed in the CERN Proton Synchrotron straight section 02 during the Long Shutdown 2013-2014, has been evaluated [1]. Time domain simulations with CST Particle Studio have been performed in order to get the longitudinal and transverse impedance of the device and make a comparison with the longitudinal impedance that was measured for a single cell prototype.

A protection septum has been installed in the CERN PS section 15 in order to mitigate irradiation of the magnetic septum 16 for fast extractions towards the SPS. Impedance studies have been performed, showing that beams circulating in the septum during extraction generate sharp resonances in the coupling impedance. Impedance measurements with the wire technique have been performed, showing a good agreement with simulations. Instability rise times of trapped modes have been evaluated and compared to extraction duration. Solutions for reducing the impact on the stability of the beam have been considered.

Since June 2011, the rapid increase of the luminosity performance of the LHC has come at the expense of increased temperature and pressure readings on specific near-beam LHC equipment. In some cases, this beam induced heating has caused delays whilie equipment cools down, beam dumps and even degradation of these devices. This contribution gathers the observations of beam induced heating attributable to beam coupling impedance, their current level of understanding and possible actions that are planned to be implemented during the long shutdown in 2013-2014.

Summary The CERN Proton Synchrotron (PS) produces beams well beyond its original parameters and especially the high-brightness beams delivered to the Large Hadron Collider are close to present stability limitations. Within the framework of the LHC Injectors Upgrade project, a signicant increase in beam intensity is planned. With this background, collective eects triggered by the self-induced electromagnetic elds, which are generated by the interaction of the beam with the surrounding environment, may play an important role in beam stability and machine performance. In this paper we study the short range wakeelds and the corresponding longitudinal broadband coupling impedance of the PS by measuring the incoherent quadrupole synchrotron frequency as a function of beam intensity and comparing the results with the evaluation of the contribution of several machine installations to the total impedance budget.

The future beam brightness and intensities required by the HL-LHC (High-Luminosity LHC) project and for possible new neutrino production beams triggered a deep revision of the LHC injector performances. The analysis, progressing in the framework of the LHC Injectors Upgrade (LIU) project, outlined major limitations mainly related to collective effects - space charge in PSB and PS, electron cloud driven and TMCI instabilities in the SPS, longitudinal coupled bunch instabilities in the PS for example - but also to the existing hardware capability to cope with beam instabilities and losses. A summary of the observations and simulation studies carried out so far, as well as the future ones, will be presented. The solution proposed to overcome the different limitations and the plans for their implementation will be also briefly reviewed.